https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Shamgar&feedformat=atomMath - User contributions [en]2019-06-18T17:02:48ZUser contributionsMediaWiki 1.28.3https://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=16095Colloquia/Fall182018-10-01T16:33:48Z<p>Shamgar: /* Fall 2018 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| ...<br />
|[[# TBA| TBA ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| Jeremy Teitelbaum (U Connecticut)<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| Douglas Ulmer (Arizona)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 9<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 16<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 30<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Dec 7<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2019&diff=16032Colloquia/Spring20192018-09-20T21:27:25Z<p>Shamgar: /* Spring 2019 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2019 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[# TBA| TBA ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Feb 1<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 15<br />
| [https://math.uchicago.edu/~smart/ Charles Smart] (University of Chicago)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 22<br />
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)<br />
|[[# TBA| TBA ]]<br />
| Erman and Corey<br />
|<br />
|-<br />
|March 4<br />
| Vladimir Sverak (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)<br />
|[[# TBA| TBA ]]<br />
| Erman<br />
|<br />
|-<br />
|March 15<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|March 29<br />
| Jennifer Park (OSU)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|April 5<br />
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)<br />
|[[# TBA| TBA ]]<br />
| Jean-Luc<br />
|<br />
|-<br />
|April 12<br />
| Evitar Procaccia (TAMU)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| Ju-Lee Kim (MIT)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 26<br />
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|May 3<br />
| Tomasz Przebinda (Oklahoma)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2019&diff=15770Colloquia/Spring20192018-08-26T21:52:37Z<p>Shamgar: /* Mathematics Colloquium */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2019 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[# TBA| TBA ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Feb 1<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 15<br />
| [https://math.uchicago.edu/~smart/ Charles Smart] (University of Chicago)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 22<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|March 4<br />
| Vladimir Sverak (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)<br />
|[[# TBA| TBA ]]<br />
| Erman<br />
|<br />
|-<br />
|March 15<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|March 29<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|April 5<br />
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)<br />
|[[# TBA| TBA ]]<br />
| Jean-Luc<br />
|<br />
|-<br />
|April 12<br />
| Evitar Procaccia (TAMU)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| Ju-Lee Kim (MIT)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 26<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|May 3<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring2019&diff=15710Colloquia/Spring20192018-08-15T17:45:39Z<p>Shamgar: /* Spring 2019 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2019 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[# TBA| TBA ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Feb 1<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 15<br />
| [https://math.uchicago.edu/~smart/ Charles Smart] (University of Chicago)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 22<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|March 4<br />
| Vladimir Sverak (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|March 15<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|March 29<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|April 5<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|April 12<br />
| Evitar Procaccia (TAMU)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|April 26<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|May 3<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=15619Colloquia/Fall182018-07-18T06:08:11Z<p>Shamgar: /* Fall 2018 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''. The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12, 14<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[# TBA| TBA ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21<br />
| Andrew Stuart (Caltech) LAA lecture<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| Gautam Iyer (CMU)<br />
|[[# TBA| TBA ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Oct 12<br />
| Arie Levit (Yale)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 19<br />
| Jeremy Teitelbaum (U Connecticut)<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| Douglas Ulmer (Arizona)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 9<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 16<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 30<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Dec 7<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14360Colloquia/Fall182017-10-13T19:10:39Z<p>Shamgar: /* Fall 2017 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[# TBA| TBA ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1<br />
|Shaoming Guo (Indiana)<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
===October 13: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14202Colloquia/Fall182017-09-21T18:28:27Z<p>Shamgar: /* Fall 2017 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13<br />
|Tomoko L. Kitagawa (Berkeley)<br />
|[[# TBA| TBA ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[# TBA| TBA ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1<br />
|Shaoming Guo (Indiana)<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|Robert Laugwitz (Rutgers)<br />
|[[# TBA| TBA ]]<br />
|Dima Arinkin<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model. <br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14201Colloquia/Fall182017-09-21T18:27:53Z<p>Shamgar: /* Fall 2017 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13<br />
|Tomoko L. Kitagawa (Berkeley)<br />
|[[# TBA| TBA ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[# TBA| TBA ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1<br />
|Shaoming Guo (Indiana)<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|Robert Laugwitz (Caltech)<br />
|[[# TBA| TBA ]]<br />
|Dima Arinkin<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model. <br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14200Colloquia/Fall182017-09-21T18:05:54Z<p>Shamgar: /* Mathematics Colloquium */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13<br />
|Tomoko L. Kitagawa (Berkeley)<br />
|[[# TBA| TBA ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[# TBA| TBA ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1<br />
|Shaoming Guo (Indiana)<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
robert Laugwitz (Caltech)<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model. <br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=13973Colloquia/Fall182017-08-26T08:49:52Z<p>Shamgar: /* Fall 2017 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
| Tess Anderson (Madison)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
| Jaeyoung Byeon (KAIST)<br />
|[[# TBA| TBA ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13<br />
|Tomoko L. Kitagawa (Berkeley)<br />
|[[# TBA| TBA ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[# TBA| TBA ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|November 3<br />
|Alexander Yom Din (Caltech)<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=13917Colloquia/Fall182017-08-14T07:04:23Z<p>Shamgar: /* Fall 2017 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8<br />
| Tess Anderson (Madison)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
| '''Wednesday, September 20, LAA lecture<br />
| Andrew Stuart (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|September 22<br />
| Jaeyoung Byeon (KAIST)<br />
|[[# TBA| TBA ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
|<br />
|-<br />
|October 13<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[# TBA| TBA ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[# TBA| TBA ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|November 3<br />
|Alexander Yom Din (Caltech)<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=11810Colloquia/Fall182016-04-13T22:32:14Z<p>Shamgar: /* Abstracts */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
==[[Tentative Colloquia|Tentative schedule for next semester]] ==<br />
<br />
== Spring 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| '''January 22''' <br />
|<!--[https://web.math.princeton.edu/~caraiani/ Ana Caraiani] (Princeton)--><br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!--Host--><br />
|-<br />
| '''January 28 (Th 4pm VV901)''' <br />
| [https://web.math.princeton.edu/~ssivek/ Steven Sivek] (Princeton)<br />
| [[Colloquia#September 11: Speaker (University) | The augmentation category of a Legendrian knot]] <br />
| Ellenberg<br />
|-<br />
| '''January 29''' <br />
|[https://web.math.princeton.edu/~caraiani/ Ana Caraiani] (Princeton)<br />
| [[Colloquia#September 11: Ana Caraiani (Princeton) | Locally symmetric spaces, torsion classes, and the geometry of period domains]] <br />
| Ellenberg<br />
|-<br />
| '''February 5''' <br />
|[http://math.uchicago.edu/~souganidis/ Takis Souganidis] (University of Chicago)<br />
| [[Colloquia#September 11: Takis Souganidis (University of Chicago) | Scalar Conservation Laws with Rough Dependence]]<br />
| Lin<br />
|-<br />
| '''February 12''' <br />
|[http://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU) <br />
| [[Colloquia#February 12: Gautam Iyer (CMU)| Homogenization and Anomalous Diffusion]]<br />
| Jean-Luc<br />
|-<br />
| '''February 19''' <br />
| [https://people.math.osu.edu/lafont.1/ Jean-François Lafont] (Ohio State) <br />
| [[Colloquia#February 19: Jean-François Lafont (Ohio State) | Rigidity and flexibility of almost-isometries]]<br />
| Dymarz<br />
|-<br />
| '''February 26''' <br />
|Hiroyoshi Mitake (Hiroshima university) <br />
| [[Colloquia#February 26: Hiroyoshi Mitake (Hiroshima university) | On asymptotic speed of the crystal growth]]<br />
| Tran<br />
|-<br />
| '''March 4''' <br />
| [http://www.columbia.edu/~gb2030/ Guillaume Bal] (Columbia University)<br />
| [[Colloquia#September 11: Guillaume Bal (Columbia University) | Inverse and Control Transport Problems]]<br />
| Li, Jin<br />
|-<br />
| '''March 11''' <br />
| [http://math.umn.edu/~luskin Mitchell Luskin] (University of Minnesota)<br />
| [[Colloquia#March 11: Mitchell Luskin (UMN) | Mathematical Modeling of Incommensurate 2D Materials]]<br />
| Li<br />
|-<br />
| '''March 18''' <br />
| [http://www.math.lsa.umich.edu/~spatzier/ Ralf Spatzier] (University of Michigan) <br />
| CANCELED<br />
| Dymarz<br />
|-<br />
| '''March 25''' <br />
| Spring Break<!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''April 1''' <br />
| <br />
| CANCELED<br />
|<br />
|-<br />
| '''April 8''' <br />
| [https://web.math.princeton.edu/~aionescu/ Alexandru Ionescu] (Princeton) <br />
| [[Colloquia#April 8: Alexandru Ionescu (Princeton) | On long-term existence of solutions of water wave models]] <br />
| Wainger/Seeger<br />
|-<br />
| '''April 15''' <br />
| [https://www.kcl.ac.uk/nms/depts/mathematics/people/atoz/wigmani.aspx Igor Wigman] (King's College - London) <br />
| [[Colloquia#September 11: Speaker (University) |Topologies of nodal sets of random band limited functions]]<br />
| Gurevich/Marshall<br />
|-<br />
| '''April 22''' <br />
| [http://www.cims.nyu.edu/~bourgade/ Paul Bourgade] (NYU)<br />
| [[Colloquia#April 22: Paul Bourgade (NYU) | Random matrices beyond mean-field]]<br />
| Seppalainen/Valko<br />
|-<br />
| '''April 29''' <br />
| [http://www.physics.upenn.edu/~kamien/kamiengroup/ Randall Kamien] (U Penn) <br />
| [[Colloquia#April 29: Randall Kamien (U Penn) | Liquid crystals and their (algebraic) topology]] <br />
| Spagnolie<br />
|-<br />
| '''May 4''' <br />
| [https://www.math.ias.edu/people/faculty/sarnak Peter Sarnak] (Princeton and IAS) <br />
| [[Colloquia#May 4: Peter Sarnak (Princeton and IAS) | Strong approximation for Markoff surfaces]] (Note special day; still 4 pm in B239) <br />
| Marshall<br />
|-<br />
| '''May 6''' <br />
| <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
=== January 28: Steven Sivek (Princeton) === <br />
Title: The augmentation category of a Legendrian knot<br />
<br />
Abstract: A well-known principle in symplectic geometry says that information about the smooth structure on a manifold should be captured by the symplectic geometry of its cotangent bundle. One prominent example of this is Nadler and Zaslow's microlocalization correspondence, an equivalence between a category of constructible sheaves on a manifold and a symplectic invariant of its cotangent bundle called the Fukaya category.<br />
<br />
The goal of this talk is to describe a model for a relative version of this story in the simplest case, corresponding to Legendrian knots in the standard contact 3-space. This construction, called the augmentation category, is a powerful invariant which is defined in terms of holomorphic curves but can also be described combinatorially. I will describe some interesting properties of this category and relate it to a category of sheaves on the plane. This is joint work with Lenny Ng, Dan Rutherford, Vivek Shende, and Eric Maslow.<br />
<br />
=== January 29: Ana Caraiani (Princeton) === <br />
Title: Locally symmetric spaces, torsion classes, and the geometry of period domains<br />
<br />
Abstract: The Langlands program is an intricate network of conjectures, which are meant to connect different areas of mathematics, such as number theory, harmonic analysis and representation theory. One striking consequence of the Langlands program is the Ramanujan conjecture, which is a statement purely within harmonic analysis, about the growth rate of Fourier coefficients of modular forms. It turns out to be intimately connected to the Weil conjectures, a statement about the cohomology of projective, smooth varieties defined over finite fields.<br />
<br />
I will explain this connection and then move towards a mod p analogue of these ideas. More precisely, I will explain a strategy for understanding torsion occurring in the cohomology of locally symmetric spaces and how to detect which degrees torsion will contribute to. The main theorem is joint work with Peter Scholze and relies on a p-adic version of Hodge theory and on recent developments in p-adic geometry.<br />
<br />
<br />
=== February 5: Takis Souganidis (University of Chicago) === <br />
Title: Scalar Conservation Laws with Rough Dependence<br />
<br />
I will present a recently developed theory for scalar conservation laws with nonlinear multiplicative rough signal dependence. I will describe the difficulties, introduce the notion of pathwise entropy/kinetic solution and its well-posedness. I will also talk about the long time behavior of the solutions as well as some regularization by noise type results.<br />
<br />
=== February 12: Gautam Iyer (CMU) ===<br />
<br />
Homogenization and Anomalous Diffusion<br />
<br />
Homogenization is a well known technique used to approximate the macroscopic behaviour of a material with microscopic impurities.<br />
While this originally arose in the study of composite materials, it has applications to various other fields, and I will focus on a few results<br />
motivated by fluid dynamics. One well known result in this direction is by GI Taylor estimating the dispersion rate of a solute in a pipe. The<br />
length scales involved in typical pipelines, however, are too short for this result to apply. I will conclude with a few recent "intermediate time" results describing the effective behaviour in scaling regimes outside those of standard homogenization results.<br />
<br />
=== February 19: Jean-François Lafont (Ohio State) ===<br />
<br />
Rigidity and flexibility of almost-isometries<br />
<br />
An almost isometry (AI) is a quasi-isometry (QI) with multiplicative<br />
constant =1. Given two metrics on a closed manifold, Milnor-Swarc implies<br />
that the lifted metrics on the universal cover are QI to each other. When are<br />
they AI to each other? In the rigidity direction, we give various examples<br />
where the only time such lifts are AI is when they are isometric (joint with<br />
Kar and Schmidt). In the flexible direction, we show that for higher genus<br />
surfaces, any two metrics have lifts which, after possibly scaling one of the<br />
lifted metrics, are AI to each other (joint with Schmidt and van Limbeek). In<br />
the latter examples, one can further show that the AI is usually not equivariant<br />
with respect to the group actions.<br />
<br />
=== February 26: Hiroyoshi Mitake (Hiroshima University) ===<br />
In the talk, I will propose a model equation to study the crystal growth as a prototype, which is described by a level-set mean curvature flow equation with driving and source terms. We establish the well-posedness of solutions, and study the asymptotic speed. Interestingly, a new type of nonlinear phenomena in terms of asymptotic speed of solutions appears because of the double nonlinear effects coming from the surface evolution and the source term, which is sensitive to the shapes of source terms. This is a joint work with Y. Giga (U. Tokyo), and H. V. Tran (U. Wisconsin-Madison). <br />
<br />
=== March 11: Mitchell Luskin (UMN) ===<br />
Title: Mathematical Modeling of Incommensurate 2D Materials<br />
<br />
Abstract: Incommensurate materials are found in crystals, liquid crystals, and quasi-crystals. Stacking a few layers of 2D materials such as graphene and molybdenum disulfide, for example, opens the possibility to tune the elastic, electronic, and optical properties of these materials. One of the main issues encountered in the mathematical modeling of layered 2D materials is that lattice mismatch and rotations between the layers destroys the periodic character of the system. This leads to complex commensurate-incommensurate transitions and pattern formation.<br />
<br />
Even basic concepts like the Cauchy-Born strain energy density, the electronic density of states, and the Kubo-Greenwood formulas for transport properties have not been given a rigorous analysis in the incommensurate setting. New approximate approaches will be discussed and the validity and efficiency of these approximations will be examined from mathematical and numerical analysis perspectives.<br />
<br />
===March 18: Ralf Spatzier (UMichigan)===<br />
<br />
CANCELED: Rigidity in Geometry and Dynamics<br />
<br />
I will survey some rigidity phenomena in dynamics and also geometry, with emphasis on the notion of higher rank.<br />
This first emerged in Margulis’ celebrated work on superrrigidity but has also been important in more recent work on symmetry in dynamical systems.<br />
How special is it for maps commute with each other? Smale asked this problem fifty years ago, and answers are finally emerging. Much depends on the differentiability<br />
of the maps: it gets harder the more differentiable the map is. Sometimes we can even classify such maps. I’ll discuss this and<br />
related phenomena.<br />
<br />
<br />
<br />
=== April 8: Alexandru Ionescu (Princeton) ===<br />
<br />
Title: On long-term existence of solutions of water wave models<br />
<br />
I will talk about some recent work on long-term/global regularity of solutions of water wave models in 2 and 3 dimensions. The <br />
models we consider describe the evolution of an inviscid perfect fluid in<br />
a free boundary domain, under the influence of gravity and/or surface<br />
tension. This is joint work with Fabio Pusateri and, in part, with Yu Deng and<br />
Benoit Pausader.<br />
<br />
=== April 15: Igor Wigman (KC London) ===<br />
<br />
Title: Topologies of nodal sets of random band limited functions<br />
<br />
We show that the topologies and nestings of the zero and nodal sets of random (Gaussian) band limited functions have universal laws of distribution. Qualitative features of the supports of these distributions will be determined. In particular the results apply to random monochromatic waves and to random real algebraic hyper-surfaces in projective space. <br />
<br />
The talk should be understood to any advanced undergraduate student. <br />
<br />
<br />
===April 22: Paul Bourgade (NYU)===<br />
<br />
Title: Random matrices beyond mean-field<br />
<br />
<br />
Random matrix statistics were proposed by Eugene Wigner as a new class of universal statistical laws for highly correlated systems. <br />
We will first review established instances of this conjecture for mean-field matrix models. We will then propose an approach towards the spectral analysis of non mean-field models, which are closer to Wigner's original vision. <br />
A key role is played by a new patching of quantum unique ergodicity estimates.<br />
<br />
<br />
=== April 29: Randall Kamien (U Penn) ===<br />
<br />
Title: Liquid Crystals and their (Algebraic) Topology<br />
<br />
Liquid Crystals, the materials in your iPhone, are complex materials with varying degrees of internal order. I will discuss and demonstrate how algebraic topology can be used to identify and characterize long-lived configurations. I will also describe how conic sections naturally arise in these structures as intersections of simple polynomials.<br />
<br />
=== May 4: Peter Sarnak (Princeton and IAS) ===<br />
<br />
Title: Strong approximation for Markoff surfaces<br />
<br />
We discuss the transitivity properties of the group of morphisms generated by Vieta involutions on the solutions in congruences to the Markoff equation as well as to other Markoff type affine cubic surfaces. These are dictated in part by the finite orbits of these actions on the algebraic points. The latter can be determined effectively and in special cases is connected to the problem of determining all algebraic Painleve VI's. Applications to forms of strong approximation for integer points and to sieving on such affine surfaces, as well as to Markoff numbers will be given.<br />
<br />
Joint work with J.Bourgain and A.Gamburd.<br />
<br />
===<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=11809Colloquia/Fall182016-04-13T22:27:58Z<p>Shamgar: /* Spring 2016 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
==[[Tentative Colloquia|Tentative schedule for next semester]] ==<br />
<br />
== Spring 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| '''January 22''' <br />
|<!--[https://web.math.princeton.edu/~caraiani/ Ana Caraiani] (Princeton)--><br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!--Host--><br />
|-<br />
| '''January 28 (Th 4pm VV901)''' <br />
| [https://web.math.princeton.edu/~ssivek/ Steven Sivek] (Princeton)<br />
| [[Colloquia#September 11: Speaker (University) | The augmentation category of a Legendrian knot]] <br />
| Ellenberg<br />
|-<br />
| '''January 29''' <br />
|[https://web.math.princeton.edu/~caraiani/ Ana Caraiani] (Princeton)<br />
| [[Colloquia#September 11: Ana Caraiani (Princeton) | Locally symmetric spaces, torsion classes, and the geometry of period domains]] <br />
| Ellenberg<br />
|-<br />
| '''February 5''' <br />
|[http://math.uchicago.edu/~souganidis/ Takis Souganidis] (University of Chicago)<br />
| [[Colloquia#September 11: Takis Souganidis (University of Chicago) | Scalar Conservation Laws with Rough Dependence]]<br />
| Lin<br />
|-<br />
| '''February 12''' <br />
|[http://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU) <br />
| [[Colloquia#February 12: Gautam Iyer (CMU)| Homogenization and Anomalous Diffusion]]<br />
| Jean-Luc<br />
|-<br />
| '''February 19''' <br />
| [https://people.math.osu.edu/lafont.1/ Jean-François Lafont] (Ohio State) <br />
| [[Colloquia#February 19: Jean-François Lafont (Ohio State) | Rigidity and flexibility of almost-isometries]]<br />
| Dymarz<br />
|-<br />
| '''February 26''' <br />
|Hiroyoshi Mitake (Hiroshima university) <br />
| [[Colloquia#February 26: Hiroyoshi Mitake (Hiroshima university) | On asymptotic speed of the crystal growth]]<br />
| Tran<br />
|-<br />
| '''March 4''' <br />
| [http://www.columbia.edu/~gb2030/ Guillaume Bal] (Columbia University)<br />
| [[Colloquia#September 11: Guillaume Bal (Columbia University) | Inverse and Control Transport Problems]]<br />
| Li, Jin<br />
|-<br />
| '''March 11''' <br />
| [http://math.umn.edu/~luskin Mitchell Luskin] (University of Minnesota)<br />
| [[Colloquia#March 11: Mitchell Luskin (UMN) | Mathematical Modeling of Incommensurate 2D Materials]]<br />
| Li<br />
|-<br />
| '''March 18''' <br />
| [http://www.math.lsa.umich.edu/~spatzier/ Ralf Spatzier] (University of Michigan) <br />
| CANCELED<br />
| Dymarz<br />
|-<br />
| '''March 25''' <br />
| Spring Break<!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''April 1''' <br />
| <br />
| CANCELED<br />
|<br />
|-<br />
| '''April 8''' <br />
| [https://web.math.princeton.edu/~aionescu/ Alexandru Ionescu] (Princeton) <br />
| [[Colloquia#April 8: Alexandru Ionescu (Princeton) | On long-term existence of solutions of water wave models]] <br />
| Wainger/Seeger<br />
|-<br />
| '''April 15''' <br />
| [https://www.kcl.ac.uk/nms/depts/mathematics/people/atoz/wigmani.aspx Igor Wigman] (King's College - London) <br />
| [[Colloquia#September 11: Speaker (University) |Topologies of nodal sets of random band limited functions]]<br />
| Gurevich/Marshall<br />
|-<br />
| '''April 22''' <br />
| [http://www.cims.nyu.edu/~bourgade/ Paul Bourgade] (NYU)<br />
| [[Colloquia#April 22: Paul Bourgade (NYU) | Random matrices beyond mean-field]]<br />
| Seppalainen/Valko<br />
|-<br />
| '''April 29''' <br />
| [http://www.physics.upenn.edu/~kamien/kamiengroup/ Randall Kamien] (U Penn) <br />
| [[Colloquia#April 29: Randall Kamien (U Penn) | Liquid crystals and their (algebraic) topology]] <br />
| Spagnolie<br />
|-<br />
| '''May 4''' <br />
| [https://www.math.ias.edu/people/faculty/sarnak Peter Sarnak] (Princeton and IAS) <br />
| [[Colloquia#May 4: Peter Sarnak (Princeton and IAS) | Strong approximation for Markoff surfaces]] (Note special day; still 4 pm in B239) <br />
| Marshall<br />
|-<br />
| '''May 6''' <br />
| <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
=== January 28: Steven Sivek (Princeton) === <br />
Title: The augmentation category of a Legendrian knot<br />
<br />
Abstract: A well-known principle in symplectic geometry says that information about the smooth structure on a manifold should be captured by the symplectic geometry of its cotangent bundle. One prominent example of this is Nadler and Zaslow's microlocalization correspondence, an equivalence between a category of constructible sheaves on a manifold and a symplectic invariant of its cotangent bundle called the Fukaya category.<br />
<br />
The goal of this talk is to describe a model for a relative version of this story in the simplest case, corresponding to Legendrian knots in the standard contact 3-space. This construction, called the augmentation category, is a powerful invariant which is defined in terms of holomorphic curves but can also be described combinatorially. I will describe some interesting properties of this category and relate it to a category of sheaves on the plane. This is joint work with Lenny Ng, Dan Rutherford, Vivek Shende, and Eric Maslow.<br />
<br />
=== January 29: Ana Caraiani (Princeton) === <br />
Title: Locally symmetric spaces, torsion classes, and the geometry of period domains<br />
<br />
Abstract: The Langlands program is an intricate network of conjectures, which are meant to connect different areas of mathematics, such as number theory, harmonic analysis and representation theory. One striking consequence of the Langlands program is the Ramanujan conjecture, which is a statement purely within harmonic analysis, about the growth rate of Fourier coefficients of modular forms. It turns out to be intimately connected to the Weil conjectures, a statement about the cohomology of projective, smooth varieties defined over finite fields.<br />
<br />
I will explain this connection and then move towards a mod p analogue of these ideas. More precisely, I will explain a strategy for understanding torsion occurring in the cohomology of locally symmetric spaces and how to detect which degrees torsion will contribute to. The main theorem is joint work with Peter Scholze and relies on a p-adic version of Hodge theory and on recent developments in p-adic geometry.<br />
<br />
<br />
=== February 5: Takis Souganidis (University of Chicago) === <br />
Title: Scalar Conservation Laws with Rough Dependence<br />
<br />
I will present a recently developed theory for scalar conservation laws with nonlinear multiplicative rough signal dependence. I will describe the difficulties, introduce the notion of pathwise entropy/kinetic solution and its well-posedness. I will also talk about the long time behavior of the solutions as well as some regularization by noise type results.<br />
<br />
=== February 12: Gautam Iyer (CMU) ===<br />
<br />
Homogenization and Anomalous Diffusion<br />
<br />
Homogenization is a well known technique used to approximate the macroscopic behaviour of a material with microscopic impurities.<br />
While this originally arose in the study of composite materials, it has applications to various other fields, and I will focus on a few results<br />
motivated by fluid dynamics. One well known result in this direction is by GI Taylor estimating the dispersion rate of a solute in a pipe. The<br />
length scales involved in typical pipelines, however, are too short for this result to apply. I will conclude with a few recent "intermediate time" results describing the effective behaviour in scaling regimes outside those of standard homogenization results.<br />
<br />
=== February 19: Jean-François Lafont (Ohio State) ===<br />
<br />
Rigidity and flexibility of almost-isometries<br />
<br />
An almost isometry (AI) is a quasi-isometry (QI) with multiplicative<br />
constant =1. Given two metrics on a closed manifold, Milnor-Swarc implies<br />
that the lifted metrics on the universal cover are QI to each other. When are<br />
they AI to each other? In the rigidity direction, we give various examples<br />
where the only time such lifts are AI is when they are isometric (joint with<br />
Kar and Schmidt). In the flexible direction, we show that for higher genus<br />
surfaces, any two metrics have lifts which, after possibly scaling one of the<br />
lifted metrics, are AI to each other (joint with Schmidt and van Limbeek). In<br />
the latter examples, one can further show that the AI is usually not equivariant<br />
with respect to the group actions.<br />
<br />
=== February 26: Hiroyoshi Mitake (Hiroshima University) ===<br />
In the talk, I will propose a model equation to study the crystal growth as a prototype, which is described by a level-set mean curvature flow equation with driving and source terms. We establish the well-posedness of solutions, and study the asymptotic speed. Interestingly, a new type of nonlinear phenomena in terms of asymptotic speed of solutions appears because of the double nonlinear effects coming from the surface evolution and the source term, which is sensitive to the shapes of source terms. This is a joint work with Y. Giga (U. Tokyo), and H. V. Tran (U. Wisconsin-Madison). <br />
<br />
=== March 11: Mitchell Luskin (UMN) ===<br />
Title: Mathematical Modeling of Incommensurate 2D Materials<br />
<br />
Abstract: Incommensurate materials are found in crystals, liquid crystals, and quasi-crystals. Stacking a few layers of 2D materials such as graphene and molybdenum disulfide, for example, opens the possibility to tune the elastic, electronic, and optical properties of these materials. One of the main issues encountered in the mathematical modeling of layered 2D materials is that lattice mismatch and rotations between the layers destroys the periodic character of the system. This leads to complex commensurate-incommensurate transitions and pattern formation.<br />
<br />
Even basic concepts like the Cauchy-Born strain energy density, the electronic density of states, and the Kubo-Greenwood formulas for transport properties have not been given a rigorous analysis in the incommensurate setting. New approximate approaches will be discussed and the validity and efficiency of these approximations will be examined from mathematical and numerical analysis perspectives.<br />
<br />
===March 18: Ralf Spatzier (UMichigan)===<br />
<br />
CANCELED: Rigidity in Geometry and Dynamics<br />
<br />
I will survey some rigidity phenomena in dynamics and also geometry, with emphasis on the notion of higher rank.<br />
This first emerged in Margulis’ celebrated work on superrrigidity but has also been important in more recent work on symmetry in dynamical systems.<br />
How special is it for maps commute with each other? Smale asked this problem fifty years ago, and answers are finally emerging. Much depends on the differentiability<br />
of the maps: it gets harder the more differentiable the map is. Sometimes we can even classify such maps. I’ll discuss this and<br />
related phenomena.<br />
<br />
<br />
<br />
=== April 8: Alexandru Ionescu (Princeton) ===<br />
<br />
Title: On long-term existence of solutions of water wave models<br />
<br />
I will talk about some recent work on long-term/global regularity of solutions of water wave models in 2 and 3 dimensions. The <br />
models we consider describe the evolution of an inviscid perfect fluid in<br />
a free boundary domain, under the influence of gravity and/or surface<br />
tension. This is joint work with Fabio Pusateri and, in part, with Yu Deng and<br />
Benoit Pausader.<br />
<br />
<br />
===April 22: Paul Bourgade (NYU)===<br />
<br />
Title: Random matrices beyond mean-field<br />
<br />
<br />
Random matrix statistics were proposed by Eugene Wigner as a new class of universal statistical laws for highly correlated systems. <br />
We will first review established instances of this conjecture for mean-field matrix models. We will then propose an approach towards the spectral analysis of non mean-field models, which are closer to Wigner's original vision. <br />
A key role is played by a new patching of quantum unique ergodicity estimates.<br />
<br />
<br />
=== April 29: Randall Kamien (U Penn) ===<br />
<br />
Title: Liquid Crystals and their (Algebraic) Topology<br />
<br />
Liquid Crystals, the materials in your iPhone, are complex materials with varying degrees of internal order. I will discuss and demonstrate how algebraic topology can be used to identify and characterize long-lived configurations. I will also describe how conic sections naturally arise in these structures as intersections of simple polynomials.<br />
<br />
=== May 4: Peter Sarnak (Princeton and IAS) ===<br />
<br />
Title: Strong approximation for Markoff surfaces<br />
<br />
We discuss the transitivity properties of the group of morphisms generated by Vieta involutions on the solutions in congruences to the Markoff equation as well as to other Markoff type affine cubic surfaces. These are dictated in part by the finite orbits of these actions on the algebraic points. The latter can be determined effectively and in special cases is connected to the problem of determining all algebraic Painleve VI's. Applications to forms of strong approximation for integer points and to sieving on such affine surfaces, as well as to Markoff numbers will be given.<br />
<br />
Joint work with J.Bourgain and A.Gamburd.<br />
===<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=NTS_Spring_2016&diff=10860NTS Spring 20162015-12-14T02:55:33Z<p>Shamgar: </p>
<hr />
<div>This page is a ''tentative'' calendar for the Spring 2016 semester.<br />
<br />
The current semester is [https://www.math.wisc.edu/wiki/index.php/NTS Fall 2015].<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 21<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Jan 28<br />
| bgcolor="#F0B0B0" align="center" | Amir Mohammadi<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 04<br />
| bgcolor="#F0B0B0" align="center" | Shamgar Gurevich<br />
| bgcolor="#BCE2FE"| Low Dimensional Representations of Finite Classical Groups<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 11<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 18<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 25<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Mar 03<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 10<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Mar 17<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Mar 24<br />
| bgcolor="#F0B0B0" align="center" | ''Spring Break''<br />
| bgcolor="#BCE2FE"|<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 31<br />
| bgcolor="#F0B0B0" align="center" | Jacob Tsimerman<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Apr 07<br />
| bgcolor="#F0B0B0" align="center" | Zeev Rudnick<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Apr 14<br />
| bgcolor="#F0B0B0" align="center" | Eyal Goren<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Apr 21<br />
| bgcolor="#F0B0B0" align="center" | Rafael von Kanel<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Apr 28<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 05<br />
| bgcolor="#F0B0B0" align="center" | [http://www.ma.utexas.edu/users/mirela/ Mirela Çiperiani]<br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br></div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=NTS_Spring_2016&diff=10859NTS Spring 20162015-12-14T02:54:50Z<p>Shamgar: </p>
<hr />
<div>This page is a ''tentative'' calendar for the Spring 2016 semester.<br />
<br />
The current semester is [https://www.math.wisc.edu/wiki/index.php/NTS Fall 2015].<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 21<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Jan 28<br />
| bgcolor="#F0B0B0" align="center" | Amir Mohammadi<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 04<br />
| bgcolor="#F0B0B0" align="center" | Shamgar Gurevich<br />
| bgcolor="#BCE2FE"| Low<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 11<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 18<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 25<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Mar 03<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 10<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Mar 17<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Mar 24<br />
| bgcolor="#F0B0B0" align="center" | ''Spring Break''<br />
| bgcolor="#BCE2FE"|<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 31<br />
| bgcolor="#F0B0B0" align="center" | Jacob Tsimerman<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Apr 07<br />
| bgcolor="#F0B0B0" align="center" | Zeev Rudnick<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Apr 14<br />
| bgcolor="#F0B0B0" align="center" | Eyal Goren<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Apr 21<br />
| bgcolor="#F0B0B0" align="center" | Rafael von Kanel<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Apr 28<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 05<br />
| bgcolor="#F0B0B0" align="center" | [http://www.ma.utexas.edu/users/mirela/ Mirela Çiperiani]<br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br></div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=10055Colloquia/Fall182015-08-29T20:53:16Z<p>Shamgar: /* Abstracts */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Fall 2015 ==<br />
<br />
Go to next semester, [[Colloquia/Spring 2016|Spring 2016]].<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|- <br />
| '''September 4''' <br />
| [http://homepages.math.uic.edu/~isaac/ Isaac Goldbring] (UIC) <br />
| <!-- [[Colloquia#September 4: Isaac Goldbring (UIC) | title]] --><br />
| Andrews/Lempp<br />
|-<br />
| '''September 11''' <br />
| [https://sites.google.com/site/doronpuder/ Doron Puder] (IAS) <br />
| [[Colloquia#September 11: Doron Puder (IAS) | Word-Measures on Groups]]<br />
| Gurevich<br />
|-<br />
| '''September 18''' <br />
| [http://homepages.math.uic.edu/~coskun/ Izzet Coskun] (UIC)<br />
| [[Colloquia#September 18: Izzet Coskun (UIC) | The geometry of points in the plane]] <br />
| Erman<br />
|-<br />
| '''September 25''' <br />
| [https://pantherfile.uwm.edu/ourmazd/www/ Abbas Ourmazd] (UW-Milwaukee) <br />
| <!-- [[Colloquia#September 25: Abbas Ourmazd (UW-Milwaukee) | TBA]] --><br />
| Mitchell<br />
|-<br />
| '''October 2''' <br />
| <br />
| <br />
| <br />
|-<br />
| '''October 9''' <br />
| [https://www.engr.ucsb.edu/~mgroup Igor Mezic] (UC Santa Barbara) <br />
| <!-- [[Colloquia#October 9: Igor Mezic (UC Santa Barbara) | TBA]] --><br />
| Budisic, Thiffeault<br />
|-<br />
| '''October 16''' <br />
| [http://mysite.science.uottawa.ca/hsalmasi/ Hadi Salmasian] (Ottawa) <br />
| <!-- [[Colloquia#October 23: Speaker (University) | title]] --><br />
| Gurevich<br />
|-<br />
| '''October 23''' <br />
| Wisconsin Science Festival. <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October16: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 30''' <br />
| [http://people.brandeis.edu/~charney/Charney15.html Ruth Charney] (Brandeis) <br />
| <!-- [[Colloquia#October 30: Ruth Charney (Brandeis) | title]] --><br />
| Dymarz<br />
|-<br />
| '''November 6''' <br />
| Reserved *S <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 13''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 20''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 27''' <br />
| University Holiday<br />
| No Colloquium<br />
|<br />
|-<br />
| '''December 4''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''December 11''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===September 4: Isaac Goldbring (UIC) ===<br />
<br />
==== ====<br />
<br />
<br />
===September 11: Doron Puder (IAS) ===<br />
Title: Word-Measures on Groups.<br />
<br />
Abstract: Let w be a word in the free group on k generators, and let G be a finite (compact) group. The word w induces a measure on G by substituting the letters of w with k independent uniformly (Haar) chosen random elements of G and evaluating the product. Questions about word-measures on groups attracted attention in recent years both for their own sake and as a tool to analyze random walks on groups.<br />
<br />
We will explain some properties of word-measure, give examples and state conjectures. We will also talk about recent results regarding word-measures on symmetric groups and word-measures on unitary groups.<br />
==== ====<br />
<br />
===September 18: Izzet Coskun (UIC) ===<br />
Title: The geometry of points in the plane<br />
<br />
Abstract: Grothendieck's Hilbert scheme of points is a smooth compactification of the configuration space of points in the plane. It has close connections with combinatorics, representation theory, mathematical physics and algebraic geometry. In this talk, I will survey some of the basic properties of this beautiful space. If time permits, I will discuss joint work with Arcara, Bertram and Huizenga on codimension one subvarieties of the Hilbert scheme.<br />
==== ====<br />
<br />
===October 9: Igor Mezic (UC Santa Barbara) ===<br />
<br />
==== ====<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=10054Colloquia/Fall182015-08-29T18:49:25Z<p>Shamgar: /* Fall 2015 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Fall 2015 ==<br />
<br />
Go to next semester, [[Colloquia/Spring 2016|Spring 2016]].<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|- <br />
| '''September 4''' <br />
| [http://homepages.math.uic.edu/~isaac/ Isaac Goldbring] (UIC) <br />
| <!-- [[Colloquia#September 4: Isaac Goldbring (UIC) | title]] --><br />
| Andrews/Lempp<br />
|-<br />
| '''September 11''' <br />
| [https://sites.google.com/site/doronpuder/ Doron Puder] (IAS) <br />
| [[Colloquia#September 11: Doron Puder (IAS) | Word-Measures on Groups]]<br />
| Gurevich<br />
|-<br />
| '''September 18''' <br />
| [http://homepages.math.uic.edu/~coskun/ Izzet Coskun] (UIC)<br />
| [[Colloquia#September 18: Izzet Coskun (UIC) | The geometry of points in the plane]] <br />
| Erman<br />
|-<br />
| '''September 25''' <br />
| [https://pantherfile.uwm.edu/ourmazd/www/ Abbas Ourmazd] (UW-Milwaukee) <br />
| <!-- [[Colloquia#September 25: Abbas Ourmazd (UW-Milwaukee) | TBA]] --><br />
| Mitchell<br />
|-<br />
| '''October 2''' <br />
| <br />
| <br />
| <br />
|-<br />
| '''October 9''' <br />
| [https://www.engr.ucsb.edu/~mgroup Igor Mezic] (UC Santa Barbara) <br />
| <!-- [[Colloquia#October 9: Igor Mezic (UC Santa Barbara) | TBA]] --><br />
| Budisic, Thiffeault<br />
|-<br />
| '''October 16''' <br />
| [http://mysite.science.uottawa.ca/hsalmasi/ Hadi Salmasian] (Ottawa) <br />
| <!-- [[Colloquia#October 23: Speaker (University) | title]] --><br />
| Gurevich<br />
|-<br />
| '''October 23''' <br />
| Wisconsin Science Festival. <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October16: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 30''' <br />
| [http://people.brandeis.edu/~charney/Charney15.html Ruth Charney] (Brandeis) <br />
| <!-- [[Colloquia#October 30: Ruth Charney (Brandeis) | title]] --><br />
| Dymarz<br />
|-<br />
| '''November 6''' <br />
| Reserved *S <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 13''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 20''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 27''' <br />
| University Holiday<br />
| No Colloquium<br />
|<br />
|-<br />
| '''December 4''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''December 11''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===September 4: Isaac Goldbring (UIC) ===<br />
<br />
==== ====<br />
<br />
<br />
===September 18: Izzet Coskun (UIC) ===<br />
Title: The geometry of points in the plane<br />
<br />
Abstract: Grothendieck's Hilbert scheme of points is a smooth compactification of the configuration space of points in the plane. It has close connections with combinatorics, representation theory, mathematical physics and algebraic geometry. In this talk, I will survey some of the basic properties of this beautiful space. If time permits, I will discuss joint work with Arcara, Bertram and Huizenga on codimension one subvarieties of the Hilbert scheme.<br />
==== ====<br />
===October 9: Igor Mezic (UC Santa Barbara) ===<br />
<br />
==== ====<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring_2016&diff=9957Colloquia/Spring 20162015-08-24T18:01:21Z<p>Shamgar: /* Spring 2016 */</p>
<hr />
<div>== Spring 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| '''January 22''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''January 29''' <br />
| Amir Mohammadi (Texas-Austin) <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| Marshall<br />
|-<br />
| '''February 5''' <br />
|Takis Souganidis (University of Chicago)<br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| Lin<br />
|-<br />
| '''February 12''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''February 19''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''February 26''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''March 4''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''March 11''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''March 18''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''March 25''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''April 1''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''April 8''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''April 15''' <br />
| [https://www.kcl.ac.uk/nms/depts/mathematics/people/atoz/wigmani.aspx Igor Wigman] (King's College - London) <br />
| [[Colloquia#September 11: Speaker (University) |Nodal Domains of Eigenfunctions]]<br />
| Gurevich/Marshall<br />
|-<br />
| '''April 22''' <br />
| [http://www.cims.nyu.edu/~bourgade/ Paul Bourgade] (NYU)<br />
| [[Colloquia#April 22: Paul Bourgade (NYU) | TBA]]<br />
| Seppalainen/Valko<br />
|-<br />
| '''April 29''' <br />
| [http://www.physics.upenn.edu/~kamien/kamiengroup/ Randall Kamien] (U Penn) <br />
| [[Colloquia#April 29: Randall Kamien (U Penn) | TBA]] <br />
| Spagnolie<br />
|-<br />
| '''May 6''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|}</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring_2016&diff=9956Colloquia/Spring 20162015-08-24T17:57:15Z<p>Shamgar: /* Spring 2016 */</p>
<hr />
<div>== Spring 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| '''January 22''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''January 29''' <br />
| Amir Mohammadi (Texas-Austin) <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| Marshall<br />
|-<br />
| '''February 5''' <br />
|Takis Souganidis (University of Chicago)<br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| Lin<br />
|-<br />
| '''February 12''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''February 19''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''February 26''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''March 4''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''March 11''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''March 18''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''March 25''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''April 1''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''April 8''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''April 15''' <br />
| [https://www.kcl.ac.uk/nms/depts/mathematics/people/atoz/wigmani.aspx Igor Wigman] (King's College - London) <br />
| [[Colloquia#September 11: Speaker (University) | title]]<br />
| Gurevich/Marshall<br />
|-<br />
| '''April 22''' <br />
| [http://www.cims.nyu.edu/~bourgade/ Paul Bourgade] (NYU)<br />
| [[Colloquia#April 22: Paul Bourgade (NYU) | TBA]]<br />
| Seppalainen/Valko<br />
|-<br />
| '''April 29''' <br />
| [http://www.physics.upenn.edu/~kamien/kamiengroup/ Randall Kamien] (U Penn) <br />
| [[Colloquia#April 29: Randall Kamien (U Penn) | TBA]] <br />
| Spagnolie<br />
|-<br />
| '''May 6''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|}</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Spring_2016&diff=9955Colloquia/Spring 20162015-08-24T17:54:07Z<p>Shamgar: /* Spring 2016 */</p>
<hr />
<div>== Spring 2016 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| '''January 22''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''January 29''' <br />
| Amir Mohammadi (Texas-Austin) <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| Marshall<br />
|-<br />
| '''February 5''' <br />
|Takis Souganidis (University of Chicago)<br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| Lin<br />
|-<br />
| '''February 12''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''February 19''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''February 26''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''March 4''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''March 11''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''March 18''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''March 25''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''April 1''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''April 8''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''April 15''' <br />
| <!-- [https://www.kcl.ac.uk/nms/depts/mathematics/people/atoz/wigmani.aspx Igor Wigman] (King's College - London) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- Gurevich/Marshall --><br />
|-<br />
| '''April 22''' <br />
| [http://www.cims.nyu.edu/~bourgade/ Paul Bourgade] (NYU)<br />
| [[Colloquia#April 22: Paul Bourgade (NYU) | TBA]]<br />
| Seppalainen/Valko<br />
|-<br />
| '''April 29''' <br />
| [http://www.physics.upenn.edu/~kamien/kamiengroup/ Randall Kamien] (U Penn) <br />
| [[Colloquia#April 29: Randall Kamien (U Penn) | TBA]] <br />
| Spagnolie<br />
|-<br />
| '''May 6''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|}</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=9838Colloquia/Fall182015-07-21T05:12:10Z<p>Shamgar: /* Fall 2015 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Fall 2015 ==<br />
<br />
Go to next semester, [[Colloquia/Spring 2016|Spring 2016]].<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|- <br />
| '''September 4''' <br />
| [http://homepages.math.uic.edu/~isaac/ Isaac Goldbring] (UIC) <br />
| <!-- [[Colloquia#September 4: Isaac Goldbring (UIC) | title]] --><br />
| Andrews/Lempp<br />
|-<br />
| '''September 11''' <br />
| [https://sites.google.com/site/doronpuder/ Doron Puder] (IAS) <br />
| <!-- [[Colloquia#September 18: Doron Puder (IAS) | title]] --><br />
| Gurevich<br />
|-<br />
| '''September 18''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''September 25''' <br />
| [https://pantherfile.uwm.edu/ourmazd/www/ Abbas Ourmazd] (UW-Milwaukee) <br />
| <!-- [[Colloquia#September 25: Abbas Ourmazd (UW-Milwaukee) | TBA]] --><br />
| Mitchell<br />
|-<br />
| '''October 2''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 9''' <br />
| [https://www.engr.ucsb.edu/~mgroup Igor Mezic] (UC Santa Barbara) <br />
| <!-- [[Colloquia#October 9: Igor Mezic (UC Santa Barbara) | TBA]] --><br />
| Budisic, Thiffeault<br />
|-<br />
| '''October 16''' <br />
| [http://mysite.science.uottawa.ca/hsalmasi/ Hadi Salmasian] (Ottawa) <br />
| <!-- [[Colloquia#October 23: Speaker (University) | title]] --><br />
| Gurevich<br />
|-<br />
| '''October 23''' <br />
| Wisconsin Science Festival. <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October16: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 30''' <br />
| [http://people.brandeis.edu/~charney/Charney15.html Ruth Charney] (Brandeis) <br />
| <!-- [[Colloquia#October 30: Ruth Charney (Brandeis) | title]] --><br />
| Dymarz<br />
|-<br />
| '''November 6''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 13''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 20''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 27''' <br />
| University Holiday<br />
| No Colloquium<br />
|<br />
|-<br />
| '''December 4''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''December 11''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===September 4: Isaac Goldbring (UIC) ===<br />
<br />
==== ====<br />
<br />
===October 9: Igor Mezic (UC Santa Barbara) ===<br />
<br />
==== ====<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall2015&diff=9689Colloquia/Fall20152015-04-27T16:27:25Z<p>Shamgar: /* Fall 2015 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Future Colloquia =<br />
<br />
<!--- All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
== Fall 2015 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| '''September 4''' <br />
| [http://homepages.math.uic.edu/~isaac/ Isaac Goldbring] (UIC) <br />
| <!-- [[Colloquia#September 4: Isaac Goldbring (UIC) | title]] --><br />
| Andrews/Lempp<br />
|-<br />
| '''September 11''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''September 18''' <br />
| [https://sites.google.com/site/doronpuder/ Doron Puder] (IAS) <br />
| <!-- [[Colloquia#September 18: Doron Puder (IAS) | title]] --><br />
| Gurevich<br />
|-<br />
| '''September 25''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 25: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 2''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 2: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 9''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 9: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 16''' <br />
| [http://mysite.science.uottawa.ca/hsalmasi/ Hadi Salmasian] (Ottawa) <br />
| <!-- [[Colloquia#October 23: Speaker (University) | title]] --><br />
| Gurevich<br />
|-<br />
| '''October 23''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October16: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 30''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 30: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''November 6''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 13''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 20''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 27''' <br />
| University Holiday<br />
| No Colloquium<br />
|<br />
|-<br />
| '''December 4''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''December 11''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<!--- ===September 4: Speaker (University)=== ---><br />
<br />
<!--- ====Title==== ---><br />
<br />
<!--- Abstract ---><br />
<br />
<!--- == Past Colloquia ==<br />
<br />
[[Colloquia/Spring2015|Spring 2014]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]] <br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]] ---></div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall2015&diff=9671Colloquia/Fall20152015-04-21T21:07:05Z<p>Shamgar: /* Fall 2015 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Future Colloquia =<br />
<br />
<!--- All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
== Fall 2015 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| '''September 4''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 4: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''September 11''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''September 18''' <br />
| [https://sites.google.com/site/doronpuder/ Doron Puder] (IAS) <br />
| <!-- [[Colloquia#September 18: Doron Puder (IAS) | title]] --><br />
| Gurevich<br />
|-<br />
| '''September 25''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 25: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 2''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 2: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 9''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 9: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 16''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October16: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 23''' <br />
| [http://mysite.science.uottawa.ca/hsalmasi/ Hadi Salmasian] (Ottawa) <br />
| <!-- [[Colloquia#October 23: Speaker (University) | title]] --><br />
| Gurevich<br />
|-<br />
| '''October 30''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 30: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''November 6''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 13''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 20''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 27''' <br />
| University Holiday<br />
| No Colloquium<br />
|<br />
|-<br />
| '''December 4''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''December 11''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<!--- ===September 4: Speaker (University)=== ---><br />
<br />
<!--- ====Title==== ---><br />
<br />
<!--- Abstract ---><br />
<br />
<!--- == Past Colloquia ==<br />
<br />
[[Colloquia/Spring2015|Spring 2014]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]] <br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]] ---></div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall2015&diff=9670Colloquia/Fall20152015-04-21T21:04:22Z<p>Shamgar: /* Fall 2015 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Future Colloquia =<br />
<br />
<!--- All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
== Fall 2015 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| '''September 4''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 4: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''September 11''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''September 18''' <br />
| [https://sites.google.com/site/doronpuder/ Doron Puder] (IAS) <br />
| <!-- [[Colloquia#September 18: Doron Puder (IAS) | title]] --><br />
| Gurevich<br />
|-<br />
| '''September 25''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 25: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 2''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 2: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 9''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 9: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 16''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October16: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 23''' <br />
| <!-- [http://mysite.science.uottawa.ca/hsalmasi/ Hadi Salmasian] (Ottawa) --> <br />
| <!-- [[Colloquia#October 23: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 30''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 30: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''November 6''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 13''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 20''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 27''' <br />
| University Holiday<br />
| No Colloquium<br />
|<br />
|-<br />
| '''December 4''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''December 11''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<!--- ===September 4: Speaker (University)=== ---><br />
<br />
<!--- ====Title==== ---><br />
<br />
<!--- Abstract ---><br />
<br />
<!--- == Past Colloquia ==<br />
<br />
[[Colloquia/Spring2015|Spring 2014]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]] <br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]] ---></div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall2015&diff=9448Colloquia/Fall20152015-03-02T13:36:46Z<p>Shamgar: /* Fall 2015 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Future Colloquia =<br />
<br />
<!--- All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
== Fall 2015 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| '''September 4''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 4: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''September 11''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''September 18''' <br />
| [https://sites.google.com/site/doronpuder/ Doron Puder] (IAS) <br />
| [[Colloquia#September 18: Doron Puder (IAS) | title]]<br />
| Gurevich<br />
|-<br />
| '''September 25''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 25: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 2''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 2: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 9''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 9: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 16''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October16: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 23''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 23: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 30''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 30: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''November 6''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 13''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 20''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 27''' <br />
| University Holiday<br />
| No Colloquium<br />
|<br />
|-<br />
| '''December 4''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''December 11''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<!--- ===September 4: Speaker (University)=== ---><br />
<br />
<!--- ====Title==== ---><br />
<br />
<!--- Abstract ---><br />
<br />
<!--- == Past Colloquia ==<br />
<br />
[[Colloquia/Spring2015|Spring 2014]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]] <br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]] ---></div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall2015&diff=9447Colloquia/Fall20152015-03-02T13:35:48Z<p>Shamgar: /* Fall 2015 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Future Colloquia =<br />
<br />
<!--- All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
== Fall 2015 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| '''September 4''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 4: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''September 11''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''September 18''' <br />
| [https://sites.google.com/site/doronpuder/] (IAS) <br />
| [[Colloquia#September 18: Doron Puder (IAS) | title]]<br />
| Gurevich<br />
|-<br />
| '''September 25''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 25: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 2''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 2: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 9''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 9: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 16''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October16: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 23''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 23: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 30''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 30: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''November 6''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 13''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 20''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 27''' <br />
| University Holiday<br />
| No Colloquium<br />
|<br />
|-<br />
| '''December 4''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''December 11''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<!--- ===September 4: Speaker (University)=== ---><br />
<br />
<!--- ====Title==== ---><br />
<br />
<!--- Abstract ---><br />
<br />
<!--- == Past Colloquia ==<br />
<br />
[[Colloquia/Spring2015|Spring 2014]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]] <br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]] ---></div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall2015&diff=9444Colloquia/Fall20152015-03-02T01:27:21Z<p>Shamgar: /* Fall 2015 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Future Colloquia =<br />
<br />
<!--- All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
== Fall 2015 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| '''September 4''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 4: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''September 11''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 11: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''September 18''' <br />
| <!-- [https://sites.google.com/site/doronpuder/] (IAS) --> <br />
| <!-- [[Colloquia#September 18: Doron Puder (IAS) | title]] --><br />
| <!-- Gurevich --><br />
|-<br />
| '''September 25''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#September 25: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 2''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 2: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 9''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 9: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 16''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October16: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 23''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 23: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''October 30''' <br />
| <!-- [webpage Speaker Name] (University) --> <br />
| <!-- [[Colloquia#October 30: Speaker (University) | title]] --><br />
| <!-- host --><br />
|-<br />
| '''November 6''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 13''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 20''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''November 27''' <br />
| University Holiday<br />
| No Colloquium<br />
|<br />
|-<br />
| '''December 4''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|-<br />
| '''December 11''' <br />
| Reserved <!-- Remove if no job talks --><br />
|<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<!--- ===September 4: Speaker (University)=== ---><br />
<br />
<!--- ====Title==== ---><br />
<br />
<!--- Abstract ---><br />
<br />
<!--- == Past Colloquia ==<br />
<br />
[[Colloquia/Spring2015|Spring 2014]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]] <br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]] ---></div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=8669Colloquia/Fall182014-10-28T01:22:16Z<p>Shamgar: /* Abstracts */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
[[Colloquia/Spring 2015 | Tentative schedule for Spring 2015]]<br />
<br />
== Fall 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 12<br />
| [http://mduchin.math.tufts.edu/index.html Moon Duchin] (Tufts University)<br />
| [[Colloquia#September 12: Moon Duchin (Tufts University) | Geometry and counting in the Heisenberg group]]<br />
| Dymarz and WIMAW<br />
|-<br />
|September 19<br />
|[http://www.mast.queensu.ca/~ggsmith/ Gregory G. Smith] (Queen's University)<br />
|[[Colloquia#September 19: Gregory G. Smith (Queen's University) | Nonnegative sections and sums of squares]]<br />
|Erman<br />
|-<br />
|September 26<br />
|[http://www.math.uci.edu/~jxin/ Jack Xin] (UC Irvine)<br />
|[[Colloquia#September 26: Jack Xin (UC Irvine) | G-equations and Front Motion in Fluid Flows]]<br />
|Jin<br />
|-<br />
|October 3<br />
|[http://math.arizona.edu/~tiep/ Pham Huu Tiep] (University of Arizona)<br />
|[[Colloquia#October 3: Pham Huu Tiep (Arizona) | Adequate subgroups]]<br />
|Gurevich<br />
|-<br />
|October 10<br />
|[http://www.math.ubc.ca/~adem/ Alejandro Adem] (UBC)<br />
|[[Colloquia#October 10: Alejandro Adem (UBC) | Topology of Commuting Matrices]]<br />
|Yang<br />
|-<br />
|October 17<br />
|[http://www.icse.cornell.edu/ziagroup/ Roseanna Zia] (Cornell University)<br />
|[[Colloquia#October 17: Roseanna Zia (Cornell) | A micro-mechanical study of coarsening and rheology of colloidal gels: Cage building, cage hopping, and Smoluchowski’s ratchet]]<br />
|Spagnolie<br />
|-<br />
|October 24<br />
|[http://www.math.utoronto.ca/almut/ Almut Burchard] (Toronto)<br />
|[[Colloquia#October 24: Almut Burchard (Toronto) | Symmetrization, sharp inequalities, and geometric stability for integral functionals]]<br />
|Stovall<br />
|-<br />
|October 31<br />
|[http://www.math.uchicago.edu/~ngo/ Bao Chau Ngo] (Chicago)<br />
|[[Colloquia#October 31: Bao Chau Ngo (Chicago) | L-Function, Trace Formula and Moduli Spaces]]<br />
|Gurevich<br />
|-<br />
|November 7<br />
|Reserved for possible job interview<br />
|<br />
|<br />
|-<br />
|November 14<br />
|Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|November 21<br />
|Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|November 28<br />
|University holiday<br />
|<br />
| <br />
|-<br />
|December 5<br />
|Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|December 12<br />
| Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===September 12: Moon Duchin (Tufts University)===<br />
<br />
====Geometry and counting in the Heisenberg group====<br />
<br />
The growth function of a finitely-generated group enumerates how many words can be spelled with each possible number of letters-- this should be thought of as a sort of volume growth in any geometric model of the group. A major theorem of Gromov tells us exactly which groups have growth in the polynomial range: those that are (virtually) nilpotent. But we can still wonder how regular the growth of a nilpotent group is: is it actually a polynomial? Or could it exhibit some transcendentality together with pretty slow growth? <br />
<br />
I'll talk about some themes and techniques in the study of group growth and outline a geometry of numbers for nilpotent groups, including a recent result with M. Shapiro settling a long-standing question: the Heisenberg group -- the simplest non-abelian nilpotent group -- has rational growth in any generating set. <br />
<br />
===September 19: Gregory G. Smith (Queen's University)===<br />
<br />
====Nonnegative sections and sums of squares====<br />
<br />
A polynomial with real coefficients is nonnegative if it takes on only nonnegative values. For example, any sum of squares is obviously nonnegative. For a homogeneous polynomial with respect to the standard grading, Hilbert famously characterized when the converse holds, that is when every nonnegative homogeneous polynomial is a sum of squares. After reviewing some history of this problem, we will examine this converse in more general settings such as global sections of a line bundles. This line of inquiry has unexpected connections to classical algebraic geometry and leads to new examples in which every nonnegative homogeneous polynomial is a sum of squares. This talk is based on joint work with Grigoriy Blekherman and Mauricio Velasco.<br />
<br />
===September 26: Jack Xin (UC Irvine)===<br />
<br />
====G-equations and Front Motion in Fluid Flows====<br />
<br />
G-equations are level set Hamilton-Jacobi equations (HJE) for modeling flame fronts in turbulent combustion where a fundamental problem is to characterize the turbulent flame speeds s_T. The existence of s_T is connected with the homogenization of HJE, however classical theory does not apply due to the non-coercive and non-convex nature of the level set Hamiltonian. We shall illustrate the asymptotic properties of s_T from both Eulerian and Lagrangian perspectives in the case of two dimensional periodic incompressible flows, in particular cellular flows.<br />
<br />
Analytical and numerical results demonstrate that G-equations capture well the enhancement, slow down and quenching phenomena observed in fluid experiments. We also comment on s_T in chaotic flows. This is joint work with Yifeng Yu and Yu-Yu Liu.<br />
<br />
===October 3: Pham Huu Tiep (Arizona)===<br />
<br />
====Adequate subgroups====<br />
<br />
The notion of adequate subgroups was introduced by Thorne. It is a weakening of the notion of big subgroups used in generalizations of the Taylor-Wiles method for proving the automorphy of certain Galois representations. Using this idea, Thorne was able to strengthen many automorphy lifting theorems. It was shown recently by Guralnick, Herzig, Taylor, and Thorne that if the degree is small compared to the characteristic then all absolutely irreducible representations are adequate. We will discuss extensions of this result obtained recently in joint work with R. M. Guralnick and F. Herzig. In particular, we show that almost all absolutely irreducible representations in characteristic p of degree less than p are adequate. We will also address a question of Serre about<br />
indecomposable modules in characteristic p of dimension less than 2p-2.<br />
<br />
===October 10: Alejandro Adem (UBC)===<br />
<br />
====Topology of Commuting Matrices====<br />
<br />
In this talk we will describe basic topological properties of the space of commuting unitary matrices. In particular we will show that they can be assembled to form a space which classifies commutativity for vector bundles and which has very interesting homotopy-theoretic properties.<br />
<br />
===October 17: Roseanna Zia (Cornell) ===<br />
<br />
====A micro-mechanical study of coarsening and rheology of colloidal gels: Cage building, cage hopping, and Smoluchowski’s ratchet====<br />
<br />
Reconfigurable soft solids such as viscoelastic gels have emerged in the past decade as a promising material in numerous applications ranging from engineered tissue to drug delivery to injectable sensors. These include colloidal gels, which microscopically comprise a scaffoldlike network of interconnected particles embedded in a solvent. Network bonds can be permanent or reversible, depending on the nature and strength of interparticle attractions. When attractions are on the order of just a few kT, bonds easily rupture and reform. On a macroscopic scale, bond reversibility allows a gel to transition from solidlike behavior during storage, to liquidlike behavior during flow (e.g., injection or shear), and back to solidlike behavior in situ. On a microscopic scale, thermal fluctuations of the solvent are occasionally strong enough to break colloidal bonds, temporarily allowing particles to migrate and exchange neighbors before rebonding to the network, leading to structural evolution over time. Prior studies of colloidal gels have examined evolution of length scales and dynamics such as decorrelation times. Left open were additional questions such as how the particle-rich regions are structured (liquidlike, glassy, crystalline), how restructuring takes place (via bulk diffusion, surface migration, coalescence of large structures), and the impact of the evolution on rheology. In this talk I discuss these themes as explored in our recent dynamic simulations. We find that the network strands comprise a glassy, immobile interior near random-close packing, enclosed by a liquidlike surface along which the diffusive migration of particles drives structural coarsening. We show that coarsening is a three-step process of cage forming, cage hopping, and cage arrest, where particles migrate to ever-deeper energy wells via “Smoluchowski’s ratchet.” Both elastic and viscous high-frequency moduli are found to scale with the square-root of the frequency, similar to the perfectly viscoelastic behavior of non-hydrodynamically interacting, purely repulsive dispersions. But here, the behavior is elastic over all frequencies, with a quantitative offset between elastic and viscous moduli, which owes its origin to the hindrance of diffusion by particle attractions. Propagation of this elasticity via the network gives rise to age-stiffening as the gel coarsens. This simple phenomenological model suggests a rescaling of the moduli on dominant network length scale that collapses moduli for all ages onto a single curve. We propose a Rouse-like theoretical model and, from it, derive an analytical expression that predicts the effects of structural aging on rheology whereby linear response can be determined at any age by measurement of dominant network length scale—or vice versa.<br />
<br />
===October 24: Almut Burchard (Toronto)===<br />
<br />
====Symmetrization, sharp inequalities, and geometric stability for integral functionals====<br />
<br />
Many integral functionals are maximized (under appropriate constraints) by radially symmetric functions. For example, the Coulomb energy of a positive charge density --- the double integral of the Newton potential against the density --- increases under symmetrization. The physical reason is that the interaction energy between the charges grows as the typical distance between the charges shrinks. The energy increases strictly, unless the charge density is already radially decreasing about some point. Is this characterization of equality cases "stable"? In other words, must near-maximizers be close to maximizers?<br />
<br />
Such stability questions have been well-studied for the isoperimetric inequality and other functionals that involve gradients since the 1990's; the first results in that direction are due to Bonnesen in the 1920's. For example, the excess perimeter of a set (as compared to a ball of the same volume) controls its difference from a suitable translate of that ball. Much less is known about convolutions and other multiple integrals that describe "non-local" interactions. In some cases, not even a complete list of maximizers is known. I will discuss very recent developments (due to M. Christ, Figalli, Jerison, and others), mention open problems, and present joint work with Greg Chambers on the Coulomb energy.<br />
<br />
<br />
===October 31: Bao Chau Ngo (Chicago)===<br />
<br />
====L-function, trace formula, and moduli space====<br />
<br />
In his PhD thesis, J. Tate recast the construction of Riemann's<br />
zeta function in term of harmonic analysis on the group of ideles. This <br />
construction was generalized by Godement and Jacquet to principal <br />
L-function of automorphic forms. In a minimalistic view, Langlands program<br />
consists in understanding analytic properties of all automorphic L-functions.<br />
Braverman and Kazhdan proposed a generalization of Godement-Jacquet's <br />
construction. I will talk about these construction in connection with the trace<br />
formula and the geometry of certain moduli spaces.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=8668Colloquia/Fall182014-10-28T01:20:12Z<p>Shamgar: /* Fall 2014 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
[[Colloquia/Spring 2015 | Tentative schedule for Spring 2015]]<br />
<br />
== Fall 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 12<br />
| [http://mduchin.math.tufts.edu/index.html Moon Duchin] (Tufts University)<br />
| [[Colloquia#September 12: Moon Duchin (Tufts University) | Geometry and counting in the Heisenberg group]]<br />
| Dymarz and WIMAW<br />
|-<br />
|September 19<br />
|[http://www.mast.queensu.ca/~ggsmith/ Gregory G. Smith] (Queen's University)<br />
|[[Colloquia#September 19: Gregory G. Smith (Queen's University) | Nonnegative sections and sums of squares]]<br />
|Erman<br />
|-<br />
|September 26<br />
|[http://www.math.uci.edu/~jxin/ Jack Xin] (UC Irvine)<br />
|[[Colloquia#September 26: Jack Xin (UC Irvine) | G-equations and Front Motion in Fluid Flows]]<br />
|Jin<br />
|-<br />
|October 3<br />
|[http://math.arizona.edu/~tiep/ Pham Huu Tiep] (University of Arizona)<br />
|[[Colloquia#October 3: Pham Huu Tiep (Arizona) | Adequate subgroups]]<br />
|Gurevich<br />
|-<br />
|October 10<br />
|[http://www.math.ubc.ca/~adem/ Alejandro Adem] (UBC)<br />
|[[Colloquia#October 10: Alejandro Adem (UBC) | Topology of Commuting Matrices]]<br />
|Yang<br />
|-<br />
|October 17<br />
|[http://www.icse.cornell.edu/ziagroup/ Roseanna Zia] (Cornell University)<br />
|[[Colloquia#October 17: Roseanna Zia (Cornell) | A micro-mechanical study of coarsening and rheology of colloidal gels: Cage building, cage hopping, and Smoluchowski’s ratchet]]<br />
|Spagnolie<br />
|-<br />
|October 24<br />
|[http://www.math.utoronto.ca/almut/ Almut Burchard] (Toronto)<br />
|[[Colloquia#October 24: Almut Burchard (Toronto) | Symmetrization, sharp inequalities, and geometric stability for integral functionals]]<br />
|Stovall<br />
|-<br />
|October 31<br />
|[http://www.math.uchicago.edu/~ngo/ Bao Chau Ngo] (Chicago)<br />
|[[Colloquia#October 31: Bao Chau Ngo (Chicago) | L-Function, Trace Formula and Moduli Spaces]]<br />
|Gurevich<br />
|-<br />
|November 7<br />
|Reserved for possible job interview<br />
|<br />
|<br />
|-<br />
|November 14<br />
|Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|November 21<br />
|Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|November 28<br />
|University holiday<br />
|<br />
| <br />
|-<br />
|December 5<br />
|Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|December 12<br />
| Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===September 12: Moon Duchin (Tufts University)===<br />
<br />
====Geometry and counting in the Heisenberg group====<br />
<br />
The growth function of a finitely-generated group enumerates how many words can be spelled with each possible number of letters-- this should be thought of as a sort of volume growth in any geometric model of the group. A major theorem of Gromov tells us exactly which groups have growth in the polynomial range: those that are (virtually) nilpotent. But we can still wonder how regular the growth of a nilpotent group is: is it actually a polynomial? Or could it exhibit some transcendentality together with pretty slow growth? <br />
<br />
I'll talk about some themes and techniques in the study of group growth and outline a geometry of numbers for nilpotent groups, including a recent result with M. Shapiro settling a long-standing question: the Heisenberg group -- the simplest non-abelian nilpotent group -- has rational growth in any generating set. <br />
<br />
===September 19: Gregory G. Smith (Queen's University)===<br />
<br />
====Nonnegative sections and sums of squares====<br />
<br />
A polynomial with real coefficients is nonnegative if it takes on only nonnegative values. For example, any sum of squares is obviously nonnegative. For a homogeneous polynomial with respect to the standard grading, Hilbert famously characterized when the converse holds, that is when every nonnegative homogeneous polynomial is a sum of squares. After reviewing some history of this problem, we will examine this converse in more general settings such as global sections of a line bundles. This line of inquiry has unexpected connections to classical algebraic geometry and leads to new examples in which every nonnegative homogeneous polynomial is a sum of squares. This talk is based on joint work with Grigoriy Blekherman and Mauricio Velasco.<br />
<br />
===September 26: Jack Xin (UC Irvine)===<br />
<br />
====G-equations and Front Motion in Fluid Flows====<br />
<br />
G-equations are level set Hamilton-Jacobi equations (HJE) for modeling flame fronts in turbulent combustion where a fundamental problem is to characterize the turbulent flame speeds s_T. The existence of s_T is connected with the homogenization of HJE, however classical theory does not apply due to the non-coercive and non-convex nature of the level set Hamiltonian. We shall illustrate the asymptotic properties of s_T from both Eulerian and Lagrangian perspectives in the case of two dimensional periodic incompressible flows, in particular cellular flows.<br />
<br />
Analytical and numerical results demonstrate that G-equations capture well the enhancement, slow down and quenching phenomena observed in fluid experiments. We also comment on s_T in chaotic flows. This is joint work with Yifeng Yu and Yu-Yu Liu.<br />
<br />
===October 3: Pham Huu Tiep (Arizona)===<br />
<br />
====Adequate subgroups====<br />
<br />
The notion of adequate subgroups was introduced by Thorne. It is a weakening of the notion of big subgroups used in generalizations of the Taylor-Wiles method for proving the automorphy of certain Galois representations. Using this idea, Thorne was able to strengthen many automorphy lifting theorems. It was shown recently by Guralnick, Herzig, Taylor, and Thorne that if the degree is small compared to the characteristic then all absolutely irreducible representations are adequate. We will discuss extensions of this result obtained recently in joint work with R. M. Guralnick and F. Herzig. In particular, we show that almost all absolutely irreducible representations in characteristic p of degree less than p are adequate. We will also address a question of Serre about<br />
indecomposable modules in characteristic p of dimension less than 2p-2.<br />
<br />
===October 10: Alejandro Adem (UBC)===<br />
<br />
====Topology of Commuting Matrices====<br />
<br />
In this talk we will describe basic topological properties of the space of commuting unitary matrices. In particular we will show that they can be assembled to form a space which classifies commutativity for vector bundles and which has very interesting homotopy-theoretic properties.<br />
<br />
===October 17: Roseanna Zia (Cornell) ===<br />
<br />
====A micro-mechanical study of coarsening and rheology of colloidal gels: Cage building, cage hopping, and Smoluchowski’s ratchet====<br />
<br />
Reconfigurable soft solids such as viscoelastic gels have emerged in the past decade as a promising material in numerous applications ranging from engineered tissue to drug delivery to injectable sensors. These include colloidal gels, which microscopically comprise a scaffoldlike network of interconnected particles embedded in a solvent. Network bonds can be permanent or reversible, depending on the nature and strength of interparticle attractions. When attractions are on the order of just a few kT, bonds easily rupture and reform. On a macroscopic scale, bond reversibility allows a gel to transition from solidlike behavior during storage, to liquidlike behavior during flow (e.g., injection or shear), and back to solidlike behavior in situ. On a microscopic scale, thermal fluctuations of the solvent are occasionally strong enough to break colloidal bonds, temporarily allowing particles to migrate and exchange neighbors before rebonding to the network, leading to structural evolution over time. Prior studies of colloidal gels have examined evolution of length scales and dynamics such as decorrelation times. Left open were additional questions such as how the particle-rich regions are structured (liquidlike, glassy, crystalline), how restructuring takes place (via bulk diffusion, surface migration, coalescence of large structures), and the impact of the evolution on rheology. In this talk I discuss these themes as explored in our recent dynamic simulations. We find that the network strands comprise a glassy, immobile interior near random-close packing, enclosed by a liquidlike surface along which the diffusive migration of particles drives structural coarsening. We show that coarsening is a three-step process of cage forming, cage hopping, and cage arrest, where particles migrate to ever-deeper energy wells via “Smoluchowski’s ratchet.” Both elastic and viscous high-frequency moduli are found to scale with the square-root of the frequency, similar to the perfectly viscoelastic behavior of non-hydrodynamically interacting, purely repulsive dispersions. But here, the behavior is elastic over all frequencies, with a quantitative offset between elastic and viscous moduli, which owes its origin to the hindrance of diffusion by particle attractions. Propagation of this elasticity via the network gives rise to age-stiffening as the gel coarsens. This simple phenomenological model suggests a rescaling of the moduli on dominant network length scale that collapses moduli for all ages onto a single curve. We propose a Rouse-like theoretical model and, from it, derive an analytical expression that predicts the effects of structural aging on rheology whereby linear response can be determined at any age by measurement of dominant network length scale—or vice versa.<br />
<br />
===October 24: Almut Burchard (Toronto)===<br />
<br />
====Symmetrization, sharp inequalities, and geometric stability for integral functionals====<br />
<br />
Many integral functionals are maximized (under appropriate constraints) by radially symmetric functions. For example, the Coulomb energy of a positive charge density --- the double integral of the Newton potential against the density --- increases under symmetrization. The physical reason is that the interaction energy between the charges grows as the typical distance between the charges shrinks. The energy increases strictly, unless the charge density is already radially decreasing about some point. Is this characterization of equality cases "stable"? In other words, must near-maximizers be close to maximizers?<br />
<br />
Such stability questions have been well-studied for the isoperimetric inequality and other functionals that involve gradients since the 1990's; the first results in that direction are due to Bonnesen in the 1920's. For example, the excess perimeter of a set (as compared to a ball of the same volume) controls its difference from a suitable translate of that ball. Much less is known about convolutions and other multiple integrals that describe "non-local" interactions. In some cases, not even a complete list of maximizers is known. I will discuss very recent developments (due to M. Christ, Figalli, Jerison, and others), mention open problems, and present joint work with Greg Chambers on the Coulomb energy.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=8657Colloquia/Fall182014-10-26T00:53:05Z<p>Shamgar: /* Fall 2014 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
[[Colloquia/Spring 2015 | Tentative schedule for Spring 2015]]<br />
<br />
== Fall 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 12<br />
| [http://mduchin.math.tufts.edu/index.html Moon Duchin] (Tufts University)<br />
| [[Colloquia#September 12: Moon Duchin (Tufts University) | Geometry and counting in the Heisenberg group]]<br />
| Dymarz and WIMAW<br />
|-<br />
|September 19<br />
|[http://www.mast.queensu.ca/~ggsmith/ Gregory G. Smith] (Queen's University)<br />
|[[Colloquia#September 19: Gregory G. Smith (Queen's University) | Nonnegative sections and sums of squares]]<br />
|Erman<br />
|-<br />
|September 26<br />
|[http://www.math.uci.edu/~jxin/ Jack Xin] (UC Irvine)<br />
|[[Colloquia#September 26: Jack Xin (UC Irvine) | G-equations and Front Motion in Fluid Flows]]<br />
|Jin<br />
|-<br />
|October 3<br />
|[http://math.arizona.edu/~tiep/ Pham Huu Tiep] (University of Arizona)<br />
|[[Colloquia#October 3: Pham Huu Tiep (Arizona) | Adequate subgroups]]<br />
|Gurevich<br />
|-<br />
|October 10<br />
|[http://www.math.ubc.ca/~adem/ Alejandro Adem] (UBC)<br />
|[[Colloquia#October 10: Alejandro Adem (UBC) | Topology of Commuting Matrices]]<br />
|Yang<br />
|-<br />
|October 17<br />
|[http://www.icse.cornell.edu/ziagroup/ Roseanna Zia] (Cornell University)<br />
|[[Colloquia#October 17: Roseanna Zia (Cornell) | A micro-mechanical study of coarsening and rheology of colloidal gels: Cage building, cage hopping, and Smoluchowski’s ratchet]]<br />
|Spagnolie<br />
|-<br />
|October 24<br />
|[http://www.math.utoronto.ca/almut/ Almut Burchard] (Toronto)<br />
|[[Colloquia#October 24: Almut Burchard (Toronto) | Symmetrization, sharp inequalities, and geometric stability for integral functionals]]<br />
|Stovall<br />
|-<br />
|October 31<br />
|[http://www.math.uchicago.edu/~ngo/ Bao Chau Ngo] (University of Chicago)<br />
|Automorphic L-function, trace formula and geometry<br />
|Gurevich<br />
|-<br />
|November 7<br />
|Reserved for possible job interview<br />
|<br />
|<br />
|-<br />
|November 14<br />
|Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|November 21<br />
|Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|November 28<br />
|University holiday<br />
|<br />
| <br />
|-<br />
|December 5<br />
|Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|December 12<br />
| Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===September 12: Moon Duchin (Tufts University)===<br />
<br />
====Geometry and counting in the Heisenberg group====<br />
<br />
The growth function of a finitely-generated group enumerates how many words can be spelled with each possible number of letters-- this should be thought of as a sort of volume growth in any geometric model of the group. A major theorem of Gromov tells us exactly which groups have growth in the polynomial range: those that are (virtually) nilpotent. But we can still wonder how regular the growth of a nilpotent group is: is it actually a polynomial? Or could it exhibit some transcendentality together with pretty slow growth? <br />
<br />
I'll talk about some themes and techniques in the study of group growth and outline a geometry of numbers for nilpotent groups, including a recent result with M. Shapiro settling a long-standing question: the Heisenberg group -- the simplest non-abelian nilpotent group -- has rational growth in any generating set. <br />
<br />
===September 19: Gregory G. Smith (Queen's University)===<br />
<br />
====Nonnegative sections and sums of squares====<br />
<br />
A polynomial with real coefficients is nonnegative if it takes on only nonnegative values. For example, any sum of squares is obviously nonnegative. For a homogeneous polynomial with respect to the standard grading, Hilbert famously characterized when the converse holds, that is when every nonnegative homogeneous polynomial is a sum of squares. After reviewing some history of this problem, we will examine this converse in more general settings such as global sections of a line bundles. This line of inquiry has unexpected connections to classical algebraic geometry and leads to new examples in which every nonnegative homogeneous polynomial is a sum of squares. This talk is based on joint work with Grigoriy Blekherman and Mauricio Velasco.<br />
<br />
===September 26: Jack Xin (UC Irvine)===<br />
<br />
====G-equations and Front Motion in Fluid Flows====<br />
<br />
G-equations are level set Hamilton-Jacobi equations (HJE) for modeling flame fronts in turbulent combustion where a fundamental problem is to characterize the turbulent flame speeds s_T. The existence of s_T is connected with the homogenization of HJE, however classical theory does not apply due to the non-coercive and non-convex nature of the level set Hamiltonian. We shall illustrate the asymptotic properties of s_T from both Eulerian and Lagrangian perspectives in the case of two dimensional periodic incompressible flows, in particular cellular flows.<br />
<br />
Analytical and numerical results demonstrate that G-equations capture well the enhancement, slow down and quenching phenomena observed in fluid experiments. We also comment on s_T in chaotic flows. This is joint work with Yifeng Yu and Yu-Yu Liu.<br />
<br />
===October 3: Pham Huu Tiep (Arizona)===<br />
<br />
====Adequate subgroups====<br />
<br />
The notion of adequate subgroups was introduced by Thorne. It is a weakening of the notion of big subgroups used in generalizations of the Taylor-Wiles method for proving the automorphy of certain Galois representations. Using this idea, Thorne was able to strengthen many automorphy lifting theorems. It was shown recently by Guralnick, Herzig, Taylor, and Thorne that if the degree is small compared to the characteristic then all absolutely irreducible representations are adequate. We will discuss extensions of this result obtained recently in joint work with R. M. Guralnick and F. Herzig. In particular, we show that almost all absolutely irreducible representations in characteristic p of degree less than p are adequate. We will also address a question of Serre about<br />
indecomposable modules in characteristic p of dimension less than 2p-2.<br />
<br />
===October 10: Alejandro Adem (UBC)===<br />
<br />
====Topology of Commuting Matrices====<br />
<br />
In this talk we will describe basic topological properties of the space of commuting unitary matrices. In particular we will show that they can be assembled to form a space which classifies commutativity for vector bundles and which has very interesting homotopy-theoretic properties.<br />
<br />
===October 17: Roseanna Zia (Cornell) ===<br />
<br />
====A micro-mechanical study of coarsening and rheology of colloidal gels: Cage building, cage hopping, and Smoluchowski’s ratchet====<br />
<br />
Reconfigurable soft solids such as viscoelastic gels have emerged in the past decade as a promising material in numerous applications ranging from engineered tissue to drug delivery to injectable sensors. These include colloidal gels, which microscopically comprise a scaffoldlike network of interconnected particles embedded in a solvent. Network bonds can be permanent or reversible, depending on the nature and strength of interparticle attractions. When attractions are on the order of just a few kT, bonds easily rupture and reform. On a macroscopic scale, bond reversibility allows a gel to transition from solidlike behavior during storage, to liquidlike behavior during flow (e.g., injection or shear), and back to solidlike behavior in situ. On a microscopic scale, thermal fluctuations of the solvent are occasionally strong enough to break colloidal bonds, temporarily allowing particles to migrate and exchange neighbors before rebonding to the network, leading to structural evolution over time. Prior studies of colloidal gels have examined evolution of length scales and dynamics such as decorrelation times. Left open were additional questions such as how the particle-rich regions are structured (liquidlike, glassy, crystalline), how restructuring takes place (via bulk diffusion, surface migration, coalescence of large structures), and the impact of the evolution on rheology. In this talk I discuss these themes as explored in our recent dynamic simulations. We find that the network strands comprise a glassy, immobile interior near random-close packing, enclosed by a liquidlike surface along which the diffusive migration of particles drives structural coarsening. We show that coarsening is a three-step process of cage forming, cage hopping, and cage arrest, where particles migrate to ever-deeper energy wells via “Smoluchowski’s ratchet.” Both elastic and viscous high-frequency moduli are found to scale with the square-root of the frequency, similar to the perfectly viscoelastic behavior of non-hydrodynamically interacting, purely repulsive dispersions. But here, the behavior is elastic over all frequencies, with a quantitative offset between elastic and viscous moduli, which owes its origin to the hindrance of diffusion by particle attractions. Propagation of this elasticity via the network gives rise to age-stiffening as the gel coarsens. This simple phenomenological model suggests a rescaling of the moduli on dominant network length scale that collapses moduli for all ages onto a single curve. We propose a Rouse-like theoretical model and, from it, derive an analytical expression that predicts the effects of structural aging on rheology whereby linear response can be determined at any age by measurement of dominant network length scale—or vice versa.<br />
<br />
===October 24: Almut Burchard (Toronto)===<br />
<br />
====Symmetrization, sharp inequalities, and geometric stability for integral functionals====<br />
<br />
Many integral functionals are maximized (under appropriate constraints) by radially symmetric functions. For example, the Coulomb energy of a positive charge density --- the double integral of the Newton potential against the density --- increases under symmetrization. The physical reason is that the interaction energy between the charges grows as the typical distance between the charges shrinks. The energy increases strictly, unless the charge density is already radially decreasing about some point. Is this characterization of equality cases "stable"? In other words, must near-maximizers be close to maximizers?<br />
<br />
Such stability questions have been well-studied for the isoperimetric inequality and other functionals that involve gradients since the 1990's; the first results in that direction are due to Bonnesen in the 1920's. For example, the excess perimeter of a set (as compared to a ball of the same volume) controls its difference from a suitable translate of that ball. Much less is known about convolutions and other multiple integrals that describe "non-local" interactions. In some cases, not even a complete list of maximizers is known. I will discuss very recent developments (due to M. Christ, Figalli, Jerison, and others), mention open problems, and present joint work with Greg Chambers on the Coulomb energy.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=8656Colloquia/Fall182014-10-26T00:52:05Z<p>Shamgar: /* Fall 2014 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
[[Colloquia/Spring 2015 | Tentative schedule for Spring 2015]]<br />
<br />
== Fall 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 12<br />
| [http://mduchin.math.tufts.edu/index.html Moon Duchin] (Tufts University)<br />
| [[Colloquia#September 12: Moon Duchin (Tufts University) | Geometry and counting in the Heisenberg group]]<br />
| Dymarz and WIMAW<br />
|-<br />
|September 19<br />
|[http://www.mast.queensu.ca/~ggsmith/ Gregory G. Smith] (Queen's University)<br />
|[[Colloquia#September 19: Gregory G. Smith (Queen's University) | Nonnegative sections and sums of squares]]<br />
|Erman<br />
|-<br />
|September 26<br />
|[http://www.math.uci.edu/~jxin/ Jack Xin] (UC Irvine)<br />
|[[Colloquia#September 26: Jack Xin (UC Irvine) | G-equations and Front Motion in Fluid Flows]]<br />
|Jin<br />
|-<br />
|October 3<br />
|[http://math.arizona.edu/~tiep/ Pham Huu Tiep] (University of Arizona)<br />
|[[Colloquia#October 3: Pham Huu Tiep (Arizona) | Adequate subgroups]]<br />
|Gurevich<br />
|-<br />
|October 10<br />
|[http://www.math.ubc.ca/~adem/ Alejandro Adem] (UBC)<br />
|[[Colloquia#October 10: Alejandro Adem (UBC) | Topology of Commuting Matrices]]<br />
|Yang<br />
|-<br />
|October 17<br />
|[http://www.icse.cornell.edu/ziagroup/ Roseanna Zia] (Cornell University)<br />
|[[Colloquia#October 17: Roseanna Zia (Cornell) | A micro-mechanical study of coarsening and rheology of colloidal gels: Cage building, cage hopping, and Smoluchowski’s ratchet]]<br />
|Spagnolie<br />
|-<br />
|October 24<br />
|[http://www.math.utoronto.ca/almut/ Almut Burchard] (Toronto)<br />
|[[Colloquia#October 24: Almut Burchard (Toronto) | Symmetrization, sharp inequalities, and geometric stability for integral functionals]]<br />
|Stovall<br />
|-<br />
|October 31<br />
|[http://www.math.uchicago.edu/~ngo/ Bao Chau Ngo] (University of Chicago)<br />
Automorphic L-function, trace formula and geometry<br />
|Gurevich<br />
|-<br />
|November 7<br />
|Reserved for possible job interview<br />
|<br />
|<br />
|-<br />
|November 14<br />
|Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|November 21<br />
|Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|November 28<br />
|University holiday<br />
|<br />
| <br />
|-<br />
|December 5<br />
|Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|December 12<br />
| Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===September 12: Moon Duchin (Tufts University)===<br />
<br />
====Geometry and counting in the Heisenberg group====<br />
<br />
The growth function of a finitely-generated group enumerates how many words can be spelled with each possible number of letters-- this should be thought of as a sort of volume growth in any geometric model of the group. A major theorem of Gromov tells us exactly which groups have growth in the polynomial range: those that are (virtually) nilpotent. But we can still wonder how regular the growth of a nilpotent group is: is it actually a polynomial? Or could it exhibit some transcendentality together with pretty slow growth? <br />
<br />
I'll talk about some themes and techniques in the study of group growth and outline a geometry of numbers for nilpotent groups, including a recent result with M. Shapiro settling a long-standing question: the Heisenberg group -- the simplest non-abelian nilpotent group -- has rational growth in any generating set. <br />
<br />
===September 19: Gregory G. Smith (Queen's University)===<br />
<br />
====Nonnegative sections and sums of squares====<br />
<br />
A polynomial with real coefficients is nonnegative if it takes on only nonnegative values. For example, any sum of squares is obviously nonnegative. For a homogeneous polynomial with respect to the standard grading, Hilbert famously characterized when the converse holds, that is when every nonnegative homogeneous polynomial is a sum of squares. After reviewing some history of this problem, we will examine this converse in more general settings such as global sections of a line bundles. This line of inquiry has unexpected connections to classical algebraic geometry and leads to new examples in which every nonnegative homogeneous polynomial is a sum of squares. This talk is based on joint work with Grigoriy Blekherman and Mauricio Velasco.<br />
<br />
===September 26: Jack Xin (UC Irvine)===<br />
<br />
====G-equations and Front Motion in Fluid Flows====<br />
<br />
G-equations are level set Hamilton-Jacobi equations (HJE) for modeling flame fronts in turbulent combustion where a fundamental problem is to characterize the turbulent flame speeds s_T. The existence of s_T is connected with the homogenization of HJE, however classical theory does not apply due to the non-coercive and non-convex nature of the level set Hamiltonian. We shall illustrate the asymptotic properties of s_T from both Eulerian and Lagrangian perspectives in the case of two dimensional periodic incompressible flows, in particular cellular flows.<br />
<br />
Analytical and numerical results demonstrate that G-equations capture well the enhancement, slow down and quenching phenomena observed in fluid experiments. We also comment on s_T in chaotic flows. This is joint work with Yifeng Yu and Yu-Yu Liu.<br />
<br />
===October 3: Pham Huu Tiep (Arizona)===<br />
<br />
====Adequate subgroups====<br />
<br />
The notion of adequate subgroups was introduced by Thorne. It is a weakening of the notion of big subgroups used in generalizations of the Taylor-Wiles method for proving the automorphy of certain Galois representations. Using this idea, Thorne was able to strengthen many automorphy lifting theorems. It was shown recently by Guralnick, Herzig, Taylor, and Thorne that if the degree is small compared to the characteristic then all absolutely irreducible representations are adequate. We will discuss extensions of this result obtained recently in joint work with R. M. Guralnick and F. Herzig. In particular, we show that almost all absolutely irreducible representations in characteristic p of degree less than p are adequate. We will also address a question of Serre about<br />
indecomposable modules in characteristic p of dimension less than 2p-2.<br />
<br />
===October 10: Alejandro Adem (UBC)===<br />
<br />
====Topology of Commuting Matrices====<br />
<br />
In this talk we will describe basic topological properties of the space of commuting unitary matrices. In particular we will show that they can be assembled to form a space which classifies commutativity for vector bundles and which has very interesting homotopy-theoretic properties.<br />
<br />
===October 17: Roseanna Zia (Cornell) ===<br />
<br />
====A micro-mechanical study of coarsening and rheology of colloidal gels: Cage building, cage hopping, and Smoluchowski’s ratchet====<br />
<br />
Reconfigurable soft solids such as viscoelastic gels have emerged in the past decade as a promising material in numerous applications ranging from engineered tissue to drug delivery to injectable sensors. These include colloidal gels, which microscopically comprise a scaffoldlike network of interconnected particles embedded in a solvent. Network bonds can be permanent or reversible, depending on the nature and strength of interparticle attractions. When attractions are on the order of just a few kT, bonds easily rupture and reform. On a macroscopic scale, bond reversibility allows a gel to transition from solidlike behavior during storage, to liquidlike behavior during flow (e.g., injection or shear), and back to solidlike behavior in situ. On a microscopic scale, thermal fluctuations of the solvent are occasionally strong enough to break colloidal bonds, temporarily allowing particles to migrate and exchange neighbors before rebonding to the network, leading to structural evolution over time. Prior studies of colloidal gels have examined evolution of length scales and dynamics such as decorrelation times. Left open were additional questions such as how the particle-rich regions are structured (liquidlike, glassy, crystalline), how restructuring takes place (via bulk diffusion, surface migration, coalescence of large structures), and the impact of the evolution on rheology. In this talk I discuss these themes as explored in our recent dynamic simulations. We find that the network strands comprise a glassy, immobile interior near random-close packing, enclosed by a liquidlike surface along which the diffusive migration of particles drives structural coarsening. We show that coarsening is a three-step process of cage forming, cage hopping, and cage arrest, where particles migrate to ever-deeper energy wells via “Smoluchowski’s ratchet.” Both elastic and viscous high-frequency moduli are found to scale with the square-root of the frequency, similar to the perfectly viscoelastic behavior of non-hydrodynamically interacting, purely repulsive dispersions. But here, the behavior is elastic over all frequencies, with a quantitative offset between elastic and viscous moduli, which owes its origin to the hindrance of diffusion by particle attractions. Propagation of this elasticity via the network gives rise to age-stiffening as the gel coarsens. This simple phenomenological model suggests a rescaling of the moduli on dominant network length scale that collapses moduli for all ages onto a single curve. We propose a Rouse-like theoretical model and, from it, derive an analytical expression that predicts the effects of structural aging on rheology whereby linear response can be determined at any age by measurement of dominant network length scale—or vice versa.<br />
<br />
===October 24: Almut Burchard (Toronto)===<br />
<br />
====Symmetrization, sharp inequalities, and geometric stability for integral functionals====<br />
<br />
Many integral functionals are maximized (under appropriate constraints) by radially symmetric functions. For example, the Coulomb energy of a positive charge density --- the double integral of the Newton potential against the density --- increases under symmetrization. The physical reason is that the interaction energy between the charges grows as the typical distance between the charges shrinks. The energy increases strictly, unless the charge density is already radially decreasing about some point. Is this characterization of equality cases "stable"? In other words, must near-maximizers be close to maximizers?<br />
<br />
Such stability questions have been well-studied for the isoperimetric inequality and other functionals that involve gradients since the 1990's; the first results in that direction are due to Bonnesen in the 1920's. For example, the excess perimeter of a set (as compared to a ball of the same volume) controls its difference from a suitable translate of that ball. Much less is known about convolutions and other multiple integrals that describe "non-local" interactions. In some cases, not even a complete list of maximizers is known. I will discuss very recent developments (due to M. Christ, Figalli, Jerison, and others), mention open problems, and present joint work with Greg Chambers on the Coulomb energy.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=7950Colloquia/Fall182014-08-14T02:12:45Z<p>Shamgar: /* Abstracts */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
[[Colloquia/Spring 2015 | Tentative schedule for Spring 2015]]<br />
<br />
== Fall 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 12<br />
| [http://mduchin.math.tufts.edu/index.html Moon Duchin] (Tufts University)<br />
| TBA<br />
| Dymarz and WIMAW<br />
|-<br />
|September 19<br />
|[http://www.mast.queensu.ca/~ggsmith/ Greg Smith] (Queen's University)<br />
|TBA<br />
|Erman<br />
|-<br />
|September 26<br />
|[http://www.math.uci.edu/~jxin/ Jack Xin] (UC Irvine)<br />
|TBA<br />
|Jin<br />
|-<br />
|October 3<br />
|[http://math.arizona.edu/~tiep/ Pham Huu Tiep] (University of Arizona)<br />
|Adequate subgroups<br />
|Gurevich<br />
|-<br />
|October 10<br />
|Tentatively reserved<br />
|<br />
|Yang<br />
|-<br />
|October 17<br />
|[http://www.math.uchicago.edu/~ngo/ Bao Chau Ngo] (University of Chicago)<br />
|TBA<br />
|Gurevich<br />
|-<br />
|October 24<br />
|[http://www.math.utoronto.ca/almut/ Almut Burchard] (University of Toronto)<br />
|TBA<br />
|Stovall<br />
|-<br />
|October 31<br />
| Morris Hirsch (UC Berkeley and UW Madison)<br />
| Fixed points of Lie group actions<br />
| Stovall<br />
|-<br />
|November 7<br />
|Reserved for possible job interview<br />
|<br />
|<br />
|-<br />
|November 14<br />
|Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|November 21<br />
|Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|November 28<br />
|University holiday<br />
|<br />
| <br />
|-<br />
|December 5<br />
|Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|December 12<br />
| Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===October 3: Pham Huu Tiep (Arizona)===<br />
<br />
''Adequate subgroups''<br />
<br />
The notion of adequate subgroups was introduced by Thorne. It is a weakening of the notion of big subgroups used in generalizations of the Taylor-Wiles method for proving the automorphy of certain Galois representations. Using this idea, Thorne was able to strengthen many automorphy lifting theorems. It was shown recently by Guralnick, Herzig, Taylor, and Thorne that if the degree is small compared to the characteristic then all absolutely irreducible representations are adequate. We will discuss extensions of this result obtained recently in joint work with R. M. Guralnick and F. Herzig. In particular, we show that almost all absolutely irreducible representations in characteristic p of degree less than p are adequate. We will also address a question of Serre about<br />
indecomposable modules in characteristic p of dimension less than 2p-2.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=7949Colloquia/Fall182014-08-14T02:08:24Z<p>Shamgar: /* Fall 2014 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
[[Colloquia/Spring 2015 | Tentative schedule for Spring 2015]]<br />
<br />
== Fall 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 12<br />
| [http://mduchin.math.tufts.edu/index.html Moon Duchin] (Tufts University)<br />
| TBA<br />
| Dymarz and WIMAW<br />
|-<br />
|September 19<br />
|[http://www.mast.queensu.ca/~ggsmith/ Greg Smith] (Queen's University)<br />
|TBA<br />
|Erman<br />
|-<br />
|September 26<br />
|[http://www.math.uci.edu/~jxin/ Jack Xin] (UC Irvine)<br />
|TBA<br />
|Jin<br />
|-<br />
|October 3<br />
|[http://math.arizona.edu/~tiep/ Pham Huu Tiep] (University of Arizona)<br />
|Adequate subgroups<br />
|Gurevich<br />
|-<br />
|October 10<br />
|Tentatively reserved<br />
|<br />
|Yang<br />
|-<br />
|October 17<br />
|[http://www.math.uchicago.edu/~ngo/ Bao Chau Ngo] (University of Chicago)<br />
|TBA<br />
|Gurevich<br />
|-<br />
|October 24<br />
|[http://www.math.utoronto.ca/almut/ Almut Burchard] (University of Toronto)<br />
|TBA<br />
|Stovall<br />
|-<br />
|October 31<br />
| Morris Hirsch (UC Berkeley and UW Madison)<br />
| Fixed points of Lie group actions<br />
| Stovall<br />
|-<br />
|November 7<br />
|Reserved for possible job interview<br />
|<br />
|<br />
|-<br />
|November 14<br />
|Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|November 21<br />
|Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|November 28<br />
|University holiday<br />
|<br />
| <br />
|-<br />
|December 5<br />
|Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|December 12<br />
| Reserved for possible job interview<br />
|<br />
| <br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=6934Colloquia/Fall182014-04-26T16:20:21Z<p>Shamgar: /* Abstracts */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
[[Colloquia/Fall 2014 | Tentative schedule for Fall 2014]]<br />
<br />
== Spring 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Mon, Jan 6, 4PM'''<br />
|[http://www-bcf.usc.edu/~lauda/Aaron_Laudas_Page/Home.html Aaron Lauda] (USC) <br />
|[[Colloquia#January 6: Aaron Lauda (USC) | An introduction to diagrammatic categorification]]<br />
|Caldararu<br />
|-<br />
|'''Wed, Jan 8, 4PM'''<br />
|[http://www2.math.umd.edu/~kmelnick/ Karin Melnick] (Maryland) <br />
|[[Colloquia#January 8: Karin Melnick (Maryland) | Normal forms for local flows on parabolic geometries]]<br />
|Kent<br />
|-<br />
|Jan 10, 4PM<br />
|[http://users.math.yale.edu/~yd82/ Yen Do] (Yale) <br />
|Convergence of Fourier series and multilinear analysis<br />
|Denissov<br />
|-<br />
|'''Mon, Jan 13, 4pm'''<br />
|[http://math.stanford.edu/~wangyi/ Yi Wang] (Stanford)<br />
|Isoperimetric Inequality and Q-curvature<br />
|Viaclovsky<br />
|-<br />
|'''Wen, Jan 15, 4pm'''<br />
|[http://www.maths.ox.ac.uk/people/profiles/wei.xiang Wei Xiang] (University of Oxford)<br />
|[[Colloquia#January 15: Wei Xiang (University of Oxford) |Conservation Laws and Shock Waves]]<br />
|Bolotin<br />
|-<br />
|'''Fri, Jan 17, 2:25PM, VV901'''<br />
|[http://www.math.dartmouth.edu/~gillmana/ Adrianna Gillman] (Dartmouth) <br />
|Fast direct solvers for linear partial differential equations<br />
|Thiffeault<br />
|-<br />
|'''Thu, Jan 23, 2:25, VV901'''<br />
|[http://www.stat.berkeley.edu/~mshkolni/ Mykhaylo Shkolnikov] (Berkeley)<br />
|[[Colloquia#Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) | Intertwinings, wave equations and growth models]]<br />
|Seppalainen<br />
|-<br />
|Jan 24<br />
|[http://www.yanivplan.com/ Yaniv Plan] (Michigan)<br />
|[http://www.math.wisc.edu/wiki/index.php/Applied/ACMS/absS14#Yaniv_Plan_.28Michigan.29 Low-dimensionality in mathematical signal processing]<br />
|Thiffeault<br />
|-<br />
|Jan 31<br />
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)<br />
|Underwater Networks: A Convergence of Communications, Control and Sensing<br />
|Gurevich<br />
|-<br />
|Feb 7<br />
|David Treumann (Boston College)<br />
|Functoriality, Smith theory, and the Brauer homomorphism<br />
|Street<br />
|-<br />
|Feb 14<br />
|[http://www.tc.columbia.edu/academics/index.htm?facid=apk16 Alexander Karp] (Columbia Teacher's College)<br />
|History of Mathematics Education as a Research Field and as Magistra Vitae<br />
|Kiselev<br />
|-<br />
|Feb 21<br />
|[http://www.math.uci.edu/~szhitomi/ Svetlana Jitomirskaya] (UC-Irvine)<br />
|Analytic quasiperiodic cocycles<br />
|Kiselev<br />
|-<br />
|Feb 28<br />
|[http://math.nyu.edu/faculty/shelley/ Michael Shelley] (Courant)<br />
|[[Colloquia#February 28: Michael Shelley (Courant) | Mathematical models of soft active materials]]<br />
|Spagnolie<br />
|-<br />
|March 7<br />
|[http://www.math.northwestern.edu/people/facultyProfiles/steve.zelditch.html Steve Zelditch] (Northwestern)<br />
|[[Colloquia#March 7: Steve Zelditch (Northwestern) | Shapes and sizes of eigenfunctions]]<br />
|Seeger<br />
|-<br />
|March 14<br />
|[http://www.math.brown.edu/~res/ Richard Schwartz] (Brown)<br />
|[[Colloquia#March 14: Richard Schwartz (Brown) |The projective heat map on pentagons]]<br />
|Mari-Beffa<br />
|-<br />
|<strike>March 21</strike><br />
|'''Spring Break'''<br />
|No Colloquium<br />
|<br />
|-<br />
|'''March 26, 7pm, WID'''<br />
|[https://www.dpmms.cam.ac.uk/people/t.tokieda/ Tadashi Tokieda] (Cambridge)<br />
|[http://c4.discovery.wisc.edu/events/lectures/toymodels/ Toy models]<br />
|Thiffeault (C4 von Neumann Public Lecture)<br />
|-<br />
|March 28<br />
|Cancelled<br />
|<br />
|<br />
|-<br />
|April 4<br />
|[http://matthewkahle.org/ Matthew Kahle] (OSU)<br />
|Recent progress in random topology<br />
|Dymarz<br />
|- <br />
|April 11<br />
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)<br />
|Multiresolution Matrix Factorization<br />
|Gurevich<br />
|-<br />
|April 18 (Wasow Lecture)<br />
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)<br />
|[[Colloquia#April 18: Christopher Sogge (Johns Hopkins) |Focal points and sup-norms of eigenfunctions]]<br />
|Seeger<br />
|-<br />
|April 25<br />
|[http://www.charlesdoran.net Charles Doran](University of Alberta)<br />
|[[Colloquia#April 25: Charles Doran (University of Alberta) |The Mathematics of Supersymmetry: Graphs, Codes, and Super-Curves]]<br />
|Song<br />
|-<br />
|'''Tuesday, April 29''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Matrix factorizations old and new, I<br />
|Erman<br />
|-<br />
|'''Wednesday, April 30''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Matrix factorizations old and new, II<br />
|Erman<br />
|-<br />
|May 2<br />
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)<br />
|Hypermatrices<br />
|Boston<br />
|-<br />
|May 9<br />
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)<br />
|Sampling theorems for efficient dimensionality reduction and sparse recovery<br />
|WIMAW<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===January 6: Aaron Lauda (USC)===<br />
<br />
''An introduction to diagrammatic categorification''<br />
<br />
Categorification seeks to reveal a hidden layer in mathematical<br />
structures. Often the resulting structures can be combinatorially<br />
complex objects making them difficult to study. One method of<br />
overcoming this difficulty, that has proven very successful, is to<br />
encode the categorification into a diagrammatic calculus that makes<br />
computations simple and intuitive.<br />
<br />
In this talk I will review some of the original considerations that<br />
led to the categorification philosophy. We will examine how the<br />
diagrammatic perspective has helped to produce new categorifications<br />
having profound applications to algebra, representation theory, and<br />
low-dimensional topology.<br />
<br />
===January 8: Karin Melnick (Maryland)===<br />
<br />
''Normal forms for local flows on parabolic geometries''<br />
<br />
The exponential map in Riemannian geometry conjugates the differential of an isometry at a point with the action of the isometry near the point. It thus provides a linear normal form for all isometries fixing a point. Conformal transformations are not linearizable in general. I will discuss a suite of normal forms theorems in conformal geometry and, more generally, for parabolic geometries, a rich family of geometric structures of which conformal, projective, and CR structures are examples.<br />
<br />
===January 10, 4PM: Yen Do (Yale)===<br />
<br />
''Convergence of Fourier series and multilinear analysis''<br />
<br />
Almost everywhere convergence of the Fourier series of square <br />
integrable functions was first proved by Lennart Carleson in 1966, and <br />
the proof has lead to deep developments in various multilinear settings. <br />
In this talk I would like to introduce a brief history of the subject <br />
and sketch some recent developments, some of these involve my joint <br />
works with collaborators.<br />
<br />
===Mon, January 13: Yi Wang (Stanford)===<br />
<br />
''Isoperimetric Inequality and Q-curvature''<br />
<br />
A well-known question in differential geometry is to prove the<br />
isoperimetric inequality under intrinsic curvature conditions. In<br />
dimension 2, the isoperimetric inequality is controlled by the integral of<br />
the positive part of the Gaussian curvature. In my recent work, I prove<br />
that on simply connected conformally flat manifolds of higher dimensions,<br />
the role of the Gaussian curvature can be replaced by the Branson's<br />
Q-curvature. The isoperimetric inequality is valid if the integral of the<br />
Q-curvature is below a sharp threshold. Moreover, the isoperimetric<br />
constant depends only on the integrals of the Q-curvature. The proof<br />
relies on the theory of $A_p$ weights in harmonic analysis.<br />
<br />
===January 15: Wei Xiang (University of Oxford)===<br />
<br />
''Conservation Laws and Shock Waves''<br />
<br />
The study of continuum physics gave birth to the theory of quasilinear<br />
systems in divergence form, commonly called conservation laws. In this<br />
talk, conservation laws, the Euler equations, and the definition of the<br />
corresponding weak solutions will be introduced first. Then a short history<br />
of the studying of conservation laws and shock waves will be given. Finally<br />
I would like to present two of our current research projects. One is on the<br />
mathematical analysis of shock diffraction by convex cornered wedges, and<br />
the other one is on the validation of weakly nonlinear geometric optics for<br />
entropy solutions of nonlinear hyperbolic systems of conservation laws.<br />
<br />
Fri, Jan 17, 2:25PM, VV901 Adrianna Gillman (Dartmouth) Fast direct solvers for linear partial differential equations<br />
<br />
===Fri, Jan 17: Adrianna Gillman (Dartmouth) ===<br />
''Fast direct solvers for linear partial differential equations''<br />
<br />
The cost of solving a large linear system often determines what can and cannot be modeled computationally in many areas of science and engineering. Unlike Gaussian elimination which scales cubically with the respect to the number of unknowns, fast direct solvers construct an inverse of a linear in system with a cost that scales linearly or nearly linearly. The fast direct solvers presented in this talk are designed for the linear systems arising from the discretization of linear partial differential equations. These methods are more robust, versatile and stable than iterative schemes. Since an inverse is computed, additional right-hand sides can be processed rapidly. The talk will give the audience a brief introduction to the core ideas, an overview of recent advancements, and it will conclude with a sampling of challenging application examples including the scattering of waves.<br />
<br />
===Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) ===<br />
''Intertwinings, wave equations and growth models''<br />
<br />
We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to hyperbolic partial differential equations, symmetric polynomials and the corresponding random growth models. The talk will be devoted to these recent developments which also shed new light on some beautiful old examples of intertwinings. Based on joint works with Vadim Gorin and Soumik Pal. <br />
<br />
===Jan 24: Yaniv Plan (Michigan) ===<br />
''Low-dimensionality in mathematical signal processing''<br />
<br />
Natural images tend to be compressible, i.e., the amount of information needed to encode an image is small. This conciseness of information -- in other words, low dimensionality of the signal -- is found throughout a plethora of applications ranging from MRI to quantum state tomography. It is natural to ask: can the number of measurements needed to determine a signal be comparable with the information content? We explore this question under modern models of low-dimensionality and measurement acquisition.<br />
<br />
===Thur, Jan 30: Urbashi Mitra (USC) ===<br />
''Underwater Networks: A Convergence of Communications, Control and Sensing''<br />
<br />
The oceans cover 71% of the earth’s surface and represent one of the least explored frontiers, yet the oceans are integral to climate regulation, nutrient production, oil retrieval and transportation. Future scientific and technological efforts to achieve better understanding of oceans and water-related applications will rely heavily on our ability to communicate reliably between instruments, vehicles (manned and unmanned), human operators, platforms and sensors of all types. Underwater acoustic communication techniques have not reached the same maturity as those for terrestrial radio communications and present some unique opportunities for new developments in information and communication theories. Key features of underwater acoustic communication channels are examined: slow speed of propagation, significant delay spreads, sparse multi-path, time-variation and range-dependent available bandwidth. Another unique feature of underwater networks is that the cost of communication, sensing and control are often comparable resulting in new tradeoffs between these activities. We examine some new results (with implications wider than underwater systems) in channel identifiability, communicating over channels with state and cooperative game theory motivated by the underwater network application.<br />
<br />
===Feb 7: David Treumann (Boston College) ===<br />
''Functoriality, Smith theory, and the Brauer homomorphism''<br />
<br />
Smith theory is a technique for relating the mod p homologies of X and of the fixed points of X by an automorphism of order p. I will discuss how, in the setting of locally symmetric spaces, it provides an easy method (no trace formula) for lifting mod p automorphic forms from G^{sigma} to G, where G is an arithmetic group and sigma is an automorphism of G of order p. This lift is compatible with Hecke actions via an analog of the Brauer homomorphism from modular representation theory, and is often compatible with a homomorphism of L-groups on the Galois side. The talk is based on joint work with Akshay Venkatesh. I hope understanding the talk will require less number theory background than understanding the abstract.<br />
<br />
===Feb 14: Alexander Karp (Columbia Teacher's College) ===<br />
''History of Mathematics Education as a Research Field and as Magistra Vitae''<br />
<br />
The presentation will be based on the experience of putting together and editing the Handbook<br />
on the History of Mathematics Education, which will be published by Springer in the near future. <br />
This volume, which was prepared by a large group of researchers from different countries, <br />
contains the first systematic account of the history of the development of mathematics education <br />
in the whole world (and not just in some particular country or region). The editing of such a <br />
book gave rise to thoughts about the methodology of research in this field, and also about what <br />
constitutes an object of such research. These are the thoughts that the presenter intends to share <br />
with his audience. From them, it is natural to pass to an analysis of the current situation and how <br />
it might develop.<br />
<br />
===Feb 21: Svetlana Jitomirskaya (UC-Irvine)===<br />
''Analytic quasiperiodic cocycles''<br />
<br />
Analytic quasiperiodic matrix cocycles is a simple dynamical<br />
system, where analytic and dynamical properties are related in an<br />
unexpected and remarkable way. We will focus on this relation, leading to<br />
a new approach to the proof of joint continuity of Lyapunov exponents in<br />
frequency and cocycle, at irrational frequency, first proved for SL(2,C)<br />
cocycles in Bourgain-Jitom., 2002. The approach is powerful enough to<br />
handle singular and multidimensional cocycles, thus establishing the above<br />
continuity in full generality. This has important consequences including<br />
a dense open version of Bochi-Viana theorem in this setting, with a<br />
completely different underlying mechanism of the proof. A large part of<br />
the talk is a report on a joint work with A. Avila and C. Sadel.<br />
<br />
===February 28: Michael Shelley (Courant)===<br />
''Mathematical models of soft active materials''<br />
<br />
Soft materials that have an "active" microstructure are important examples of so-called active matter. Examples include suspensions of motile microorganisms or particles, "active gels" made up of actin and myosin, and suspensions of microtubules cross-linked by motile motor-proteins. These nonequilibrium materials can have unique mechanical properties and organization, show spontaneous activity-driven flows, and are part of self-assembled structures such as the cellular cortex and mitotic spindle. I will discuss the nature and modeling of these materials, focusing on fluids driven by "active stresses" generated by swimming, motor-protein activity, and surface tension gradients. Amusingly, the latter reveals a new class of fluid flow singularities and an unexpected connection to the Keller-Segel equation.<br />
<br />
<br />
===March 7: Steve Zelditch (Northwestern)===<br />
''Shapes and sizes of eigenfunction''<br />
<br />
Eigenfunctions of the Laplacian (or Schroedinger operators) arise as stationary states in quantum mechanics. They are not apriori geometric<br />
objects but we would like to relate the nodal (zero) sets and Lp norms of eigenfunctions to the geometry of geometrics. I will explain what is<br />
known (and unknown) and norms and nodal sets of eigenfunctions. No prior knowledge of quantum mechanics is assumed.<br />
<br />
===March 14: Richard Schwartz (Brown)===<br />
''The projective heat map on pentagons''<br />
<br />
In this talk I'll describe several maps defined on<br />
the space of polygons. These maps are described in terms<br />
of simple straight-line constructions, and are therefore<br />
natural with respect to projective geometry. One of them,<br />
the pentagram map, is now known to be a discrete completely<br />
integrable system. I'll concentrate on a variant of the<br />
pentagram map, which behaves somewhat like heat flow on convex<br />
polygons but which does crazy things to non-convex polygons.<br />
I'll sketch a computer-assisted analysis of what happens<br />
for pentagons. I'll illustrate the talk with computer demos.<br />
<br />
===April 4: Matthew Kahle (OSU) ===<br />
"Recent progress in random topology"<br />
<br />
The study of random topological spaces: manifolds, simplicial<br />
complexes, knots, groups, has received a lot of attention in recent<br />
years. This talk will mostly focus on random simplicial complexes, and<br />
especially on a certain kind of topological phase transition, where<br />
the probability that that a certain homology group is trivial passes<br />
from 0 to 1 within a narrow window. The archetypal result in this area<br />
is the Erdős–Rényi theorem, which characterizes the threshold edge<br />
probability where the random graph becomes connected.<br />
<br />
One recent breakthrough has been in the application of "Garland's<br />
method", which allows one to prove homology-vanishing theorems by<br />
showing that certain Laplacians have large spectral gaps. This reduces<br />
problems in random topology to understanding eigenvalues of certain<br />
random matrices, and the method has been surprisingly successful.<br />
<br />
This talk is intended for a broad mathematical audience, and I will<br />
not assume any particular prerequisites in probability or topology.<br />
Part of this is joint work with Christopher Hoffman and Elliot<br />
Paquette.<br />
===April 11: Risi Kondor (Chicago) ===<br />
''Multiresolution Matrix Factorization''<br />
<br />
Matrices that appear in modern data analysis and machine learning problems often exhibit complex<br />
hierarchical structure, which goes beyond what can be uncovered by traditional linear algebra tools,<br />
such as eigendecomposition. In this talk I describe a new notion of matrix factorization inspired by <br />
multiresolution analysis that can capture structure in matrices at multiple different scales. <br />
The resulting Multiresolution Matrix Factorizations (MMFs) not only provide a<br />
wavelet basis for sparse approximation, but can also be used for matrix compression and as a prior <br />
for matrix completion. The work presented in this talk is joint with Nedelina Teneva and Vikas Garg.<br />
<br />
<br />
===April 18: Christopher Sogge (Johns Hopkins) ===<br />
''Focal points and sup-norms of eigenfunctions''<br />
<br />
If (M,g) is a compact real analytic Riemannian manifold, we give a necessary and<br />
sufficient condition for there to be a sequence of quasimodes saturating sup-norm <br />
estimates. The condition is that there exists a self-focal point x_0\in M for the<br />
geodesic flow at which the associated Perron-Frobenius operator<br />
U: L^2(S_{x_0}^*M) \to L^2(S_{x_0}^*M) has a nontrivial invariant function. The proof is<br />
based on von Neumann's ergodic theorem and stationary phase. This is joint work with<br />
Steve Zelditch.<br />
<br />
===April 25: Charles Doran (University of Alberta) ===<br />
''The Mathematics of Supersymmetry: Graphs, Codes, and Super-Curves''<br />
<br />
In physics, supersymmetry is a pairing between bosons and fermions appearing in theories of subatomic particles. One may study supersymmetry mathematically by using Adinkras, which are graphs with vertices representing the particles in a supersymmetric theory and edges corresponding to the supersymmetry pairings. In combinatorial terms, Adinkras are N-regular, edge N-colored bipartite graphs with signs assigned to the edges and heights assigned to the vertices, subject to certain conditions. We will see how to capture some of the structure of an Adinkra using binary linear error-correcting codes, and all of it using a very special case of a geometric construction due to Grothendieck. The talk is designed to be accessible to an undergraduate audience.<br />
<br />
===April 29 and 30: David Eisenbud (University of California, Berkeley and MSRI) ===<br />
''Matrix factorizations old and new''<br />
<br />
You cannot factor f=xy-z^2 nontrivially as a product of power series, but you can factor f times a 2x2 identity matrix as the product of the matrices<br />
<br><br />
<div align=center><br />
<table class="matrix"><br />
<tr><br />
<td>x</td><br />
<td>z</td><br />
<td> </td><br />
<td>and </td><br />
<td> </td><br />
<td>y</td><br />
<td>-z</td><br />
</tr><br />
<tr><br />
<td>z</td><br />
<td>y</td><br />
<td> </td><br />
<td></td><br />
<td> </td><br />
<td>-z</td><br />
<td>x.</td><br />
</tr><br />
</table><br />
</div><br />
It turns out that any power series of order at least has a "matrix factorization" in this sense, and that this is the key to understanding the simplest infinite free resolutions, as I proved in the 1980s. Such matrix factorizations have since proven useful in many contexts. Recently Irena Peeva and I have discovered what I believe is the natural extension of this<br />
idea to systems of polynomials called complete intersections. I'll explain some of the old theory and sketch the new development.<br />
<br />
The first talk will be aimed at a general audience and the second talk will cover some of the recent advances.<br />
<br />
===May 2: Lek-Heng Lim (Chicago)===<br />
'' Hypermatrices.''<br />
<br />
<br />
This talk is intended for those who, like the speaker, have at some point<br />
wondered whether there is a theory of three- or higher-dimensional<br />
matrices that parallels matrix theory. We will explain why a d-dimensional<br />
hypermatrix is related to but not quite the same as an order-d tensor.<br />
<br />
We discuss how notions like rank, norm, determinant, eigen and singular<br />
values may be generalized to hypermatrices. We will see that, far from<br />
being artificial constructs, these notions have appeared naturally in a<br />
wide range of applications and can be enormously useful. We will examine<br />
several examples, highlighting three from the speaker's recent work: (i)<br />
rank of 3-hypermatrices and blind source separation in signal processing,<br />
(ii) positive definiteness of 6-hypermatrices and self-concordance in<br />
convex optimization, (iii) nuclear norm of 3-hypermatrices and bipartite<br />
separability in quantum computing.<br />
<br />
(i) is joint work with Pierre Comon and (iii) is joint work with Shmuel<br />
Friedland<br />
<br />
===May 9: Rachel Ward (UT Austin)===<br />
'' Sampling theorems for efficient dimensionality reduction and sparse recovery.''<br />
<br />
Embedding high-dimensional data sets into subspaces of much lower dimension is important for reducing storage cost and speeding up computation in several applications, including numerical linear algebra, manifold learning, and theoretical computer science. Moreover, central to the relatively new field of compressive sensing, if the original data set is known to be sparsely representable in a given basis, then it is possible to efficiently 'invert’ a random dimension-reducing map to recover the high-dimensional data via e.g. l1-minimization. We will survey recent results in these areas, and then show how near-equivalences between fundamental concepts such as restricted isometries and Johnson-Lindenstrauss embeddings can be used to leverage results in one domain and apply to another. Finally, we discuss how these and other recent results for structured random matrices can be used to derive sampling strategies in various settings, from low-rank matrix completion to function interpolation.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=6933Colloquia/Fall182014-04-26T16:18:31Z<p>Shamgar: /* Spring 2014 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
[[Colloquia/Fall 2014 | Tentative schedule for Fall 2014]]<br />
<br />
== Spring 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Mon, Jan 6, 4PM'''<br />
|[http://www-bcf.usc.edu/~lauda/Aaron_Laudas_Page/Home.html Aaron Lauda] (USC) <br />
|[[Colloquia#January 6: Aaron Lauda (USC) | An introduction to diagrammatic categorification]]<br />
|Caldararu<br />
|-<br />
|'''Wed, Jan 8, 4PM'''<br />
|[http://www2.math.umd.edu/~kmelnick/ Karin Melnick] (Maryland) <br />
|[[Colloquia#January 8: Karin Melnick (Maryland) | Normal forms for local flows on parabolic geometries]]<br />
|Kent<br />
|-<br />
|Jan 10, 4PM<br />
|[http://users.math.yale.edu/~yd82/ Yen Do] (Yale) <br />
|Convergence of Fourier series and multilinear analysis<br />
|Denissov<br />
|-<br />
|'''Mon, Jan 13, 4pm'''<br />
|[http://math.stanford.edu/~wangyi/ Yi Wang] (Stanford)<br />
|Isoperimetric Inequality and Q-curvature<br />
|Viaclovsky<br />
|-<br />
|'''Wen, Jan 15, 4pm'''<br />
|[http://www.maths.ox.ac.uk/people/profiles/wei.xiang Wei Xiang] (University of Oxford)<br />
|[[Colloquia#January 15: Wei Xiang (University of Oxford) |Conservation Laws and Shock Waves]]<br />
|Bolotin<br />
|-<br />
|'''Fri, Jan 17, 2:25PM, VV901'''<br />
|[http://www.math.dartmouth.edu/~gillmana/ Adrianna Gillman] (Dartmouth) <br />
|Fast direct solvers for linear partial differential equations<br />
|Thiffeault<br />
|-<br />
|'''Thu, Jan 23, 2:25, VV901'''<br />
|[http://www.stat.berkeley.edu/~mshkolni/ Mykhaylo Shkolnikov] (Berkeley)<br />
|[[Colloquia#Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) | Intertwinings, wave equations and growth models]]<br />
|Seppalainen<br />
|-<br />
|Jan 24<br />
|[http://www.yanivplan.com/ Yaniv Plan] (Michigan)<br />
|[http://www.math.wisc.edu/wiki/index.php/Applied/ACMS/absS14#Yaniv_Plan_.28Michigan.29 Low-dimensionality in mathematical signal processing]<br />
|Thiffeault<br />
|-<br />
|Jan 31<br />
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)<br />
|Underwater Networks: A Convergence of Communications, Control and Sensing<br />
|Gurevich<br />
|-<br />
|Feb 7<br />
|David Treumann (Boston College)<br />
|Functoriality, Smith theory, and the Brauer homomorphism<br />
|Street<br />
|-<br />
|Feb 14<br />
|[http://www.tc.columbia.edu/academics/index.htm?facid=apk16 Alexander Karp] (Columbia Teacher's College)<br />
|History of Mathematics Education as a Research Field and as Magistra Vitae<br />
|Kiselev<br />
|-<br />
|Feb 21<br />
|[http://www.math.uci.edu/~szhitomi/ Svetlana Jitomirskaya] (UC-Irvine)<br />
|Analytic quasiperiodic cocycles<br />
|Kiselev<br />
|-<br />
|Feb 28<br />
|[http://math.nyu.edu/faculty/shelley/ Michael Shelley] (Courant)<br />
|[[Colloquia#February 28: Michael Shelley (Courant) | Mathematical models of soft active materials]]<br />
|Spagnolie<br />
|-<br />
|March 7<br />
|[http://www.math.northwestern.edu/people/facultyProfiles/steve.zelditch.html Steve Zelditch] (Northwestern)<br />
|[[Colloquia#March 7: Steve Zelditch (Northwestern) | Shapes and sizes of eigenfunctions]]<br />
|Seeger<br />
|-<br />
|March 14<br />
|[http://www.math.brown.edu/~res/ Richard Schwartz] (Brown)<br />
|[[Colloquia#March 14: Richard Schwartz (Brown) |The projective heat map on pentagons]]<br />
|Mari-Beffa<br />
|-<br />
|<strike>March 21</strike><br />
|'''Spring Break'''<br />
|No Colloquium<br />
|<br />
|-<br />
|'''March 26, 7pm, WID'''<br />
|[https://www.dpmms.cam.ac.uk/people/t.tokieda/ Tadashi Tokieda] (Cambridge)<br />
|[http://c4.discovery.wisc.edu/events/lectures/toymodels/ Toy models]<br />
|Thiffeault (C4 von Neumann Public Lecture)<br />
|-<br />
|March 28<br />
|Cancelled<br />
|<br />
|<br />
|-<br />
|April 4<br />
|[http://matthewkahle.org/ Matthew Kahle] (OSU)<br />
|Recent progress in random topology<br />
|Dymarz<br />
|- <br />
|April 11<br />
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)<br />
|Multiresolution Matrix Factorization<br />
|Gurevich<br />
|-<br />
|April 18 (Wasow Lecture)<br />
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)<br />
|[[Colloquia#April 18: Christopher Sogge (Johns Hopkins) |Focal points and sup-norms of eigenfunctions]]<br />
|Seeger<br />
|-<br />
|April 25<br />
|[http://www.charlesdoran.net Charles Doran](University of Alberta)<br />
|[[Colloquia#April 25: Charles Doran (University of Alberta) |The Mathematics of Supersymmetry: Graphs, Codes, and Super-Curves]]<br />
|Song<br />
|-<br />
|'''Tuesday, April 29''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Matrix factorizations old and new, I<br />
|Erman<br />
|-<br />
|'''Wednesday, April 30''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Matrix factorizations old and new, II<br />
|Erman<br />
|-<br />
|May 2<br />
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)<br />
|Hypermatrices<br />
|Boston<br />
|-<br />
|May 9<br />
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)<br />
|Sampling theorems for efficient dimensionality reduction and sparse recovery<br />
|WIMAW<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===January 6: Aaron Lauda (USC)===<br />
<br />
''An introduction to diagrammatic categorification''<br />
<br />
Categorification seeks to reveal a hidden layer in mathematical<br />
structures. Often the resulting structures can be combinatorially<br />
complex objects making them difficult to study. One method of<br />
overcoming this difficulty, that has proven very successful, is to<br />
encode the categorification into a diagrammatic calculus that makes<br />
computations simple and intuitive.<br />
<br />
In this talk I will review some of the original considerations that<br />
led to the categorification philosophy. We will examine how the<br />
diagrammatic perspective has helped to produce new categorifications<br />
having profound applications to algebra, representation theory, and<br />
low-dimensional topology.<br />
<br />
===January 8: Karin Melnick (Maryland)===<br />
<br />
''Normal forms for local flows on parabolic geometries''<br />
<br />
The exponential map in Riemannian geometry conjugates the differential of an isometry at a point with the action of the isometry near the point. It thus provides a linear normal form for all isometries fixing a point. Conformal transformations are not linearizable in general. I will discuss a suite of normal forms theorems in conformal geometry and, more generally, for parabolic geometries, a rich family of geometric structures of which conformal, projective, and CR structures are examples.<br />
<br />
===January 10, 4PM: Yen Do (Yale)===<br />
<br />
''Convergence of Fourier series and multilinear analysis''<br />
<br />
Almost everywhere convergence of the Fourier series of square <br />
integrable functions was first proved by Lennart Carleson in 1966, and <br />
the proof has lead to deep developments in various multilinear settings. <br />
In this talk I would like to introduce a brief history of the subject <br />
and sketch some recent developments, some of these involve my joint <br />
works with collaborators.<br />
<br />
===Mon, January 13: Yi Wang (Stanford)===<br />
<br />
''Isoperimetric Inequality and Q-curvature''<br />
<br />
A well-known question in differential geometry is to prove the<br />
isoperimetric inequality under intrinsic curvature conditions. In<br />
dimension 2, the isoperimetric inequality is controlled by the integral of<br />
the positive part of the Gaussian curvature. In my recent work, I prove<br />
that on simply connected conformally flat manifolds of higher dimensions,<br />
the role of the Gaussian curvature can be replaced by the Branson's<br />
Q-curvature. The isoperimetric inequality is valid if the integral of the<br />
Q-curvature is below a sharp threshold. Moreover, the isoperimetric<br />
constant depends only on the integrals of the Q-curvature. The proof<br />
relies on the theory of $A_p$ weights in harmonic analysis.<br />
<br />
===January 15: Wei Xiang (University of Oxford)===<br />
<br />
''Conservation Laws and Shock Waves''<br />
<br />
The study of continuum physics gave birth to the theory of quasilinear<br />
systems in divergence form, commonly called conservation laws. In this<br />
talk, conservation laws, the Euler equations, and the definition of the<br />
corresponding weak solutions will be introduced first. Then a short history<br />
of the studying of conservation laws and shock waves will be given. Finally<br />
I would like to present two of our current research projects. One is on the<br />
mathematical analysis of shock diffraction by convex cornered wedges, and<br />
the other one is on the validation of weakly nonlinear geometric optics for<br />
entropy solutions of nonlinear hyperbolic systems of conservation laws.<br />
<br />
Fri, Jan 17, 2:25PM, VV901 Adrianna Gillman (Dartmouth) Fast direct solvers for linear partial differential equations<br />
<br />
===Fri, Jan 17: Adrianna Gillman (Dartmouth) ===<br />
''Fast direct solvers for linear partial differential equations''<br />
<br />
The cost of solving a large linear system often determines what can and cannot be modeled computationally in many areas of science and engineering. Unlike Gaussian elimination which scales cubically with the respect to the number of unknowns, fast direct solvers construct an inverse of a linear in system with a cost that scales linearly or nearly linearly. The fast direct solvers presented in this talk are designed for the linear systems arising from the discretization of linear partial differential equations. These methods are more robust, versatile and stable than iterative schemes. Since an inverse is computed, additional right-hand sides can be processed rapidly. The talk will give the audience a brief introduction to the core ideas, an overview of recent advancements, and it will conclude with a sampling of challenging application examples including the scattering of waves.<br />
<br />
===Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) ===<br />
''Intertwinings, wave equations and growth models''<br />
<br />
We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to hyperbolic partial differential equations, symmetric polynomials and the corresponding random growth models. The talk will be devoted to these recent developments which also shed new light on some beautiful old examples of intertwinings. Based on joint works with Vadim Gorin and Soumik Pal. <br />
<br />
===Jan 24: Yaniv Plan (Michigan) ===<br />
''Low-dimensionality in mathematical signal processing''<br />
<br />
Natural images tend to be compressible, i.e., the amount of information needed to encode an image is small. This conciseness of information -- in other words, low dimensionality of the signal -- is found throughout a plethora of applications ranging from MRI to quantum state tomography. It is natural to ask: can the number of measurements needed to determine a signal be comparable with the information content? We explore this question under modern models of low-dimensionality and measurement acquisition.<br />
<br />
===Thur, Jan 30: Urbashi Mitra (USC) ===<br />
''Underwater Networks: A Convergence of Communications, Control and Sensing''<br />
<br />
The oceans cover 71% of the earth’s surface and represent one of the least explored frontiers, yet the oceans are integral to climate regulation, nutrient production, oil retrieval and transportation. Future scientific and technological efforts to achieve better understanding of oceans and water-related applications will rely heavily on our ability to communicate reliably between instruments, vehicles (manned and unmanned), human operators, platforms and sensors of all types. Underwater acoustic communication techniques have not reached the same maturity as those for terrestrial radio communications and present some unique opportunities for new developments in information and communication theories. Key features of underwater acoustic communication channels are examined: slow speed of propagation, significant delay spreads, sparse multi-path, time-variation and range-dependent available bandwidth. Another unique feature of underwater networks is that the cost of communication, sensing and control are often comparable resulting in new tradeoffs between these activities. We examine some new results (with implications wider than underwater systems) in channel identifiability, communicating over channels with state and cooperative game theory motivated by the underwater network application.<br />
<br />
===Feb 7: David Treumann (Boston College) ===<br />
''Functoriality, Smith theory, and the Brauer homomorphism''<br />
<br />
Smith theory is a technique for relating the mod p homologies of X and of the fixed points of X by an automorphism of order p. I will discuss how, in the setting of locally symmetric spaces, it provides an easy method (no trace formula) for lifting mod p automorphic forms from G^{sigma} to G, where G is an arithmetic group and sigma is an automorphism of G of order p. This lift is compatible with Hecke actions via an analog of the Brauer homomorphism from modular representation theory, and is often compatible with a homomorphism of L-groups on the Galois side. The talk is based on joint work with Akshay Venkatesh. I hope understanding the talk will require less number theory background than understanding the abstract.<br />
<br />
===Feb 14: Alexander Karp (Columbia Teacher's College) ===<br />
''History of Mathematics Education as a Research Field and as Magistra Vitae''<br />
<br />
The presentation will be based on the experience of putting together and editing the Handbook<br />
on the History of Mathematics Education, which will be published by Springer in the near future. <br />
This volume, which was prepared by a large group of researchers from different countries, <br />
contains the first systematic account of the history of the development of mathematics education <br />
in the whole world (and not just in some particular country or region). The editing of such a <br />
book gave rise to thoughts about the methodology of research in this field, and also about what <br />
constitutes an object of such research. These are the thoughts that the presenter intends to share <br />
with his audience. From them, it is natural to pass to an analysis of the current situation and how <br />
it might develop.<br />
<br />
===Feb 21: Svetlana Jitomirskaya (UC-Irvine)===<br />
''Analytic quasiperiodic cocycles''<br />
<br />
Analytic quasiperiodic matrix cocycles is a simple dynamical<br />
system, where analytic and dynamical properties are related in an<br />
unexpected and remarkable way. We will focus on this relation, leading to<br />
a new approach to the proof of joint continuity of Lyapunov exponents in<br />
frequency and cocycle, at irrational frequency, first proved for SL(2,C)<br />
cocycles in Bourgain-Jitom., 2002. The approach is powerful enough to<br />
handle singular and multidimensional cocycles, thus establishing the above<br />
continuity in full generality. This has important consequences including<br />
a dense open version of Bochi-Viana theorem in this setting, with a<br />
completely different underlying mechanism of the proof. A large part of<br />
the talk is a report on a joint work with A. Avila and C. Sadel.<br />
<br />
===February 28: Michael Shelley (Courant)===<br />
''Mathematical models of soft active materials''<br />
<br />
Soft materials that have an "active" microstructure are important examples of so-called active matter. Examples include suspensions of motile microorganisms or particles, "active gels" made up of actin and myosin, and suspensions of microtubules cross-linked by motile motor-proteins. These nonequilibrium materials can have unique mechanical properties and organization, show spontaneous activity-driven flows, and are part of self-assembled structures such as the cellular cortex and mitotic spindle. I will discuss the nature and modeling of these materials, focusing on fluids driven by "active stresses" generated by swimming, motor-protein activity, and surface tension gradients. Amusingly, the latter reveals a new class of fluid flow singularities and an unexpected connection to the Keller-Segel equation.<br />
<br />
<br />
===March 7: Steve Zelditch (Northwestern)===<br />
''Shapes and sizes of eigenfunction''<br />
<br />
Eigenfunctions of the Laplacian (or Schroedinger operators) arise as stationary states in quantum mechanics. They are not apriori geometric<br />
objects but we would like to relate the nodal (zero) sets and Lp norms of eigenfunctions to the geometry of geometrics. I will explain what is<br />
known (and unknown) and norms and nodal sets of eigenfunctions. No prior knowledge of quantum mechanics is assumed.<br />
<br />
===March 14: Richard Schwartz (Brown)===<br />
''The projective heat map on pentagons''<br />
<br />
In this talk I'll describe several maps defined on<br />
the space of polygons. These maps are described in terms<br />
of simple straight-line constructions, and are therefore<br />
natural with respect to projective geometry. One of them,<br />
the pentagram map, is now known to be a discrete completely<br />
integrable system. I'll concentrate on a variant of the<br />
pentagram map, which behaves somewhat like heat flow on convex<br />
polygons but which does crazy things to non-convex polygons.<br />
I'll sketch a computer-assisted analysis of what happens<br />
for pentagons. I'll illustrate the talk with computer demos.<br />
<br />
===April 4: Matthew Kahle (OSU) ===<br />
"Recent progress in random topology"<br />
<br />
The study of random topological spaces: manifolds, simplicial<br />
complexes, knots, groups, has received a lot of attention in recent<br />
years. This talk will mostly focus on random simplicial complexes, and<br />
especially on a certain kind of topological phase transition, where<br />
the probability that that a certain homology group is trivial passes<br />
from 0 to 1 within a narrow window. The archetypal result in this area<br />
is the Erdős–Rényi theorem, which characterizes the threshold edge<br />
probability where the random graph becomes connected.<br />
<br />
One recent breakthrough has been in the application of "Garland's<br />
method", which allows one to prove homology-vanishing theorems by<br />
showing that certain Laplacians have large spectral gaps. This reduces<br />
problems in random topology to understanding eigenvalues of certain<br />
random matrices, and the method has been surprisingly successful.<br />
<br />
This talk is intended for a broad mathematical audience, and I will<br />
not assume any particular prerequisites in probability or topology.<br />
Part of this is joint work with Christopher Hoffman and Elliot<br />
Paquette.<br />
===April 11: Risi Kondor (Chicago) ===<br />
''Multiresolution Matrix Factorization''<br />
<br />
Matrices that appear in modern data analysis and machine learning problems often exhibit complex<br />
hierarchical structure, which goes beyond what can be uncovered by traditional linear algebra tools,<br />
such as eigendecomposition. In this talk I describe a new notion of matrix factorization inspired by <br />
multiresolution analysis that can capture structure in matrices at multiple different scales. <br />
The resulting Multiresolution Matrix Factorizations (MMFs) not only provide a<br />
wavelet basis for sparse approximation, but can also be used for matrix compression and as a prior <br />
for matrix completion. The work presented in this talk is joint with Nedelina Teneva and Vikas Garg.<br />
<br />
<br />
===April 18: Christopher Sogge (Johns Hopkins) ===<br />
''Focal points and sup-norms of eigenfunctions''<br />
<br />
If (M,g) is a compact real analytic Riemannian manifold, we give a necessary and<br />
sufficient condition for there to be a sequence of quasimodes saturating sup-norm <br />
estimates. The condition is that there exists a self-focal point x_0\in M for the<br />
geodesic flow at which the associated Perron-Frobenius operator<br />
U: L^2(S_{x_0}^*M) \to L^2(S_{x_0}^*M) has a nontrivial invariant function. The proof is<br />
based on von Neumann's ergodic theorem and stationary phase. This is joint work with<br />
Steve Zelditch.<br />
<br />
===April 25: Charles Doran (University of Alberta) ===<br />
''The Mathematics of Supersymmetry: Graphs, Codes, and Super-Curves''<br />
<br />
In physics, supersymmetry is a pairing between bosons and fermions appearing in theories of subatomic particles. One may study supersymmetry mathematically by using Adinkras, which are graphs with vertices representing the particles in a supersymmetric theory and edges corresponding to the supersymmetry pairings. In combinatorial terms, Adinkras are N-regular, edge N-colored bipartite graphs with signs assigned to the edges and heights assigned to the vertices, subject to certain conditions. We will see how to capture some of the structure of an Adinkra using binary linear error-correcting codes, and all of it using a very special case of a geometric construction due to Grothendieck. The talk is designed to be accessible to an undergraduate audience.<br />
<br />
===April 29 and 30: David Eisenbud (University of California, Berkeley and MSRI) ===<br />
''Matrix factorizations old and new''<br />
<br />
You cannot factor f=xy-z^2 nontrivially as a product of power series, but you can factor f times a 2x2 identity matrix as the product of the matrices<br />
<br><br />
<div align=center><br />
<table class="matrix"><br />
<tr><br />
<td>x</td><br />
<td>z</td><br />
<td> </td><br />
<td>and </td><br />
<td> </td><br />
<td>y</td><br />
<td>-z</td><br />
</tr><br />
<tr><br />
<td>z</td><br />
<td>y</td><br />
<td> </td><br />
<td></td><br />
<td> </td><br />
<td>-z</td><br />
<td>x.</td><br />
</tr><br />
</table><br />
</div><br />
It turns out that any power series of order at least has a "matrix factorization" in this sense, and that this is the key to understanding the simplest infinite free resolutions, as I proved in the 1980s. Such matrix factorizations have since proven useful in many contexts. Recently Irena Peeva and I have discovered what I believe is the natural extension of this<br />
idea to systems of polynomials called complete intersections. I'll explain some of the old theory and sketch the new development.<br />
<br />
The first talk will be aimed at a general audience and the second talk will cover some of the recent advances.<br />
<br />
===May 9: Rachel Ward (UT Austin)===<br />
'' Sampling theorems for efficient dimensionality reduction and sparse recovery.''<br />
<br />
Embedding high-dimensional data sets into subspaces of much lower dimension is important for reducing storage cost and speeding up computation in several applications, including numerical linear algebra, manifold learning, and theoretical computer science. Moreover, central to the relatively new field of compressive sensing, if the original data set is known to be sparsely representable in a given basis, then it is possible to efficiently 'invert’ a random dimension-reducing map to recover the high-dimensional data via e.g. l1-minimization. We will survey recent results in these areas, and then show how near-equivalences between fundamental concepts such as restricted isometries and Johnson-Lindenstrauss embeddings can be used to leverage results in one domain and apply to another. Finally, we discuss how these and other recent results for structured random matrices can be used to derive sampling strategies in various settings, from low-rank matrix completion to function interpolation.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall_2014&diff=6919Colloquia/Fall 20142014-04-21T17:05:38Z<p>Shamgar: /* Fall 2014 */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Fall 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 19<br />
|[http://www.mast.queensu.ca/~ggsmith/ Greg Smith] (Queen's University)<br />
|TBA<br />
|Erman<br />
|-<br />
|September 26<br />
|[http://www.math.uci.edu/~jxin/ Jack Xin] (UC Irvine)<br />
|TBA<br />
|Jin<br />
|-<br />
|October 3<br />
|[http://math.arizona.edu/~tiep/ Pham Huu Tiep] (University of Arizona)<br />
|TBA<br />
|Gurevich<br />
|-<br />
|October 17<br />
|[http://www.math.uchicago.edu/~ngo/ Bao Chau Ngo] (University of Chicago)<br />
|TBA<br />
|Gurevich<br />
|}<br />
<br />
== Abstracts ==</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=6803Colloquia/Fall182014-03-26T20:03:28Z<p>Shamgar: /* Abstracts */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
[[Colloquia/Fall 2014 | Tentative schedule for Fall 2014]]<br />
<br />
== Spring 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Mon, Jan 6, 4PM'''<br />
|[http://www-bcf.usc.edu/~lauda/Aaron_Laudas_Page/Home.html Aaron Lauda] (USC) <br />
|[[Colloquia#January 6: Aaron Lauda (USC) | An introduction to diagrammatic categorification]]<br />
|Caldararu<br />
|-<br />
|'''Wed, Jan 8, 4PM'''<br />
|[http://www2.math.umd.edu/~kmelnick/ Karin Melnick] (Maryland) <br />
|[[Colloquia#January 8: Karin Melnick (Maryland) | Normal forms for local flows on parabolic geometries]]<br />
|Kent<br />
|-<br />
|Jan 10, 4PM<br />
|[http://users.math.yale.edu/~yd82/ Yen Do] (Yale) <br />
|Convergence of Fourier series and multilinear analysis<br />
|Denissov<br />
|-<br />
|'''Mon, Jan 13, 4pm'''<br />
|[http://math.stanford.edu/~wangyi/ Yi Wang] (Stanford)<br />
|Isoperimetric Inequality and Q-curvature<br />
|Viaclovsky<br />
|-<br />
|'''Wen, Jan 15, 4pm'''<br />
|[http://www.maths.ox.ac.uk/people/profiles/wei.xiang Wei Xiang] (University of Oxford)<br />
|[[Colloquia#January 15: Wei Xiang (University of Oxford) |Conservation Laws and Shock Waves]]<br />
|Bolotin<br />
|-<br />
|'''Fri, Jan 17, 2:25PM, VV901'''<br />
|[http://www.math.dartmouth.edu/~gillmana/ Adrianna Gillman] (Dartmouth) <br />
|Fast direct solvers for linear partial differential equations<br />
|Thiffeault<br />
|-<br />
|'''Thu, Jan 23, 2:25, VV901'''<br />
|[http://www.stat.berkeley.edu/~mshkolni/ Mykhaylo Shkolnikov] (Berkeley)<br />
|[[Colloquia#Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) | Intertwinings, wave equations and growth models]]<br />
|Seppalainen<br />
|-<br />
|Jan 24<br />
|[http://www.yanivplan.com/ Yaniv Plan] (Michigan)<br />
|[http://www.math.wisc.edu/wiki/index.php/Applied/ACMS/absS14#Yaniv_Plan_.28Michigan.29 Low-dimensionality in mathematical signal processing]<br />
|Thiffeault<br />
|-<br />
|Jan 31<br />
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)<br />
|Underwater Networks: A Convergence of Communications, Control and Sensing<br />
|Gurevich<br />
|-<br />
|Feb 7<br />
|David Treumann (Boston College)<br />
|Functoriality, Smith theory, and the Brauer homomorphism<br />
|Street<br />
|-<br />
|Feb 14<br />
|[http://www.tc.columbia.edu/academics/index.htm?facid=apk16 Alexander Karp] (Columbia Teacher's College)<br />
|History of Mathematics Education as a Research Field and as Magistra Vitae<br />
|Kiselev<br />
|-<br />
|Feb 21<br />
|[http://www.math.uci.edu/~szhitomi/ Svetlana Jitomirskaya] (UC-Irvine)<br />
|Analytic quasiperiodic cocycles<br />
|Kiselev<br />
|-<br />
|Feb 28<br />
|[http://math.nyu.edu/faculty/shelley/ Michael Shelley] (Courant)<br />
|[[Colloquia#February 28: Michael Shelley (Courant) | Mathematical models of soft active materials]]<br />
|Spagnolie<br />
|-<br />
|March 7<br />
|[http://www.math.northwestern.edu/people/facultyProfiles/steve.zelditch.html Steve Zelditch] (Northwestern)<br />
|[[Colloquia#March 7: Steve Zelditch (Northwestern) | Shapes and sizes of eigenfunctions]]<br />
|Seeger<br />
|-<br />
|March 14<br />
|[http://www.math.brown.edu/~res/ Richard Schwartz] (Brown)<br />
|[[Colloquia#March 14: Richard Schwartz (Brown) |The projective heat map on pentagons]]<br />
|Mari-Beffa<br />
|-<br />
|<strike>March 21</strike><br />
|'''Spring Break'''<br />
|No Colloquium<br />
|<br />
|-<br />
|'''March 26, 7pm, WID'''<br />
|[https://www.dpmms.cam.ac.uk/people/t.tokieda/ Tadashi Tokieda] (Cambridge)<br />
|[http://c4.discovery.wisc.edu/events/lectures/toymodels/ Toy models]<br />
|Thiffeault (C4 von Neumann Public Lecture)<br />
|-<br />
|March 28<br />
|[http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)<br />
|The two weight inequality for Hilbert and Cauchy operators on the disk<br />
|Street<br />
|-<br />
|April 4<br />
|[http://matthewkahle.org/ Matthew Kahle] (OSU)<br />
|<br />
|Dymarz<br />
|- <br />
|April 11<br />
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)<br />
|Multiresolution Matrix Factorization<br />
|Gurevich<br />
|-<br />
|April 18 (Wasow Lecture)<br />
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)<br />
|Focal points and sup-norms of eigenfunctions<br />
|Seeger<br />
|-<br />
|April 25<br />
|[http://www.charlesdoran.net Charles Doran](University of Alberta)<br />
|<br />
|Song<br />
|-<br />
|'''Monday, April 28''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|A mystery concerning algebraic plane curves<br />
|Maxim<br />
|-<br />
|'''Tuesday, April 29''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Matrix factorizations old and new<br />
|Maxim<br />
|-<br />
|'''Wednesday, April 30''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Easy solution of polynomial equations over finite fields<br />
|Maxim<br />
|-<br />
|May 2<br />
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)<br />
|<br />
|Boston<br />
|-<br />
|May 9<br />
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)<br />
|<br />
|WIMAW<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===January 6: Aaron Lauda (USC)===<br />
<br />
''An introduction to diagrammatic categorification''<br />
<br />
Categorification seeks to reveal a hidden layer in mathematical<br />
structures. Often the resulting structures can be combinatorially<br />
complex objects making them difficult to study. One method of<br />
overcoming this difficulty, that has proven very successful, is to<br />
encode the categorification into a diagrammatic calculus that makes<br />
computations simple and intuitive.<br />
<br />
In this talk I will review some of the original considerations that<br />
led to the categorification philosophy. We will examine how the<br />
diagrammatic perspective has helped to produce new categorifications<br />
having profound applications to algebra, representation theory, and<br />
low-dimensional topology.<br />
<br />
===January 8: Karin Melnick (Maryland)===<br />
<br />
''Normal forms for local flows on parabolic geometries''<br />
<br />
The exponential map in Riemannian geometry conjugates the differential of an isometry at a point with the action of the isometry near the point. It thus provides a linear normal form for all isometries fixing a point. Conformal transformations are not linearizable in general. I will discuss a suite of normal forms theorems in conformal geometry and, more generally, for parabolic geometries, a rich family of geometric structures of which conformal, projective, and CR structures are examples.<br />
<br />
===January 10, 4PM: Yen Do (Yale)===<br />
<br />
''Convergence of Fourier series and multilinear analysis''<br />
<br />
Almost everywhere convergence of the Fourier series of square <br />
integrable functions was first proved by Lennart Carleson in 1966, and <br />
the proof has lead to deep developments in various multilinear settings. <br />
In this talk I would like to introduce a brief history of the subject <br />
and sketch some recent developments, some of these involve my joint <br />
works with collaborators.<br />
<br />
===Mon, January 13: Yi Wang (Stanford)===<br />
<br />
''Isoperimetric Inequality and Q-curvature''<br />
<br />
A well-known question in differential geometry is to prove the<br />
isoperimetric inequality under intrinsic curvature conditions. In<br />
dimension 2, the isoperimetric inequality is controlled by the integral of<br />
the positive part of the Gaussian curvature. In my recent work, I prove<br />
that on simply connected conformally flat manifolds of higher dimensions,<br />
the role of the Gaussian curvature can be replaced by the Branson's<br />
Q-curvature. The isoperimetric inequality is valid if the integral of the<br />
Q-curvature is below a sharp threshold. Moreover, the isoperimetric<br />
constant depends only on the integrals of the Q-curvature. The proof<br />
relies on the theory of $A_p$ weights in harmonic analysis.<br />
<br />
===January 15: Wei Xiang (University of Oxford)===<br />
<br />
''Conservation Laws and Shock Waves''<br />
<br />
The study of continuum physics gave birth to the theory of quasilinear<br />
systems in divergence form, commonly called conservation laws. In this<br />
talk, conservation laws, the Euler equations, and the definition of the<br />
corresponding weak solutions will be introduced first. Then a short history<br />
of the studying of conservation laws and shock waves will be given. Finally<br />
I would like to present two of our current research projects. One is on the<br />
mathematical analysis of shock diffraction by convex cornered wedges, and<br />
the other one is on the validation of weakly nonlinear geometric optics for<br />
entropy solutions of nonlinear hyperbolic systems of conservation laws.<br />
<br />
Fri, Jan 17, 2:25PM, VV901 Adrianna Gillman (Dartmouth) Fast direct solvers for linear partial differential equations<br />
<br />
===Fri, Jan 17: Adrianna Gillman (Dartmouth) ===<br />
''Fast direct solvers for linear partial differential equations''<br />
<br />
The cost of solving a large linear system often determines what can and cannot be modeled computationally in many areas of science and engineering. Unlike Gaussian elimination which scales cubically with the respect to the number of unknowns, fast direct solvers construct an inverse of a linear in system with a cost that scales linearly or nearly linearly. The fast direct solvers presented in this talk are designed for the linear systems arising from the discretization of linear partial differential equations. These methods are more robust, versatile and stable than iterative schemes. Since an inverse is computed, additional right-hand sides can be processed rapidly. The talk will give the audience a brief introduction to the core ideas, an overview of recent advancements, and it will conclude with a sampling of challenging application examples including the scattering of waves.<br />
<br />
===Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) ===<br />
''Intertwinings, wave equations and growth models''<br />
<br />
We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to hyperbolic partial differential equations, symmetric polynomials and the corresponding random growth models. The talk will be devoted to these recent developments which also shed new light on some beautiful old examples of intertwinings. Based on joint works with Vadim Gorin and Soumik Pal. <br />
<br />
===Jan 24: Yaniv Plan (Michigan) ===<br />
''Low-dimensionality in mathematical signal processing''<br />
<br />
Natural images tend to be compressible, i.e., the amount of information needed to encode an image is small. This conciseness of information -- in other words, low dimensionality of the signal -- is found throughout a plethora of applications ranging from MRI to quantum state tomography. It is natural to ask: can the number of measurements needed to determine a signal be comparable with the information content? We explore this question under modern models of low-dimensionality and measurement acquisition.<br />
<br />
===Thur, Jan 30: Urbashi Mitra (USC) ===<br />
''Underwater Networks: A Convergence of Communications, Control and Sensing''<br />
<br />
The oceans cover 71% of the earth’s surface and represent one of the least explored frontiers, yet the oceans are integral to climate regulation, nutrient production, oil retrieval and transportation. Future scientific and technological efforts to achieve better understanding of oceans and water-related applications will rely heavily on our ability to communicate reliably between instruments, vehicles (manned and unmanned), human operators, platforms and sensors of all types. Underwater acoustic communication techniques have not reached the same maturity as those for terrestrial radio communications and present some unique opportunities for new developments in information and communication theories. Key features of underwater acoustic communication channels are examined: slow speed of propagation, significant delay spreads, sparse multi-path, time-variation and range-dependent available bandwidth. Another unique feature of underwater networks is that the cost of communication, sensing and control are often comparable resulting in new tradeoffs between these activities. We examine some new results (with implications wider than underwater systems) in channel identifiability, communicating over channels with state and cooperative game theory motivated by the underwater network application.<br />
<br />
===Feb 7: David Treumann (Boston College) ===<br />
''Functoriality, Smith theory, and the Brauer homomorphism''<br />
<br />
Smith theory is a technique for relating the mod p homologies of X and of the fixed points of X by an automorphism of order p. I will discuss how, in the setting of locally symmetric spaces, it provides an easy method (no trace formula) for lifting mod p automorphic forms from G^{sigma} to G, where G is an arithmetic group and sigma is an automorphism of G of order p. This lift is compatible with Hecke actions via an analog of the Brauer homomorphism from modular representation theory, and is often compatible with a homomorphism of L-groups on the Galois side. The talk is based on joint work with Akshay Venkatesh. I hope understanding the talk will require less number theory background than understanding the abstract.<br />
<br />
===Feb 14: Alexander Karp (Columbia Teacher's College) ===<br />
''History of Mathematics Education as a Research Field and as Magistra Vitae''<br />
<br />
The presentation will be based on the experience of putting together and editing the Handbook<br />
on the History of Mathematics Education, which will be published by Springer in the near future. <br />
This volume, which was prepared by a large group of researchers from different countries, <br />
contains the first systematic account of the history of the development of mathematics education <br />
in the whole world (and not just in some particular country or region). The editing of such a <br />
book gave rise to thoughts about the methodology of research in this field, and also about what <br />
constitutes an object of such research. These are the thoughts that the presenter intends to share <br />
with his audience. From them, it is natural to pass to an analysis of the current situation and how <br />
it might develop.<br />
<br />
===Feb 21: Svetlana Jitomirskaya (UC-Irvine)===<br />
''Analytic quasiperiodic cocycles''<br />
<br />
Analytic quasiperiodic matrix cocycles is a simple dynamical<br />
system, where analytic and dynamical properties are related in an<br />
unexpected and remarkable way. We will focus on this relation, leading to<br />
a new approach to the proof of joint continuity of Lyapunov exponents in<br />
frequency and cocycle, at irrational frequency, first proved for SL(2,C)<br />
cocycles in Bourgain-Jitom., 2002. The approach is powerful enough to<br />
handle singular and multidimensional cocycles, thus establishing the above<br />
continuity in full generality. This has important consequences including<br />
a dense open version of Bochi-Viana theorem in this setting, with a<br />
completely different underlying mechanism of the proof. A large part of<br />
the talk is a report on a joint work with A. Avila and C. Sadel.<br />
<br />
===February 28: Michael Shelley (Courant)===<br />
''Mathematical models of soft active materials''<br />
<br />
Soft materials that have an "active" microstructure are important examples of so-called active matter. Examples include suspensions of motile microorganisms or particles, "active gels" made up of actin and myosin, and suspensions of microtubules cross-linked by motile motor-proteins. These nonequilibrium materials can have unique mechanical properties and organization, show spontaneous activity-driven flows, and are part of self-assembled structures such as the cellular cortex and mitotic spindle. I will discuss the nature and modeling of these materials, focusing on fluids driven by "active stresses" generated by swimming, motor-protein activity, and surface tension gradients. Amusingly, the latter reveals a new class of fluid flow singularities and an unexpected connection to the Keller-Segel equation.<br />
<br />
<br />
===March 7: Steve Zelditch (Northwestern)===<br />
''Shapes and sizes of eigenfunction''<br />
<br />
Eigenfunctions of the Laplacian (or Schroedinger operators) arise as stationary states in quantum mechanics. They are not apriori geometric<br />
objects but we would like to relate the nodal (zero) sets and Lp norms of eigenfunctions to the geometry of geometrics. I will explain what is<br />
known (and unknown) and norms and nodal sets of eigenfunctions. No prior knowledge of quantum mechanics is assumed.<br />
<br />
===March 14: Richard Schwartz (Brown)===<br />
''The projective heat map on pentagons''<br />
<br />
In this talk I'll describe several maps defined on<br />
the space of polygons. These maps are described in terms<br />
of simple straight-line constructions, and are therefore<br />
natural with respect to projective geometry. One of them,<br />
the pentagram map, is now known to be a discrete completely<br />
integrable system. I'll concentrate on a variant of the<br />
pentagram map, which behaves somewhat like heat flow on convex<br />
polygons but which does crazy things to non-convex polygons.<br />
I'll sketch a computer-assisted analysis of what happens<br />
for pentagons. I'll illustrate the talk with computer demos.<br />
<br />
===March 28: Michael Lacey (GA Tech) ===<br />
''The two weight inequality for Hilbert and Cauchy operators on the disk''<br />
<br />
Put one weight on the unit circle, <br />
and take a function f, square integrable <br />
with respect to this weight. For which <br />
weights in the disk is the analytic extension <br />
of f also square integrable? If one considers <br />
the Poisson extension, the question goes <br />
back 50 years to Carleson. And in the setting <br />
of the Cauchy operator, the question has deep <br />
implications in function and operator theory. <br />
<br />
We will survey the history, and recent solution <br />
of this question, reporting on work of the <br />
speaker, and Sawyer, Uriate-Tuero, C-Y Shen, <br />
and Wick.<br />
<br />
===April 11: Risi Kondor (Chicago) ===<br />
''Multiresolution Matrix Factorization''<br />
<br />
Matrices that appear in modern data analysis and machine learning problems often exhibit complex<br />
hierarchical structure, which goes beyond what can be uncovered by traditional linear algebra tools,<br />
such as eigendecomposition. In this talk I describe a new notion of matrix factorization inspired by <br />
multiresolution analysis that can capture structure in matrices at multiple different scales. <br />
The resulting Multiresolution Matrix Factorizations (MMFs) not only provide a<br />
wavelet basis for sparse approximation, but can also be used for matrix compression and as a prior <br />
for matrix completion. The work presented in this talk is joint with Nedelina Teneva and Vikas Garg.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=6802Colloquia/Fall182014-03-26T19:57:32Z<p>Shamgar: /* Spring 2014 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
[[Colloquia/Fall 2014 | Tentative schedule for Fall 2014]]<br />
<br />
== Spring 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Mon, Jan 6, 4PM'''<br />
|[http://www-bcf.usc.edu/~lauda/Aaron_Laudas_Page/Home.html Aaron Lauda] (USC) <br />
|[[Colloquia#January 6: Aaron Lauda (USC) | An introduction to diagrammatic categorification]]<br />
|Caldararu<br />
|-<br />
|'''Wed, Jan 8, 4PM'''<br />
|[http://www2.math.umd.edu/~kmelnick/ Karin Melnick] (Maryland) <br />
|[[Colloquia#January 8: Karin Melnick (Maryland) | Normal forms for local flows on parabolic geometries]]<br />
|Kent<br />
|-<br />
|Jan 10, 4PM<br />
|[http://users.math.yale.edu/~yd82/ Yen Do] (Yale) <br />
|Convergence of Fourier series and multilinear analysis<br />
|Denissov<br />
|-<br />
|'''Mon, Jan 13, 4pm'''<br />
|[http://math.stanford.edu/~wangyi/ Yi Wang] (Stanford)<br />
|Isoperimetric Inequality and Q-curvature<br />
|Viaclovsky<br />
|-<br />
|'''Wen, Jan 15, 4pm'''<br />
|[http://www.maths.ox.ac.uk/people/profiles/wei.xiang Wei Xiang] (University of Oxford)<br />
|[[Colloquia#January 15: Wei Xiang (University of Oxford) |Conservation Laws and Shock Waves]]<br />
|Bolotin<br />
|-<br />
|'''Fri, Jan 17, 2:25PM, VV901'''<br />
|[http://www.math.dartmouth.edu/~gillmana/ Adrianna Gillman] (Dartmouth) <br />
|Fast direct solvers for linear partial differential equations<br />
|Thiffeault<br />
|-<br />
|'''Thu, Jan 23, 2:25, VV901'''<br />
|[http://www.stat.berkeley.edu/~mshkolni/ Mykhaylo Shkolnikov] (Berkeley)<br />
|[[Colloquia#Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) | Intertwinings, wave equations and growth models]]<br />
|Seppalainen<br />
|-<br />
|Jan 24<br />
|[http://www.yanivplan.com/ Yaniv Plan] (Michigan)<br />
|[http://www.math.wisc.edu/wiki/index.php/Applied/ACMS/absS14#Yaniv_Plan_.28Michigan.29 Low-dimensionality in mathematical signal processing]<br />
|Thiffeault<br />
|-<br />
|Jan 31<br />
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)<br />
|Underwater Networks: A Convergence of Communications, Control and Sensing<br />
|Gurevich<br />
|-<br />
|Feb 7<br />
|David Treumann (Boston College)<br />
|Functoriality, Smith theory, and the Brauer homomorphism<br />
|Street<br />
|-<br />
|Feb 14<br />
|[http://www.tc.columbia.edu/academics/index.htm?facid=apk16 Alexander Karp] (Columbia Teacher's College)<br />
|History of Mathematics Education as a Research Field and as Magistra Vitae<br />
|Kiselev<br />
|-<br />
|Feb 21<br />
|[http://www.math.uci.edu/~szhitomi/ Svetlana Jitomirskaya] (UC-Irvine)<br />
|Analytic quasiperiodic cocycles<br />
|Kiselev<br />
|-<br />
|Feb 28<br />
|[http://math.nyu.edu/faculty/shelley/ Michael Shelley] (Courant)<br />
|[[Colloquia#February 28: Michael Shelley (Courant) | Mathematical models of soft active materials]]<br />
|Spagnolie<br />
|-<br />
|March 7<br />
|[http://www.math.northwestern.edu/people/facultyProfiles/steve.zelditch.html Steve Zelditch] (Northwestern)<br />
|[[Colloquia#March 7: Steve Zelditch (Northwestern) | Shapes and sizes of eigenfunctions]]<br />
|Seeger<br />
|-<br />
|March 14<br />
|[http://www.math.brown.edu/~res/ Richard Schwartz] (Brown)<br />
|[[Colloquia#March 14: Richard Schwartz (Brown) |The projective heat map on pentagons]]<br />
|Mari-Beffa<br />
|-<br />
|<strike>March 21</strike><br />
|'''Spring Break'''<br />
|No Colloquium<br />
|<br />
|-<br />
|'''March 26, 7pm, WID'''<br />
|[https://www.dpmms.cam.ac.uk/people/t.tokieda/ Tadashi Tokieda] (Cambridge)<br />
|[http://c4.discovery.wisc.edu/events/lectures/toymodels/ Toy models]<br />
|Thiffeault (C4 von Neumann Public Lecture)<br />
|-<br />
|March 28<br />
|[http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)<br />
|The two weight inequality for Hilbert and Cauchy operators on the disk<br />
|Street<br />
|-<br />
|April 4<br />
|[http://matthewkahle.org/ Matthew Kahle] (OSU)<br />
|<br />
|Dymarz<br />
|- <br />
|April 11<br />
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)<br />
|Multiresolution Matrix Factorization<br />
|Gurevich<br />
|-<br />
|April 18 (Wasow Lecture)<br />
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)<br />
|Focal points and sup-norms of eigenfunctions<br />
|Seeger<br />
|-<br />
|April 25<br />
|[http://www.charlesdoran.net Charles Doran](University of Alberta)<br />
|<br />
|Song<br />
|-<br />
|'''Monday, April 28''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|A mystery concerning algebraic plane curves<br />
|Maxim<br />
|-<br />
|'''Tuesday, April 29''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Matrix factorizations old and new<br />
|Maxim<br />
|-<br />
|'''Wednesday, April 30''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Easy solution of polynomial equations over finite fields<br />
|Maxim<br />
|-<br />
|May 2<br />
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)<br />
|<br />
|Boston<br />
|-<br />
|May 9<br />
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)<br />
|<br />
|WIMAW<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===January 6: Aaron Lauda (USC)===<br />
<br />
''An introduction to diagrammatic categorification''<br />
<br />
Categorification seeks to reveal a hidden layer in mathematical<br />
structures. Often the resulting structures can be combinatorially<br />
complex objects making them difficult to study. One method of<br />
overcoming this difficulty, that has proven very successful, is to<br />
encode the categorification into a diagrammatic calculus that makes<br />
computations simple and intuitive.<br />
<br />
In this talk I will review some of the original considerations that<br />
led to the categorification philosophy. We will examine how the<br />
diagrammatic perspective has helped to produce new categorifications<br />
having profound applications to algebra, representation theory, and<br />
low-dimensional topology.<br />
<br />
===January 8: Karin Melnick (Maryland)===<br />
<br />
''Normal forms for local flows on parabolic geometries''<br />
<br />
The exponential map in Riemannian geometry conjugates the differential of an isometry at a point with the action of the isometry near the point. It thus provides a linear normal form for all isometries fixing a point. Conformal transformations are not linearizable in general. I will discuss a suite of normal forms theorems in conformal geometry and, more generally, for parabolic geometries, a rich family of geometric structures of which conformal, projective, and CR structures are examples.<br />
<br />
===January 10, 4PM: Yen Do (Yale)===<br />
<br />
''Convergence of Fourier series and multilinear analysis''<br />
<br />
Almost everywhere convergence of the Fourier series of square <br />
integrable functions was first proved by Lennart Carleson in 1966, and <br />
the proof has lead to deep developments in various multilinear settings. <br />
In this talk I would like to introduce a brief history of the subject <br />
and sketch some recent developments, some of these involve my joint <br />
works with collaborators.<br />
<br />
===Mon, January 13: Yi Wang (Stanford)===<br />
<br />
''Isoperimetric Inequality and Q-curvature''<br />
<br />
A well-known question in differential geometry is to prove the<br />
isoperimetric inequality under intrinsic curvature conditions. In<br />
dimension 2, the isoperimetric inequality is controlled by the integral of<br />
the positive part of the Gaussian curvature. In my recent work, I prove<br />
that on simply connected conformally flat manifolds of higher dimensions,<br />
the role of the Gaussian curvature can be replaced by the Branson's<br />
Q-curvature. The isoperimetric inequality is valid if the integral of the<br />
Q-curvature is below a sharp threshold. Moreover, the isoperimetric<br />
constant depends only on the integrals of the Q-curvature. The proof<br />
relies on the theory of $A_p$ weights in harmonic analysis.<br />
<br />
===January 15: Wei Xiang (University of Oxford)===<br />
<br />
''Conservation Laws and Shock Waves''<br />
<br />
The study of continuum physics gave birth to the theory of quasilinear<br />
systems in divergence form, commonly called conservation laws. In this<br />
talk, conservation laws, the Euler equations, and the definition of the<br />
corresponding weak solutions will be introduced first. Then a short history<br />
of the studying of conservation laws and shock waves will be given. Finally<br />
I would like to present two of our current research projects. One is on the<br />
mathematical analysis of shock diffraction by convex cornered wedges, and<br />
the other one is on the validation of weakly nonlinear geometric optics for<br />
entropy solutions of nonlinear hyperbolic systems of conservation laws.<br />
<br />
Fri, Jan 17, 2:25PM, VV901 Adrianna Gillman (Dartmouth) Fast direct solvers for linear partial differential equations<br />
<br />
===Fri, Jan 17: Adrianna Gillman (Dartmouth) ===<br />
''Fast direct solvers for linear partial differential equations''<br />
<br />
The cost of solving a large linear system often determines what can and cannot be modeled computationally in many areas of science and engineering. Unlike Gaussian elimination which scales cubically with the respect to the number of unknowns, fast direct solvers construct an inverse of a linear in system with a cost that scales linearly or nearly linearly. The fast direct solvers presented in this talk are designed for the linear systems arising from the discretization of linear partial differential equations. These methods are more robust, versatile and stable than iterative schemes. Since an inverse is computed, additional right-hand sides can be processed rapidly. The talk will give the audience a brief introduction to the core ideas, an overview of recent advancements, and it will conclude with a sampling of challenging application examples including the scattering of waves.<br />
<br />
===Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) ===<br />
''Intertwinings, wave equations and growth models''<br />
<br />
We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to hyperbolic partial differential equations, symmetric polynomials and the corresponding random growth models. The talk will be devoted to these recent developments which also shed new light on some beautiful old examples of intertwinings. Based on joint works with Vadim Gorin and Soumik Pal. <br />
<br />
===Jan 24: Yaniv Plan (Michigan) ===<br />
''Low-dimensionality in mathematical signal processing''<br />
<br />
Natural images tend to be compressible, i.e., the amount of information needed to encode an image is small. This conciseness of information -- in other words, low dimensionality of the signal -- is found throughout a plethora of applications ranging from MRI to quantum state tomography. It is natural to ask: can the number of measurements needed to determine a signal be comparable with the information content? We explore this question under modern models of low-dimensionality and measurement acquisition.<br />
<br />
===Thur, Jan 30: Urbashi Mitra (USC) ===<br />
''Underwater Networks: A Convergence of Communications, Control and Sensing''<br />
<br />
The oceans cover 71% of the earth’s surface and represent one of the least explored frontiers, yet the oceans are integral to climate regulation, nutrient production, oil retrieval and transportation. Future scientific and technological efforts to achieve better understanding of oceans and water-related applications will rely heavily on our ability to communicate reliably between instruments, vehicles (manned and unmanned), human operators, platforms and sensors of all types. Underwater acoustic communication techniques have not reached the same maturity as those for terrestrial radio communications and present some unique opportunities for new developments in information and communication theories. Key features of underwater acoustic communication channels are examined: slow speed of propagation, significant delay spreads, sparse multi-path, time-variation and range-dependent available bandwidth. Another unique feature of underwater networks is that the cost of communication, sensing and control are often comparable resulting in new tradeoffs between these activities. We examine some new results (with implications wider than underwater systems) in channel identifiability, communicating over channels with state and cooperative game theory motivated by the underwater network application.<br />
<br />
===Feb 7: David Treumann (Boston College) ===<br />
''Functoriality, Smith theory, and the Brauer homomorphism''<br />
<br />
Smith theory is a technique for relating the mod p homologies of X and of the fixed points of X by an automorphism of order p. I will discuss how, in the setting of locally symmetric spaces, it provides an easy method (no trace formula) for lifting mod p automorphic forms from G^{sigma} to G, where G is an arithmetic group and sigma is an automorphism of G of order p. This lift is compatible with Hecke actions via an analog of the Brauer homomorphism from modular representation theory, and is often compatible with a homomorphism of L-groups on the Galois side. The talk is based on joint work with Akshay Venkatesh. I hope understanding the talk will require less number theory background than understanding the abstract.<br />
<br />
===Feb 14: Alexander Karp (Columbia Teacher's College) ===<br />
''History of Mathematics Education as a Research Field and as Magistra Vitae''<br />
<br />
The presentation will be based on the experience of putting together and editing the Handbook<br />
on the History of Mathematics Education, which will be published by Springer in the near future. <br />
This volume, which was prepared by a large group of researchers from different countries, <br />
contains the first systematic account of the history of the development of mathematics education <br />
in the whole world (and not just in some particular country or region). The editing of such a <br />
book gave rise to thoughts about the methodology of research in this field, and also about what <br />
constitutes an object of such research. These are the thoughts that the presenter intends to share <br />
with his audience. From them, it is natural to pass to an analysis of the current situation and how <br />
it might develop.<br />
<br />
===Feb 21: Svetlana Jitomirskaya (UC-Irvine)===<br />
''Analytic quasiperiodic cocycles''<br />
<br />
Analytic quasiperiodic matrix cocycles is a simple dynamical<br />
system, where analytic and dynamical properties are related in an<br />
unexpected and remarkable way. We will focus on this relation, leading to<br />
a new approach to the proof of joint continuity of Lyapunov exponents in<br />
frequency and cocycle, at irrational frequency, first proved for SL(2,C)<br />
cocycles in Bourgain-Jitom., 2002. The approach is powerful enough to<br />
handle singular and multidimensional cocycles, thus establishing the above<br />
continuity in full generality. This has important consequences including<br />
a dense open version of Bochi-Viana theorem in this setting, with a<br />
completely different underlying mechanism of the proof. A large part of<br />
the talk is a report on a joint work with A. Avila and C. Sadel.<br />
<br />
===February 28: Michael Shelley (Courant)===<br />
''Mathematical models of soft active materials''<br />
<br />
Soft materials that have an "active" microstructure are important examples of so-called active matter. Examples include suspensions of motile microorganisms or particles, "active gels" made up of actin and myosin, and suspensions of microtubules cross-linked by motile motor-proteins. These nonequilibrium materials can have unique mechanical properties and organization, show spontaneous activity-driven flows, and are part of self-assembled structures such as the cellular cortex and mitotic spindle. I will discuss the nature and modeling of these materials, focusing on fluids driven by "active stresses" generated by swimming, motor-protein activity, and surface tension gradients. Amusingly, the latter reveals a new class of fluid flow singularities and an unexpected connection to the Keller-Segel equation.<br />
<br />
<br />
===March 7: Steve Zelditch (Northwestern)===<br />
''Shapes and sizes of eigenfunction''<br />
<br />
Eigenfunctions of the Laplacian (or Schroedinger operators) arise as stationary states in quantum mechanics. They are not apriori geometric<br />
objects but we would like to relate the nodal (zero) sets and Lp norms of eigenfunctions to the geometry of geometrics. I will explain what is<br />
known (and unknown) and norms and nodal sets of eigenfunctions. No prior knowledge of quantum mechanics is assumed.<br />
<br />
===March 14: Richard Schwartz (Brown)===<br />
''The projective heat map on pentagons''<br />
<br />
In this talk I'll describe several maps defined on<br />
the space of polygons. These maps are described in terms<br />
of simple straight-line constructions, and are therefore<br />
natural with respect to projective geometry. One of them,<br />
the pentagram map, is now known to be a discrete completely<br />
integrable system. I'll concentrate on a variant of the<br />
pentagram map, which behaves somewhat like heat flow on convex<br />
polygons but which does crazy things to non-convex polygons.<br />
I'll sketch a computer-assisted analysis of what happens<br />
for pentagons. I'll illustrate the talk with computer demos.<br />
<br />
===March 28: Michael Lacey (GA Tech) ===<br />
''The two weight inequality for Hilbert and Cauchy operators on the disk''<br />
<br />
Put one weight on the unit circle, <br />
and take a function f, square integrable <br />
with respect to this weight. For which <br />
weights in the disk is the analytic extension <br />
of f also square integrable? If one considers <br />
the Poisson extension, the question goes <br />
back 50 years to Carleson. And in the setting <br />
of the Cauchy operator, the question has deep <br />
implications in function and operator theory. <br />
<br />
We will survey the history, and recent solution <br />
of this question, reporting on work of the <br />
speaker, and Sawyer, Uriate-Tuero, C-Y Shen, <br />
and Wick.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=6390Colloquia/Fall182014-01-19T23:35:31Z<p>Shamgar: /* Abstracts */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Fall 2013 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
|[http://people.math.gatech.edu/~mbaker/ Matt Baker] (Georgia Institute of Technology)<br />
|Riemann-Roch for Graphs and Applications<br />
|Ellenberg<br />
|-<br />
|Sept 13<br />
|[http://math.wisc.edu/~andrews/ Uri Andrews] (University of Wisconsin)<br />
|A hop, skip, and a jump through the degrees of relative provability<br />
|<br />
|-<br />
|Sept 20<br />
|[http://www.math.neu.edu/people/profile/valerio-toledano-laredo Valerio Toledano Laredo] (Northeastern)<br />
|Flat connections and quantum groups<br />
|Gurevich<br />
|-<br />
|'''Wed, Sept 25, 2:30PM in B139'''<br />
|[http://mypage.iu.edu/~alindens/ Ayelet Lindenstrauss] (Indiana University)<br />
|Taylor Series in Homotopy Theory<br />
|Meyer<br />
|-<br />
|'''Wed, Sept 25''' (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication-Avoiding Algorithms for Linear Algebra and Beyond<br />
|Gurevich<br />
|-<br />
|'''Thurs, Sept 26''' (LAA lecture, Joint with Applied Algebra Seminar)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Implementing Communication-Avoiding Algorithms<br />
|Gurevich<br />
|-<br />
|Sept 27 (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays<br />
|Gurevich<br />
|-<br />
|Oct 4<br />
|[http://www.math.tamu.edu/~sottile/ Frank Sottile] (Texas A&M)<br />
|Galois groups of Schubert problems<br />
|Caldararu<br />
|-<br />
|Oct 11<br />
|[http://math.uchicago.edu/~wilkinso/ Amie Wilkinson] (Chicago)<br />
|[[Colloquia#October 11: Amie Wilkinson (Chicago) | Robust mechanisms for chaos]]<br />
|WIMAW (Cladek)<br />
|-<br />
|'''Tues, Oct 15, 4PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability I]]<br />
|Valko<br />
|-<br />
|'''Wed, Oct 16, 2:30PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability II]]<br />
|Valko<br />
|-<br />
|<strike>Oct 18</strike><br />
|No colloquium due to the distinguished lecture<br />
|<br />
|<br />
|-<br />
|Oct 25<br />
|[http://www.math.umn.edu/~garrett/ Paul Garrett] (Minnesota)<br />
|[[Colloquia#October 25: Paul Garrett (Minnesota) | Boundary-value problems, generalized functions, and zeros of zeta functions]]<br />
|Gurevich<br />
|<br />
|<br />
|-<br />
|Nov 1<br />
|[http://www.cs.columbia.edu/~alewko/ Allison Lewko] (Columbia University)<br />
|On sets of large doubling, Lambda(4) sets, and error-correcting codes<br />
|Stovall<br />
|-<br />
|Nov 8<br />
|[http://www.math.cornell.edu/~riley/ Tim Riley] (Cornell)<br />
|[[Colloquia#November 8: Tim Riley (Cornell) | Hydra groups]]<br />
|Dymarz<br />
|-<br />
|Nov 15 and later<br />
|Reserved<br />
|<br />
|Street<br />
|-<br />
|Nov 22<br />
|[http://www.math.uchicago.edu/~tj/ Tianling Jin] (University of Chicago)<br />
|Solutions of some Monge-Ampere equations with degeneracy or singularities.<br />
|Bolotin<br />
|-<br />
|'''Mon, Nov 25, 4PM'''<br />
|[https://web.math.princeton.edu/~linlin/ Lin Lin] (Lawrence Berkeley National Lab)<br />
|Fast algorithms for electronic structure analysis<br />
|Jin<br />
|-<br />
|'''Tue, Nov 26, 4PM, B139'''<br />
|[http://www.math.cornell.edu/m/People/Faculty/conley Clinton Conley] (Cornell)<br />
|[[Colloquia#November 26 (Tuesday): Clinton Conley (Cornell) | Descriptive set-theoretic graph theory]]<br />
|Lempp<br />
|-<br />
|'''Mon, Dec 2, 4PM'''<br />
|[http://www.math.northwestern.edu/~slm/ Simon Marshall] (Northwestern)<br />
|[[Colloquia#December 2 (Monday): Simon Marshall (Northwestern) | Semiclassical estimates for eigenfunctions on locally symmetric spaces]]<br />
|Denissov<br />
|-<br />
|'''Wed, Dec 4, 4PM'''<br />
|[http://math.berkeley.edu/~svs/ Steven Sam] (Berkeley)<br />
|Free Resolutions and Symmetry<br />
|Boston <br />
|-<br />
|'''Fri, Dec 6'''<br />
|[http://math.mit.edu/~hand/ Paul Hand] (MIT)<br />
|[[Colloquia#December 6: Paul Hand (MIT) | Simplifications of the lifting approach for quadratic signal recovery problems]]<br />
|Thiffeault<br />
|-<br />
|'''Fri, Dec. 6 and Sat Dec. 7'''<br />
|<br />
|[http://www.math.umn.edu/~stant001/askey80 Conference in honor of Dick Askey]<br />
|<br />
|-<br />
|'''Mon, Dec. 9, 4pm, VV B239'''<br />
|[http://www.cims.nyu.edu/~jacob/ Jacob Bedrossian] (Courant Institute)<br />
|Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations<br />
|Bolotin<br />
|-<br />
|'''Wed, Dec 11, 4PM'''<br />
|[http://math.jhu.edu/~lwang/ Lu Wang] (Johns Hopkins)<br />
|Rigidity of Self-shrinkers of Mean Curvature Flow<br />
|Viaclovsky <br />
|-<br />
|'''Fri, Dec. 13, 2:25pm, VV 901'''<br />
|[http://chanwookim.wordpress.com/ Chanwoo Kim] (Cambridge)<br />
|Regularity of the Boltzmann equation in convex domains<br />
|Bolotin<br />
|-<br />
|'''Tues, Dec 17, 4PM'''<br />
|[http://www.statslab.cam.ac.uk/~ps422/ Perla Sousi] (Cambridge)<br />
|[[Colloquia#December 17: Perla Sousi (Cambridge) | The effect of drift on the volume of the Wiener sausage]]<br />
|Seppalainen <br />
|-<br />
|'''Wed, Dec 18, 4PM'''<br />
|[http://users.math.yale.edu/~dc597/ Dustin Cartwright] (Yale)<br />
|[[Colloquia#December 18: Dustin Cartwright (Yale) | Tropical Complexes]]<br />
|Gurevich<br />
|}<br />
<br />
== Spring 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Mon, Jan 6, 4PM'''<br />
|[http://www-bcf.usc.edu/~lauda/Aaron_Laudas_Page/Home.html Aaron Lauda] (USC) <br />
|[[Colloquia#January 6: Aaron Lauda (USC) | An introduction to diagrammatic categorification]]<br />
|Caldararu<br />
|-<br />
|'''Wed, Jan 8, 4PM'''<br />
|[http://www2.math.umd.edu/~kmelnick/ Karin Melnick] (Maryland) <br />
|[[Colloquia#January 8: Karin Melnick (Maryland) | Normal forms for local flows on parabolic geometries]]<br />
|Kent<br />
|-<br />
|Jan 10, 4PM<br />
|[http://users.math.yale.edu/~yd82/ Yen Do] (Yale) <br />
|Convergence of Fourier series and multilinear analysis<br />
|Denissov<br />
|-<br />
|'''Mon, Jan 13, 4pm'''<br />
|[http://math.stanford.edu/~wangyi/ Yi Wang] (Stanford)<br />
|Isoperimetric Inequality and Q-curvature<br />
|Viaclovsky<br />
|-<br />
|'''Wen, Jan 15, 4pm'''<br />
|[http://www.maths.ox.ac.uk/people/profiles/wei.xiang Wei Xiang] (University of Oxford)<br />
|[[Colloquia#January 15: Wei Xiang (University of Oxford) |Conservation Laws and Shock Waves]]<br />
|Bolotin<br />
|-<br />
|'''Fri, Jan 17, 2:25PM, VV901'''<br />
|[http://www.math.dartmouth.edu/~gillmana/ Adrianna Gillman] (Dartmouth) <br />
|Fast direct solvers for linear partial differential equations<br />
|Thiffeault<br />
|-<br />
|'''Thu, Jan 23, 2:25, VV901'''<br />
|[http://www.stat.berkeley.edu/~mshkolni/ Mykhaylo Shkolnikov] (Berkeley)<br />
|[[Colloquia#Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) | Intertwinings, wave equations and growth models]]<br />
|Seppalainen<br />
|-<br />
|Jan 24<br />
|[http://www.yanivplan.com/ Yaniv Plan] (Michigan)<br />
|Low-dimensionality in mathematical signal processing<br />
|Thiffeault<br />
|-<br />
|Jan 31<br />
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)<br />
|Underwater Networks: A Convergence of Communications, Control and Sensing<br />
|Gurevich<br />
|-<br />
|Feb 7<br />
|David Treumann (Boston College)<br />
|<br />
|Street<br />
|-<br />
|Feb 14<br />
|[http://www.tc.columbia.edu/academics/index.htm?facid=apk16 Alexander Karp] (Columbia Teacher's College)<br />
|History of Mathematics Education as a Research Field and as Magistra Vitae<br />
|Kiselev<br />
|-<br />
|Feb 21<br />
|<br />
|<br />
|<br />
|-<br />
|Feb 28<br />
|[http://math.nyu.edu/faculty/shelley/ Michael Shelley] (Courant)<br />
|<br />
|Spagnolie<br />
|-<br />
|March 7<br />
|[http://www.math.northwestern.edu/people/facultyProfiles/steve.zelditch.html Steve Zelditch] (Northwestern)<br />
|<br />
|Seeger<br />
|-<br />
|March 14<br />
|[https://www.math.ucdavis.edu/~strohmer Thomas Strohmer] (Davis)<br />
|Phase Retrieval, Random Matrices and Convex Optimization<br />
|Gurevich<br />
|- <br />
|<strike>March 21</strike><br />
|'''Spring Break'''<br />
|No Colloquium<br />
|<br />
|-<br />
|March 28<br />
|[http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)<br />
|The Two Weight Inequality for the Hilbert Transform<br />
|Street<br />
|-<br />
|April 4<br />
|[http://www.math.brown.edu/~res/ Richard Schwartz] (Brown)<br />
|<br />
|Mari-Beffa<br />
|-<br />
|April 11<br />
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)<br />
|<br />
|Gurevich<br />
|-<br />
|April 18 (Wasow Lecture)<br />
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)<br />
|<br />
|Seeger<br />
|-<br />
|April 25<br />
|[http://www.charlesdoran.net Charles Doran](University of Alberta)<br />
|<br />
|Song<br />
|-<br />
|'''Monday, April 28''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|A mystery concerning algebraic plane curves<br />
|Maxim<br />
|-<br />
|'''Tuesday, April 29''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Matrix factorizations old and new<br />
|Maxim<br />
|-<br />
|'''Wednesday, April 30''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Easy solution of polynomial equations over finite fields<br />
|Maxim<br />
|-<br />
|May 2<br />
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)<br />
|<br />
|Boston<br />
|-<br />
|May 9<br />
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)<br />
|<br />
|WIMAW<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sep 6: Matt Baker (GA Tech) ===<br />
''Riemann-Roch for Graphs and Applications''<br />
<br />
We will begin by formulating the Riemann-Roch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a Riemann-Roch theorem for tropical curves, proved by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof of the Brill-Noether theorem in algebraic geometry (work of by Cools-Draisma-Payne-Robeva), a "volume-theoretic proof" of Kirchhoff's Matrix-Tree Theorem (work of An, Kuperberg, Shokrieh, and the speaker), and a new Chabauty-Coleman style bound for the number of rational points on an algebraic curve over the rationals (work of Katz and Zureick-Brown).<br />
<br />
===Sep 13: Uri Andrews (UW-Madison) ===<br />
''A hop, skip, and a jump through the degrees of relative provability''<br />
<br />
The topic of this talk arises from two directions. On the one hand, Gödel's incompleteness theorem tell us that given any sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic, there is a statement that is true but not provable in T. On the other hand, over the past seventy years, a number of researchers studying witnessing functions for various combinatorial statements have realized the importance of fast-growing functions and the fact that their totality is often not provable over a given sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic (e.g. the Paris-Harrington and the Kirby-Paris theorems).<br />
<br />
I will talk about the structure induced by giving the order (for a fixed T) of relative provability for totality of algorithms. That is, for algorithms describing functions f and g, we say f ≤ g if T along with the totality of g suffices to prove the totality of f. It turns out that this structure is rich, and encodes many facets of the nature of provability over sufficiently strong, consistent, effectively axiomatizable theories for first-order arithmetic. (Work joint with Mingzhong Cai, David Diamondstone, Steffen Lempp, and Joseph S. Miller.)<br />
<br />
===Sep 20: Valerio Toledano Laredo (Northeastern)===<br />
''Flat connections and quantum groups''<br />
<br />
Quantum groups are natural deformations of the Lie algebra of<br />
nxn matrices, and more generally of semisimple Lie algebras.<br />
They first arose in the mid eighties in the study of solvable<br />
models in statistical mechanics.<br />
<br />
I will explain how these algebraic objects can serve as natural<br />
receptacles for the (transcendental) monodromy of flat connections<br />
arising from representation theory.<br />
<br />
These connections exist in rational, trigonometric and elliptic<br />
forms, and lead to quantum groups of increasing interest and<br />
complexity.<br />
<br />
===Wed, Sept 25, 2:30PM Ayelet Lindenstrauss (Indiana University)===<br />
''Taylor Series in Homotopy Theory''<br />
<br />
I will discuss Goodwillie's calculus of functors on topological spaces. To mimic the set-up in real analysis, topological spaces are considered small if their nontrivial homotopy groups start only in higher dimensions. They can be considered close only in relation to a map between them, but a map allows us to construct the difference between two spaces, and two spaces are close if the difference between them is small. Spaces can be summed (in different ways) by taking twisted products of them. It is straightforward to construct the analogs of constant, linear, and higher degree homogenous functors, and they can be assembled into "polynomials" and "infinite sums". There are notions of differentiability and higher derivatives, of Taylor towers, and of analytic functions.<br />
<br />
What might look like a game of analogies is an extremely useful tool because when one looks at functors that map topological spaces not into the category of topological spaces, but into the category of spectra (the stabilized version of the category of spaces, which will be explained), many of them are, in fact, analytic, so they can be constructed from the homogenous functors of different degrees. And we can use appropriate analogs of calculus theorems to understand them better. I will conclude with some recent work of Randy McCarthy and myself, applying Goodwillie's calculus to algebraic K-theory calculations.<br />
<br />
===Sep 25: Jim Demmel (Berkeley) ===<br />
''Communication Avoiding Algorithms for Linear Algebra and Beyond''<br />
<br />
Algorithm have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present algorithms that attain provable lower bounds on communication, and show large speedups compared to their conventional counterparts. These algorithms are for direct and iterative linear algebra, for dense and sparse matrices, as well as direct n-body simulations. Several of these algorithms exhibit perfect strong scaling, in both time and energy: run time (resp. energy) for a fixed problem size drops proportionally to the number of processors p (resp. is independent of p). Finally, we describe extensions to algorithms involving arbitrary loop nests and array accesses, assuming only that array subscripts are affine functions of the loop indices. <br />
<br />
===Sep 26: Jim Demmel (Berkeley) ===<br />
''Implementing Communication Avoiding Algorithms''<br />
<br />
Designing algorithms that avoiding communication, attaining<br />
lower bounds if possible, is critical for algorithms to minimize runtime and<br />
energy on current and future architectures. These new algorithms can have <br />
new numerical stability properties, new ways to encode answers, and new data<br />
structures, not just depend on loop transformations (we need those too!).<br />
We will illustrate with a variety of examples including direct linear algebra<br />
(eg new ways to perform pivoting, new deterministic and randomized<br />
eigenvalue algorithms), iterative linear algebra (eg new ways to reorganize<br />
Krylov subspace methods) and direct n-body algorithms, on architectures<br />
ranging from multicore to distributed memory to heterogeneous.<br />
The theory describing communication avoiding algorithms can give us a large<br />
design space of possible implementations, so we use autotuning to find<br />
the fastest one automatically. Finally, on parallel architectures one can<br />
frequently not expect to get bitwise identical results from multiple runs,<br />
because of dynamic scheduling and floating point nonassociativity; <br />
this can be a problem for reasons from debugging to correctness.<br />
We discuss some techniques to get reproducible results at modest cost.<br />
<br />
===Sep 27: Jim Demmel (Berkeley) ===<br />
''Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays''<br />
<br />
Our goal is to minimize communication, i.e. moving data, since it increasingly<br />
dominates the cost of arithmetic in algorithms. Motivated by this, attainable<br />
communication lower bounds have been established by many authors for a <br />
variety of algorithms including matrix computations.<br />
<br />
The lower bound approach used initially by Irony, Tiskin and Toledo <br />
for O(n^3) matrix multiplication, and later by Ballard et al <br />
for many other linear algebra algorithms, depends on a geometric result by <br />
Loomis and Whitney: this result bounds the volume of a 3D set <br />
(representing multiply-adds done in the inner loop of the algorithm) <br />
using the product of the areas of certain 2D projections of this set <br />
(representing the matrix entries available locally, i.e., without communication).<br />
<br />
Using a recent generalization of Loomis' and Whitney's result, we generalize <br />
this lower bound approach to a much larger class of algorithms, <br />
that may have arbitrary numbers of loops and arrays with arbitrary dimensions, <br />
as long as the index expressions are affine combinations of loop variables.<br />
In other words, the algorithm can do arbitrary operations on any number of <br />
variables like A(i1,i2,i2-2*i1,3-4*i3+7*i_4,…).<br />
Moreover, the result applies to recursive programs, irregular iteration spaces, <br />
sparse matrices, and other data structures as long as the computation can be<br />
logically mapped to loops and indexed data structure accesses. <br />
<br />
We also discuss when optimal algorithms exist that attain the lower bounds; <br />
this leads to new asymptotically faster algorithms for several problems.<br />
<br />
===October 4: Frank Sottile (Texas A&M) ===<br />
''Galois groups of Schubert problems''<br />
<br />
Work of Jordan from 1870 showed how Galois theory<br />
can be applied to enumerative geometry. Hermite earlier<br />
showed the equivalence of Galois groups with geometric <br />
monodromy groups, and in 1979 Harris used this to study <br />
Galois groups of many enumerative problems. Vakil gave <br />
a geometric-combinatorial criterion that implies a Galois <br />
group contains the alternating group. With Brooks and <br />
Martin del Campo, we used Vakil's criterion to show that <br />
all Schubert problems involving lines have at least <br />
alternating Galois group. White and I have given a new <br />
proof of this based on 2-transitivity.<br />
<br />
My talk will describe this background and sketch a <br />
current project to systematically determine Galois groups <br />
of all Schubert problems of moderate size on all small <br />
classical flag manifolds, investigating at least several <br />
million problems. This will use supercomputers employing <br />
several overlapping methods, including combinatorial <br />
criteria, symbolic computation, and numerical homotopy <br />
continuation, and require the development of new <br />
algorithms and software.<br />
<br />
===October 11: Amie Wilkinson (Chicago) ===<br />
<br />
''Robust mechanisms for chaos''<br />
<br />
What are the underlying mechanisms for robustly chaotic behavior in smooth dynamics?<br />
<br />
In addressing this question, I'll focus on the study of diffeomorphisms of a compact manifold, where "chaotic" means "mixing" and and "robustly" means "stable under smooth perturbations." I'll describe recent advances in constructing and using tools called "blenders" to produce stably chaotic behavior with arbitrarily little effort.<br />
<br />
===October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) ===<br />
<br />
''Integrable probability I and II''<br />
<br />
The goal of the talks is to describe the emerging field of integrable<br />
probability, whose goal is to identify and analyze exactly solvable<br />
probabilistic models. The models and results are often easy to describe,<br />
yet difficult to find, and they carry essential information about broad<br />
universality classes of stochastic processes.<br />
<br />
<br />
===October 25: Paul Garrett (Minnesota)=== <br />
<br />
''Boundary-value problems, generalized functions, and zeros of zeta functions''<br />
<br />
Modern analysis (Beppo Levi, Sobolev, Friedrichs, Schwartz) illuminates work of D. Hejhal and Y. Colin de Verdiere from 30 years<br />
ago, clarifying, as in P. Cartier's letter to A. Weil, "how the Riemann Hypothesis was not proven". (Joint with E. Bombieri.)<br />
<br />
===November 1: Allison Lewko (Columbia University) ===<br />
<br />
''On sets of large doubling, Lambda(4) sets, and error-correcting codes''<br />
<br />
We investigate the structure of finite sets A of integers such that A+A is large, presenting a counterexample to natural conjectures in the pursuit of an "anti-Freiman" theory in additive combinatorics. We will begin with a brief history of the problem and its connection to the study of Lambda(4) sets in harmonic analysis, and then we will discuss our counterexample and its construction from error-correcting codes. We will conclude by describing some related open problems.<br />
This is joint work with Mark Lewko.<br />
<br />
===November 8: Tim Riley (Cornell)===<br />
<br />
''Hydra groups''<br />
<br />
A few years ago Will Dison and I constructed a family of<br />
finitely generated groups whose workings include a string-rewriting<br />
phenomenon of extraordinary duration which is reminiscent of Hercules'<br />
battle with the hydra. I will describe this and the investigations it<br />
spurred in hyperbolic geometry, combinatorial group theory, and a<br />
problem of how to calculate efficiently with hugely compressed<br />
representations of integers.<br />
<br />
===November 22: Tianling Jin (University of Chicago)===<br />
<br />
''Solutions of some Monge-Ampere equations with degeneracy or singularities''<br />
<br />
We will first give a new proof of a celebrated theorem of<br />
Jorgens which states that every classical convex solution of det(Hess<br />
u)=1 in R^2 has to be a second order polynomial. Our arguments do not use<br />
complex analysis, and will be applied to establish such Liouville type<br />
theorems for solutions some degenerate Monge-Ampere equations. We will<br />
also discuss some results on existence, regularity, classification, and<br />
asymptotic behavior of solutions of some Monge-Ampere equations with<br />
isolated and line singularities. This is joint work with J. Xiong.<br />
<br />
===Monday, Nov 25: Lin Lin (Lawrence Berkeley National Lab)===<br />
<br />
''Fast algorithms for electronic structure analysis''<br />
<br />
Kohn-Sham density functional theory (KSDFT) is the most widely used<br />
electronic structure theory for molecules and condensed matter systems. For<br />
a system with N electrons, the standard method for solving KSDFT requires<br />
solving N eigenvectors for an O(N) * O(N) Kohn-Sham Hamiltonian matrix.<br />
The computational cost for such procedure is expensive and scales as<br />
O(N^3). We have developed pole expansion plus selected inversion (PEXSI)<br />
method, in which KSDFT is solved by evaluating the selected elements of the<br />
inverse of a series of sparse symmetric matrices, and the overall algorithm<br />
scales at most O(N^2) for all materials including insulators,<br />
semiconductors and metals. The PEXSI method can be used with orthogonal or<br />
nonorthogonal basis set, and the physical quantities including electron<br />
density, energy, atomic force, density of states, and local density of<br />
states are calculated accurately without using the eigenvalues and<br />
eigenvectors. The recently developed massively parallel PEXSI method has<br />
been implemented in SIESTA, one of the most popular electronic structure<br />
software using atomic orbital basis set. The resulting method can allow<br />
accurate treatment of electronic structure in a unprecedented scale. We<br />
demonstrate the application of the method for solving graphene-like<br />
structures with more than 20,000 atoms, and the method can be efficiently<br />
parallelized 10,000 - 100,000 processors on Department of Energy (DOE) high<br />
performance machines.<br />
<br />
===November 26 (Tuesday): Clinton Conley (Cornell)===<br />
<br />
''Descriptive set-theoretic graph theory''<br />
<br />
Familiar graph-theoretic problems (for example, vertex coloring) exhibit a<br />
stark change of character when measurability constraints are placed on the<br />
structures and functions involved. While discussing some ramifications in<br />
descriptive set theory, we also pay special attention to interactions with<br />
probability (concerning random colorings of Cayley graphs) and ergodic<br />
theory (characterizing various dynamical properties of groups). The talk<br />
will include joint work with Alexander Kechris, Andrew Marks, Benjamin<br />
Miller, and Robin Tucker-Drob.<br />
<br />
<br />
===December 2 (Monday): Simon Marshall (Northwestern)===<br />
<br />
''Semiclassical estimates for eigenfunctions on locally symmetric spaces''<br />
<br />
Let M be a compact Riemannian manifold, and f an L^2-normalised Laplace<br />
eigenfunction on M. If p > 2, a theorem of Sogge tells us how large the L^p<br />
norm of f can be in terms of its Laplace eigenvalue. For instance, when p<br />
is infinity this is asking how large the peaks of f can be. I will present<br />
an analogue of Sogge's theorem for eigenfunctions of the full ring of<br />
invariant differential operators on a locally symmetric space, and discuss<br />
some links between this result and number theory.<br />
<br />
===December 4 (Wednesday): Steven Sam (Berkeley)===<br />
<br />
''Free Resolutions and Symmetry''<br />
<br />
This talk is about the use of symmetry in the study of modules and free resolutions in commutative algebra and algebraic geometry, and specifically how it clarifies, organizes, and rigidifies calculations, and how it enables us to find finiteness in situations where it a priori does not seem to exist. I will begin the talk with an example coming from classical invariant theory and determinantal ideals using just some basic notions from linear algebra. Then I will explain some of my own work which builds on this setting in several directions. Finally, I'll discuss a recent program on twisted commutative algebras, developed jointly with Andrew Snowden, which formalizes the synthesis of representation theory and commutative algebra and leads to new finiteness results in seemingly infinite settings.<br />
<br />
===December 6: Paul Hand (MIT)===<br />
<br />
''Simplifications of the Lifting Approach for Quadratic Signal Recovery Problems''<br />
<br />
Many signal recovery problems are quadratic in nature, such as phase<br />
retrieval and sparse principal component analysis. Such problems in<br />
R^n can be convexified by introducing n^2 variables corresponding to<br />
each quadratic combination of unknowns. This approach often gives<br />
rise to an n x n matrix recovery problem that is convex and has<br />
provable recovery guarantees. Because the dimensionality has been<br />
squared, it is an important task to find simplifications that make<br />
computation more tractable. We will discuss two examples where the<br />
lifting approach can be simplified while retaining recovery<br />
guarantees. These examples will be the phase retrieval problem and a<br />
special case of sparse principal component analysis.<br />
<br />
===December 9 (Monday): Jacob Bedrossian (Courant Institute)===<br />
<br />
''Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations''<br />
<br />
We prove asymptotic stability of shear flows close to the<br />
planar, periodic Couette flow in the 2D incompressible Euler equations.<br />
That is, given an initial perturbation of the Couette flow small in a<br />
suitable regularity class, specifically Gevrey space of class smaller than<br />
2, the velocity converges strongly in L2 to a shear flow which is also<br />
close to the Couette flow. The vorticity is asymptotically mixed to small<br />
scales by an almost linear evolution and in general enstrophy is lost in<br />
the weak limit. The strong convergence of the velocity field is sometimes<br />
referred to as inviscid damping, due to the relationship with Landau<br />
damping in the Vlasov equations. Joint work with Nader Masmoudi.<br />
<br />
===Wednesday, Dec 11: Lu Wang (Johns Hopkins)===<br />
<br />
''Rigidity of Self-shrinkers of Mean Curvature Flow''<br />
<br />
The study of mean curvature flow not only is fundamental in geometry, topology and analysis, but also has important applications in applied mathematics, for instance, image processing. One of the most important problems in mean curvature flow is to understand the possible singularities of the flow and self-shrinkers, i.e., self-shrinking solutions of the flow, provide the singularity models.<br />
<br />
In this talk, I will describe the rigidity of asymptotic structures of self-shrinkers. First, I show the uniqueness of properly embedded self-shrinkers asymptotic to any given regular cone. Next, I give a partial affirmative answer to a conjecture of Ilmanen under an infinite order asymptotic assumption, which asserts that the only two-dimensional properly embedded self-shrinker asymptotic to a cylinder along some end is itself the cylinder. The feature of our results is that no completeness of self-shrinkers is required.<br />
<br />
The key ingredients in the proof are a novel reduction of unique continuation for elliptic operators to backwards uniqueness for parabolic operators and the Carleman type techniques. If time permits, I will discuss some applications of our approach to shrinking solitons of Ricci flow.<br />
<br />
===Friday, Dec 13: Chanwoo Kim (Cambridge)===<br />
<br />
''Regularity of the Boltzmann equation in convex domains''<br />
<br />
A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the Boltzmann equation in a strictly convex domain with the specular, bounce-back and diffuse boundary condition. With the aid of a distance function toward the grazing set, we construct weighted classical <math>C^{1}</math> solutions away from the grazing set for all boundary conditions. For the diffuse boundary condition, we construct <math>W^{1,p}</math> solutions for 1< p<2 and weighted <math>W^{1,p}</math> solutions for <math>2\leq p\leq \infty</math> as well. On the other hand, we show second derivatives do not exist up to the boundary in general by constructing counterexamples for all boundary conditions. This is a joint work with Guo, Tonon, Trescases.<br />
<br />
===December 17: Perla Sousi (Cambridge)===<br />
<br />
''The effect of drift on the volume of the Wiener sausage''<br />
<br />
The Wiener sausage at time t is the algebraic sum of a Brownian path on [0,t] and a ball. Does the expected volume of the Wiener sausage increase when we add drift?<br />
How do you compare the expected volume of the usual Wiener sausage to one defined as the algebraic sum of the Brownian path and a square (in 2D) or a cube (in higher dimensions)? We will answer these questions using their relation to the detection problem for Poisson Brownian motions, and rearrangement inequalities on the sphere (with Y. Peres). We will also discuss generalisations of this to Levy processes (with A. Drewitz and R. Sun) as well as an adversarial detection problem and its connections to Kakeya sets (with Babichenko, Peres, Peretz and Winkler).<br />
<br />
<br />
===December 18: Dustin Cartwright (Yale)===<br />
<br />
''Tropical Complexes''<br />
<br />
Tropical geometry is a way of understanding algebraic varieties by the limiting behavior of their degenerations. Through tropicalization, algebraic operations are replaced with combinatorial constructions and piecewise linear functions. I will introduce tropical complexes, which a way of understanding the geometry of algebraic varieties through combinatorics. Tropical complexes are Delta-complexes together with additional integral data, for which one has parallels and concrete comparisons with the behavior of algebraic varieties. <br />
<br />
===January 6: Aaron Lauda (USC)===<br />
<br />
''An introduction to diagrammatic categorification''<br />
<br />
Categorification seeks to reveal a hidden layer in mathematical<br />
structures. Often the resulting structures can be combinatorially<br />
complex objects making them difficult to study. One method of<br />
overcoming this difficulty, that has proven very successful, is to<br />
encode the categorification into a diagrammatic calculus that makes<br />
computations simple and intuitive.<br />
<br />
In this talk I will review some of the original considerations that<br />
led to the categorification philosophy. We will examine how the<br />
diagrammatic perspective has helped to produce new categorifications<br />
having profound applications to algebra, representation theory, and<br />
low-dimensional topology.<br />
<br />
===January 8: Karin Melnick (Maryland)===<br />
<br />
''Normal forms for local flows on parabolic geometries''<br />
<br />
The exponential map in Riemannian geometry conjugates the differential of an isometry at a point with the action of the isometry near the point. It thus provides a linear normal form for all isometries fixing a point. Conformal transformations are not linearizable in general. I will discuss a suite of normal forms theorems in conformal geometry and, more generally, for parabolic geometries, a rich family of geometric structures of which conformal, projective, and CR structures are examples.<br />
<br />
===January 10, 4PM: Yen Do (Yale)===<br />
<br />
''Convergence of Fourier series and multilinear analysis''<br />
<br />
Almost everywhere convergence of the Fourier series of square <br />
integrable functions was first proved by Lennart Carleson in 1966, and <br />
the proof has lead to deep developments in various multilinear settings. <br />
In this talk I would like to introduce a brief history of the subject <br />
and sketch some recent developments, some of these involve my joint <br />
works with collaborators.<br />
<br />
===Mon, January 13: Yi Wang (Stanford)===<br />
<br />
''Isoperimetric Inequality and Q-curvature''<br />
<br />
A well-known question in differential geometry is to prove the<br />
isoperimetric inequality under intrinsic curvature conditions. In<br />
dimension 2, the isoperimetric inequality is controlled by the integral of<br />
the positive part of the Gaussian curvature. In my recent work, I prove<br />
that on simply connected conformally flat manifolds of higher dimensions,<br />
the role of the Gaussian curvature can be replaced by the Branson's<br />
Q-curvature. The isoperimetric inequality is valid if the integral of the<br />
Q-curvature is below a sharp threshold. Moreover, the isoperimetric<br />
constant depends only on the integrals of the Q-curvature. The proof<br />
relies on the theory of $A_p$ weights in harmonic analysis.<br />
<br />
===January 15: Wei Xiang (University of Oxford)===<br />
<br />
''Conservation Laws and Shock Waves''<br />
<br />
The study of continuum physics gave birth to the theory of quasilinear<br />
systems in divergence form, commonly called conservation laws. In this<br />
talk, conservation laws, the Euler equations, and the definition of the<br />
corresponding weak solutions will be introduced first. Then a short history<br />
of the studying of conservation laws and shock waves will be given. Finally<br />
I would like to present two of our current research projects. One is on the<br />
mathematical analysis of shock diffraction by convex cornered wedges, and<br />
the other one is on the validation of weakly nonlinear geometric optics for<br />
entropy solutions of nonlinear hyperbolic systems of conservation laws.<br />
<br />
Fri, Jan 17, 2:25PM, VV901 Adrianna Gillman (Dartmouth) Fast direct solvers for linear partial differential equations<br />
<br />
===Fri, Jan 17: Adrianna Gillman (Dartmouth) ===<br />
''Fast direct solvers for linear partial differential equations''<br />
<br />
The cost of solving a large linear system often determines what can and cannot be modeled computationally in many areas of science and engineering. Unlike Gaussian elimination which scales cubically with the respect to the number of unknowns, fast direct solvers construct an inverse of a linear in system with a cost that scales linearly or nearly linearly. The fast direct solvers presented in this talk are designed for the linear systems arising from the discretization of linear partial differential equations. These methods are more robust, versatile and stable than iterative schemes. Since an inverse is computed, additional right-hand sides can be processed rapidly. The talk will give the audience a brief introduction to the core ideas, an overview of recent advancements, and it will conclude with a sampling of challenging application examples including the scattering of waves.<br />
<br />
===Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) ===<br />
''Intertwinings, wave equations and growth models''<br />
<br />
We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to hyperbolic partial differential equations, symmetric polynomials and the corresponding random growth models. The talk will be devoted to these recent developments which also shed new light on some beautiful old examples of intertwinings. Based on joint works with Vadim Gorin and Soumik Pal. <br />
<br />
<br />
===Jan 24: Yaniv Plan (Michigan) ===<br />
''Low-dimensionality in mathematical signal processing''<br />
<br />
Natural images tend to be compressible, i.e., the amount of information needed to encode an image is small. This conciseness of information -- in other words, low dimensionality of the signal -- is found throughout a plethora of applications ranging from MRI to quantum state tomography. It is natural to ask: can the number of measurements needed to determine a signal be comparable with the information content? We explore this question under modern models of low-dimensionality and measurement acquisition.<br />
<br />
===Thur, Jan 30: Urbashi Mitra (USC) ===<br />
''Underwater Networks: A Convergence of Communications, Control and Sensing''<br />
<br />
The oceans cover 71% of the earth’s surface and represent one of the least explored frontiers, yet the oceans are integral to climate regulation, nutrient production, oil retrieval and transportation. Future scientific and technological efforts to achieve better understanding of oceans and water-related applications will rely heavily on our ability to communicate reliably between instruments, vehicles (manned and unmanned), human operators, platforms and sensors of all types. Underwater acoustic communication techniques have not reached the same maturity as those for terrestrial radio communications and present some unique opportunities for new developments in information and communication theories. Key features of underwater acoustic communication channels are examined: slow speed of propagation, significant delay spreads, sparse multi-path, time-variation and range-dependent available bandwidth. Another unique feature of underwater networks is that the cost of communication, sensing and control are often comparable resulting in new tradeoffs between these activities. We examine some new results (with implications wider than underwater systems) in channel identifiability, communicating over channels with state and cooperative game theory motivated by the underwater network application.<br />
<br />
<br />
===Feb 14: Alexander Karp (Columbia Teacher's College) ===<br />
''History of Mathematics Education as a Research Field and as Magistra Vitae''<br />
<br />
The presentation will be based on the experience of putting together and editing the Handbook<br />
on the History of Mathematics Education, which will be published by Springer in the near future. <br />
This volume, which was prepared by a large group of researchers from different countries, <br />
contains the first systematic account of the history of the development of mathematics education <br />
in the whole world (and not just in some particular country or region). The editing of such a <br />
book gave rise to thoughts about the methodology of research in this field, and also about what <br />
constitutes an object of such research. These are the thoughts that the presenter intends to share <br />
with his audience. From them, it is natural to pass to an analysis of the current situation and how <br />
it might develop.<br />
<br />
===March 14: Thomas Strhomer (Davis) ===<br />
''Phase Retrieval, Random Matrices and Convex Optimization''<br />
<br />
Phase retrieval is the century-old problem of reconstructing a function, such as a signal or image, from intensity<br />
measurements, typically from the modulus of a diffracted wave. Phase retrieval problems - which arise in numerous<br />
areas including X-ray crystallography, astronomy, diffraction imaging and quantum physics - are notoriously<br />
difficult to solve numerically. They also pervade many areas of mathematics, such as numerical analysis, harmonic<br />
analysis, algebraic geometry, combinatorics, and differential geometry. I will introduce a novel framework for<br />
phase retrieval, which comprises tools from optimization, random matrix theory, and compressive sensing. In<br />
particular, we will see that for certain types of random measurements a function, such as a signal or image, can be<br />
recovered exactly with high probability by solving a convenient semidefinite program without any assumption about<br />
the function whatsoever and under a mild condition on the number of measurements. Our method, known as PhaseLift,<br />
is also provably stable vis-a-vis noise. I will describe how this approach carries over to the classical phase<br />
retrieval setting using structured random illuminations and discuss algorithmic aspects.<br />
I conclude with some open problems.<br />
<br />
<br />
===March 28: Michael Lacey (GA Tech) ===<br />
''The Two Weight Inequality for the Hilbert Transform''<br />
<br />
The individual two weight inequality for the Hilbert transform <br />
asks for a real variable characterization of those pairs of weights <br />
(u,v) for which the Hilbert transform H maps L^2(u) to L^2(v). <br />
This question arises naturally in different settings, most famously <br />
in work of Sarason. Answering in the positive a deep <br />
conjecture of Nazarov-Treil-Volberg, the mapping property <br />
of the Hilbert transform is characterized by a triple of conditions, <br />
the first being a two-weight Poisson A2 on the pair of weights, <br />
with a pair of so-called testing inequalities, uniform over all <br />
intervals. This is the first result of this type for a singular <br />
integral operator. (Joint work with Sawyer, C.-Y. Shen and Uriate-Tuero)<br />
<br />
== Past talks ==<br />
<br />
Last year's schedule: [[Colloquia 2012-2013]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=6389Colloquia/Fall182014-01-19T23:32:21Z<p>Shamgar: /* Spring 2014 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Fall 2013 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
|[http://people.math.gatech.edu/~mbaker/ Matt Baker] (Georgia Institute of Technology)<br />
|Riemann-Roch for Graphs and Applications<br />
|Ellenberg<br />
|-<br />
|Sept 13<br />
|[http://math.wisc.edu/~andrews/ Uri Andrews] (University of Wisconsin)<br />
|A hop, skip, and a jump through the degrees of relative provability<br />
|<br />
|-<br />
|Sept 20<br />
|[http://www.math.neu.edu/people/profile/valerio-toledano-laredo Valerio Toledano Laredo] (Northeastern)<br />
|Flat connections and quantum groups<br />
|Gurevich<br />
|-<br />
|'''Wed, Sept 25, 2:30PM in B139'''<br />
|[http://mypage.iu.edu/~alindens/ Ayelet Lindenstrauss] (Indiana University)<br />
|Taylor Series in Homotopy Theory<br />
|Meyer<br />
|-<br />
|'''Wed, Sept 25''' (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication-Avoiding Algorithms for Linear Algebra and Beyond<br />
|Gurevich<br />
|-<br />
|'''Thurs, Sept 26''' (LAA lecture, Joint with Applied Algebra Seminar)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Implementing Communication-Avoiding Algorithms<br />
|Gurevich<br />
|-<br />
|Sept 27 (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays<br />
|Gurevich<br />
|-<br />
|Oct 4<br />
|[http://www.math.tamu.edu/~sottile/ Frank Sottile] (Texas A&M)<br />
|Galois groups of Schubert problems<br />
|Caldararu<br />
|-<br />
|Oct 11<br />
|[http://math.uchicago.edu/~wilkinso/ Amie Wilkinson] (Chicago)<br />
|[[Colloquia#October 11: Amie Wilkinson (Chicago) | Robust mechanisms for chaos]]<br />
|WIMAW (Cladek)<br />
|-<br />
|'''Tues, Oct 15, 4PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability I]]<br />
|Valko<br />
|-<br />
|'''Wed, Oct 16, 2:30PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability II]]<br />
|Valko<br />
|-<br />
|<strike>Oct 18</strike><br />
|No colloquium due to the distinguished lecture<br />
|<br />
|<br />
|-<br />
|Oct 25<br />
|[http://www.math.umn.edu/~garrett/ Paul Garrett] (Minnesota)<br />
|[[Colloquia#October 25: Paul Garrett (Minnesota) | Boundary-value problems, generalized functions, and zeros of zeta functions]]<br />
|Gurevich<br />
|<br />
|<br />
|-<br />
|Nov 1<br />
|[http://www.cs.columbia.edu/~alewko/ Allison Lewko] (Columbia University)<br />
|On sets of large doubling, Lambda(4) sets, and error-correcting codes<br />
|Stovall<br />
|-<br />
|Nov 8<br />
|[http://www.math.cornell.edu/~riley/ Tim Riley] (Cornell)<br />
|[[Colloquia#November 8: Tim Riley (Cornell) | Hydra groups]]<br />
|Dymarz<br />
|-<br />
|Nov 15 and later<br />
|Reserved<br />
|<br />
|Street<br />
|-<br />
|Nov 22<br />
|[http://www.math.uchicago.edu/~tj/ Tianling Jin] (University of Chicago)<br />
|Solutions of some Monge-Ampere equations with degeneracy or singularities.<br />
|Bolotin<br />
|-<br />
|'''Mon, Nov 25, 4PM'''<br />
|[https://web.math.princeton.edu/~linlin/ Lin Lin] (Lawrence Berkeley National Lab)<br />
|Fast algorithms for electronic structure analysis<br />
|Jin<br />
|-<br />
|'''Tue, Nov 26, 4PM, B139'''<br />
|[http://www.math.cornell.edu/m/People/Faculty/conley Clinton Conley] (Cornell)<br />
|[[Colloquia#November 26 (Tuesday): Clinton Conley (Cornell) | Descriptive set-theoretic graph theory]]<br />
|Lempp<br />
|-<br />
|'''Mon, Dec 2, 4PM'''<br />
|[http://www.math.northwestern.edu/~slm/ Simon Marshall] (Northwestern)<br />
|[[Colloquia#December 2 (Monday): Simon Marshall (Northwestern) | Semiclassical estimates for eigenfunctions on locally symmetric spaces]]<br />
|Denissov<br />
|-<br />
|'''Wed, Dec 4, 4PM'''<br />
|[http://math.berkeley.edu/~svs/ Steven Sam] (Berkeley)<br />
|Free Resolutions and Symmetry<br />
|Boston <br />
|-<br />
|'''Fri, Dec 6'''<br />
|[http://math.mit.edu/~hand/ Paul Hand] (MIT)<br />
|[[Colloquia#December 6: Paul Hand (MIT) | Simplifications of the lifting approach for quadratic signal recovery problems]]<br />
|Thiffeault<br />
|-<br />
|'''Fri, Dec. 6 and Sat Dec. 7'''<br />
|<br />
|[http://www.math.umn.edu/~stant001/askey80 Conference in honor of Dick Askey]<br />
|<br />
|-<br />
|'''Mon, Dec. 9, 4pm, VV B239'''<br />
|[http://www.cims.nyu.edu/~jacob/ Jacob Bedrossian] (Courant Institute)<br />
|Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations<br />
|Bolotin<br />
|-<br />
|'''Wed, Dec 11, 4PM'''<br />
|[http://math.jhu.edu/~lwang/ Lu Wang] (Johns Hopkins)<br />
|Rigidity of Self-shrinkers of Mean Curvature Flow<br />
|Viaclovsky <br />
|-<br />
|'''Fri, Dec. 13, 2:25pm, VV 901'''<br />
|[http://chanwookim.wordpress.com/ Chanwoo Kim] (Cambridge)<br />
|Regularity of the Boltzmann equation in convex domains<br />
|Bolotin<br />
|-<br />
|'''Tues, Dec 17, 4PM'''<br />
|[http://www.statslab.cam.ac.uk/~ps422/ Perla Sousi] (Cambridge)<br />
|[[Colloquia#December 17: Perla Sousi (Cambridge) | The effect of drift on the volume of the Wiener sausage]]<br />
|Seppalainen <br />
|-<br />
|'''Wed, Dec 18, 4PM'''<br />
|[http://users.math.yale.edu/~dc597/ Dustin Cartwright] (Yale)<br />
|[[Colloquia#December 18: Dustin Cartwright (Yale) | Tropical Complexes]]<br />
|Gurevich<br />
|}<br />
<br />
== Spring 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Mon, Jan 6, 4PM'''<br />
|[http://www-bcf.usc.edu/~lauda/Aaron_Laudas_Page/Home.html Aaron Lauda] (USC) <br />
|[[Colloquia#January 6: Aaron Lauda (USC) | An introduction to diagrammatic categorification]]<br />
|Caldararu<br />
|-<br />
|'''Wed, Jan 8, 4PM'''<br />
|[http://www2.math.umd.edu/~kmelnick/ Karin Melnick] (Maryland) <br />
|[[Colloquia#January 8: Karin Melnick (Maryland) | Normal forms for local flows on parabolic geometries]]<br />
|Kent<br />
|-<br />
|Jan 10, 4PM<br />
|[http://users.math.yale.edu/~yd82/ Yen Do] (Yale) <br />
|Convergence of Fourier series and multilinear analysis<br />
|Denissov<br />
|-<br />
|'''Mon, Jan 13, 4pm'''<br />
|[http://math.stanford.edu/~wangyi/ Yi Wang] (Stanford)<br />
|Isoperimetric Inequality and Q-curvature<br />
|Viaclovsky<br />
|-<br />
|'''Wen, Jan 15, 4pm'''<br />
|[http://www.maths.ox.ac.uk/people/profiles/wei.xiang Wei Xiang] (University of Oxford)<br />
|[[Colloquia#January 15: Wei Xiang (University of Oxford) |Conservation Laws and Shock Waves]]<br />
|Bolotin<br />
|-<br />
|'''Fri, Jan 17, 2:25PM, VV901'''<br />
|[http://www.math.dartmouth.edu/~gillmana/ Adrianna Gillman] (Dartmouth) <br />
|Fast direct solvers for linear partial differential equations<br />
|Thiffeault<br />
|-<br />
|'''Thu, Jan 23, 2:25, VV901'''<br />
|[http://www.stat.berkeley.edu/~mshkolni/ Mykhaylo Shkolnikov] (Berkeley)<br />
|[[Colloquia#Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) | Intertwinings, wave equations and growth models]]<br />
|Seppalainen<br />
|-<br />
|Jan 24<br />
|[http://www.yanivplan.com/ Yaniv Plan] (Michigan)<br />
|Low-dimensionality in mathematical signal processing<br />
|Thiffeault<br />
|-<br />
|Jan 31<br />
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)<br />
|Underwater Networks: A Convergence of Communications, Control and Sensing<br />
|Gurevich<br />
|-<br />
|Feb 7<br />
|David Treumann (Boston College)<br />
|<br />
|Street<br />
|-<br />
|Feb 14<br />
|[http://www.tc.columbia.edu/academics/index.htm?facid=apk16 Alexander Karp] (Columbia Teacher's College)<br />
|History of Mathematics Education as a Research Field and as Magistra Vitae<br />
|Kiselev<br />
|-<br />
|Feb 21<br />
|<br />
|<br />
|<br />
|-<br />
|Feb 28<br />
|[http://math.nyu.edu/faculty/shelley/ Michael Shelley] (Courant)<br />
|<br />
|Spagnolie<br />
|-<br />
|March 7<br />
|[http://www.math.northwestern.edu/people/facultyProfiles/steve.zelditch.html Steve Zelditch] (Northwestern)<br />
|<br />
|Seeger<br />
|-<br />
|March 14<br />
|[https://www.math.ucdavis.edu/~strohmer Thomas Strohmer] (Davis)<br />
|Phase Retrieval, Random Matrices and Convex Optimization<br />
|Gurevich<br />
|- <br />
|<strike>March 21</strike><br />
|'''Spring Break'''<br />
|No Colloquium<br />
|<br />
|-<br />
|March 28<br />
|[http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)<br />
|The Two Weight Inequality for the Hilbert Transform<br />
|Street<br />
|-<br />
|April 4<br />
|[http://www.math.brown.edu/~res/ Richard Schwartz] (Brown)<br />
|<br />
|Mari-Beffa<br />
|-<br />
|April 11<br />
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)<br />
|<br />
|Gurevich<br />
|-<br />
|April 18 (Wasow Lecture)<br />
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)<br />
|<br />
|Seeger<br />
|-<br />
|April 25<br />
|[http://www.charlesdoran.net Charles Doran](University of Alberta)<br />
|<br />
|Song<br />
|-<br />
|'''Monday, April 28''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|A mystery concerning algebraic plane curves<br />
|Maxim<br />
|-<br />
|'''Tuesday, April 29''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Matrix factorizations old and new<br />
|Maxim<br />
|-<br />
|'''Wednesday, April 30''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Easy solution of polynomial equations over finite fields<br />
|Maxim<br />
|-<br />
|May 2<br />
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)<br />
|<br />
|Boston<br />
|-<br />
|May 9<br />
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)<br />
|<br />
|WIMAW<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sep 6: Matt Baker (GA Tech) ===<br />
''Riemann-Roch for Graphs and Applications''<br />
<br />
We will begin by formulating the Riemann-Roch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a Riemann-Roch theorem for tropical curves, proved by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof of the Brill-Noether theorem in algebraic geometry (work of by Cools-Draisma-Payne-Robeva), a "volume-theoretic proof" of Kirchhoff's Matrix-Tree Theorem (work of An, Kuperberg, Shokrieh, and the speaker), and a new Chabauty-Coleman style bound for the number of rational points on an algebraic curve over the rationals (work of Katz and Zureick-Brown).<br />
<br />
===Sep 13: Uri Andrews (UW-Madison) ===<br />
''A hop, skip, and a jump through the degrees of relative provability''<br />
<br />
The topic of this talk arises from two directions. On the one hand, Gödel's incompleteness theorem tell us that given any sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic, there is a statement that is true but not provable in T. On the other hand, over the past seventy years, a number of researchers studying witnessing functions for various combinatorial statements have realized the importance of fast-growing functions and the fact that their totality is often not provable over a given sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic (e.g. the Paris-Harrington and the Kirby-Paris theorems).<br />
<br />
I will talk about the structure induced by giving the order (for a fixed T) of relative provability for totality of algorithms. That is, for algorithms describing functions f and g, we say f ≤ g if T along with the totality of g suffices to prove the totality of f. It turns out that this structure is rich, and encodes many facets of the nature of provability over sufficiently strong, consistent, effectively axiomatizable theories for first-order arithmetic. (Work joint with Mingzhong Cai, David Diamondstone, Steffen Lempp, and Joseph S. Miller.)<br />
<br />
===Sep 20: Valerio Toledano Laredo (Northeastern)===<br />
''Flat connections and quantum groups''<br />
<br />
Quantum groups are natural deformations of the Lie algebra of<br />
nxn matrices, and more generally of semisimple Lie algebras.<br />
They first arose in the mid eighties in the study of solvable<br />
models in statistical mechanics.<br />
<br />
I will explain how these algebraic objects can serve as natural<br />
receptacles for the (transcendental) monodromy of flat connections<br />
arising from representation theory.<br />
<br />
These connections exist in rational, trigonometric and elliptic<br />
forms, and lead to quantum groups of increasing interest and<br />
complexity.<br />
<br />
===Wed, Sept 25, 2:30PM Ayelet Lindenstrauss (Indiana University)===<br />
''Taylor Series in Homotopy Theory''<br />
<br />
I will discuss Goodwillie's calculus of functors on topological spaces. To mimic the set-up in real analysis, topological spaces are considered small if their nontrivial homotopy groups start only in higher dimensions. They can be considered close only in relation to a map between them, but a map allows us to construct the difference between two spaces, and two spaces are close if the difference between them is small. Spaces can be summed (in different ways) by taking twisted products of them. It is straightforward to construct the analogs of constant, linear, and higher degree homogenous functors, and they can be assembled into "polynomials" and "infinite sums". There are notions of differentiability and higher derivatives, of Taylor towers, and of analytic functions.<br />
<br />
What might look like a game of analogies is an extremely useful tool because when one looks at functors that map topological spaces not into the category of topological spaces, but into the category of spectra (the stabilized version of the category of spaces, which will be explained), many of them are, in fact, analytic, so they can be constructed from the homogenous functors of different degrees. And we can use appropriate analogs of calculus theorems to understand them better. I will conclude with some recent work of Randy McCarthy and myself, applying Goodwillie's calculus to algebraic K-theory calculations.<br />
<br />
===Sep 25: Jim Demmel (Berkeley) ===<br />
''Communication Avoiding Algorithms for Linear Algebra and Beyond''<br />
<br />
Algorithm have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present algorithms that attain provable lower bounds on communication, and show large speedups compared to their conventional counterparts. These algorithms are for direct and iterative linear algebra, for dense and sparse matrices, as well as direct n-body simulations. Several of these algorithms exhibit perfect strong scaling, in both time and energy: run time (resp. energy) for a fixed problem size drops proportionally to the number of processors p (resp. is independent of p). Finally, we describe extensions to algorithms involving arbitrary loop nests and array accesses, assuming only that array subscripts are affine functions of the loop indices. <br />
<br />
===Sep 26: Jim Demmel (Berkeley) ===<br />
''Implementing Communication Avoiding Algorithms''<br />
<br />
Designing algorithms that avoiding communication, attaining<br />
lower bounds if possible, is critical for algorithms to minimize runtime and<br />
energy on current and future architectures. These new algorithms can have <br />
new numerical stability properties, new ways to encode answers, and new data<br />
structures, not just depend on loop transformations (we need those too!).<br />
We will illustrate with a variety of examples including direct linear algebra<br />
(eg new ways to perform pivoting, new deterministic and randomized<br />
eigenvalue algorithms), iterative linear algebra (eg new ways to reorganize<br />
Krylov subspace methods) and direct n-body algorithms, on architectures<br />
ranging from multicore to distributed memory to heterogeneous.<br />
The theory describing communication avoiding algorithms can give us a large<br />
design space of possible implementations, so we use autotuning to find<br />
the fastest one automatically. Finally, on parallel architectures one can<br />
frequently not expect to get bitwise identical results from multiple runs,<br />
because of dynamic scheduling and floating point nonassociativity; <br />
this can be a problem for reasons from debugging to correctness.<br />
We discuss some techniques to get reproducible results at modest cost.<br />
<br />
===Sep 27: Jim Demmel (Berkeley) ===<br />
''Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays''<br />
<br />
Our goal is to minimize communication, i.e. moving data, since it increasingly<br />
dominates the cost of arithmetic in algorithms. Motivated by this, attainable<br />
communication lower bounds have been established by many authors for a <br />
variety of algorithms including matrix computations.<br />
<br />
The lower bound approach used initially by Irony, Tiskin and Toledo <br />
for O(n^3) matrix multiplication, and later by Ballard et al <br />
for many other linear algebra algorithms, depends on a geometric result by <br />
Loomis and Whitney: this result bounds the volume of a 3D set <br />
(representing multiply-adds done in the inner loop of the algorithm) <br />
using the product of the areas of certain 2D projections of this set <br />
(representing the matrix entries available locally, i.e., without communication).<br />
<br />
Using a recent generalization of Loomis' and Whitney's result, we generalize <br />
this lower bound approach to a much larger class of algorithms, <br />
that may have arbitrary numbers of loops and arrays with arbitrary dimensions, <br />
as long as the index expressions are affine combinations of loop variables.<br />
In other words, the algorithm can do arbitrary operations on any number of <br />
variables like A(i1,i2,i2-2*i1,3-4*i3+7*i_4,…).<br />
Moreover, the result applies to recursive programs, irregular iteration spaces, <br />
sparse matrices, and other data structures as long as the computation can be<br />
logically mapped to loops and indexed data structure accesses. <br />
<br />
We also discuss when optimal algorithms exist that attain the lower bounds; <br />
this leads to new asymptotically faster algorithms for several problems.<br />
<br />
===October 4: Frank Sottile (Texas A&M) ===<br />
''Galois groups of Schubert problems''<br />
<br />
Work of Jordan from 1870 showed how Galois theory<br />
can be applied to enumerative geometry. Hermite earlier<br />
showed the equivalence of Galois groups with geometric <br />
monodromy groups, and in 1979 Harris used this to study <br />
Galois groups of many enumerative problems. Vakil gave <br />
a geometric-combinatorial criterion that implies a Galois <br />
group contains the alternating group. With Brooks and <br />
Martin del Campo, we used Vakil's criterion to show that <br />
all Schubert problems involving lines have at least <br />
alternating Galois group. White and I have given a new <br />
proof of this based on 2-transitivity.<br />
<br />
My talk will describe this background and sketch a <br />
current project to systematically determine Galois groups <br />
of all Schubert problems of moderate size on all small <br />
classical flag manifolds, investigating at least several <br />
million problems. This will use supercomputers employing <br />
several overlapping methods, including combinatorial <br />
criteria, symbolic computation, and numerical homotopy <br />
continuation, and require the development of new <br />
algorithms and software.<br />
<br />
===October 11: Amie Wilkinson (Chicago) ===<br />
<br />
''Robust mechanisms for chaos''<br />
<br />
What are the underlying mechanisms for robustly chaotic behavior in smooth dynamics?<br />
<br />
In addressing this question, I'll focus on the study of diffeomorphisms of a compact manifold, where "chaotic" means "mixing" and and "robustly" means "stable under smooth perturbations." I'll describe recent advances in constructing and using tools called "blenders" to produce stably chaotic behavior with arbitrarily little effort.<br />
<br />
===October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) ===<br />
<br />
''Integrable probability I and II''<br />
<br />
The goal of the talks is to describe the emerging field of integrable<br />
probability, whose goal is to identify and analyze exactly solvable<br />
probabilistic models. The models and results are often easy to describe,<br />
yet difficult to find, and they carry essential information about broad<br />
universality classes of stochastic processes.<br />
<br />
<br />
===October 25: Paul Garrett (Minnesota)=== <br />
<br />
''Boundary-value problems, generalized functions, and zeros of zeta functions''<br />
<br />
Modern analysis (Beppo Levi, Sobolev, Friedrichs, Schwartz) illuminates work of D. Hejhal and Y. Colin de Verdiere from 30 years<br />
ago, clarifying, as in P. Cartier's letter to A. Weil, "how the Riemann Hypothesis was not proven". (Joint with E. Bombieri.)<br />
<br />
===November 1: Allison Lewko (Columbia University) ===<br />
<br />
''On sets of large doubling, Lambda(4) sets, and error-correcting codes''<br />
<br />
We investigate the structure of finite sets A of integers such that A+A is large, presenting a counterexample to natural conjectures in the pursuit of an "anti-Freiman" theory in additive combinatorics. We will begin with a brief history of the problem and its connection to the study of Lambda(4) sets in harmonic analysis, and then we will discuss our counterexample and its construction from error-correcting codes. We will conclude by describing some related open problems.<br />
This is joint work with Mark Lewko.<br />
<br />
===November 8: Tim Riley (Cornell)===<br />
<br />
''Hydra groups''<br />
<br />
A few years ago Will Dison and I constructed a family of<br />
finitely generated groups whose workings include a string-rewriting<br />
phenomenon of extraordinary duration which is reminiscent of Hercules'<br />
battle with the hydra. I will describe this and the investigations it<br />
spurred in hyperbolic geometry, combinatorial group theory, and a<br />
problem of how to calculate efficiently with hugely compressed<br />
representations of integers.<br />
<br />
===November 22: Tianling Jin (University of Chicago)===<br />
<br />
''Solutions of some Monge-Ampere equations with degeneracy or singularities''<br />
<br />
We will first give a new proof of a celebrated theorem of<br />
Jorgens which states that every classical convex solution of det(Hess<br />
u)=1 in R^2 has to be a second order polynomial. Our arguments do not use<br />
complex analysis, and will be applied to establish such Liouville type<br />
theorems for solutions some degenerate Monge-Ampere equations. We will<br />
also discuss some results on existence, regularity, classification, and<br />
asymptotic behavior of solutions of some Monge-Ampere equations with<br />
isolated and line singularities. This is joint work with J. Xiong.<br />
<br />
===Monday, Nov 25: Lin Lin (Lawrence Berkeley National Lab)===<br />
<br />
''Fast algorithms for electronic structure analysis''<br />
<br />
Kohn-Sham density functional theory (KSDFT) is the most widely used<br />
electronic structure theory for molecules and condensed matter systems. For<br />
a system with N electrons, the standard method for solving KSDFT requires<br />
solving N eigenvectors for an O(N) * O(N) Kohn-Sham Hamiltonian matrix.<br />
The computational cost for such procedure is expensive and scales as<br />
O(N^3). We have developed pole expansion plus selected inversion (PEXSI)<br />
method, in which KSDFT is solved by evaluating the selected elements of the<br />
inverse of a series of sparse symmetric matrices, and the overall algorithm<br />
scales at most O(N^2) for all materials including insulators,<br />
semiconductors and metals. The PEXSI method can be used with orthogonal or<br />
nonorthogonal basis set, and the physical quantities including electron<br />
density, energy, atomic force, density of states, and local density of<br />
states are calculated accurately without using the eigenvalues and<br />
eigenvectors. The recently developed massively parallel PEXSI method has<br />
been implemented in SIESTA, one of the most popular electronic structure<br />
software using atomic orbital basis set. The resulting method can allow<br />
accurate treatment of electronic structure in a unprecedented scale. We<br />
demonstrate the application of the method for solving graphene-like<br />
structures with more than 20,000 atoms, and the method can be efficiently<br />
parallelized 10,000 - 100,000 processors on Department of Energy (DOE) high<br />
performance machines.<br />
<br />
===November 26 (Tuesday): Clinton Conley (Cornell)===<br />
<br />
''Descriptive set-theoretic graph theory''<br />
<br />
Familiar graph-theoretic problems (for example, vertex coloring) exhibit a<br />
stark change of character when measurability constraints are placed on the<br />
structures and functions involved. While discussing some ramifications in<br />
descriptive set theory, we also pay special attention to interactions with<br />
probability (concerning random colorings of Cayley graphs) and ergodic<br />
theory (characterizing various dynamical properties of groups). The talk<br />
will include joint work with Alexander Kechris, Andrew Marks, Benjamin<br />
Miller, and Robin Tucker-Drob.<br />
<br />
<br />
===December 2 (Monday): Simon Marshall (Northwestern)===<br />
<br />
''Semiclassical estimates for eigenfunctions on locally symmetric spaces''<br />
<br />
Let M be a compact Riemannian manifold, and f an L^2-normalised Laplace<br />
eigenfunction on M. If p > 2, a theorem of Sogge tells us how large the L^p<br />
norm of f can be in terms of its Laplace eigenvalue. For instance, when p<br />
is infinity this is asking how large the peaks of f can be. I will present<br />
an analogue of Sogge's theorem for eigenfunctions of the full ring of<br />
invariant differential operators on a locally symmetric space, and discuss<br />
some links between this result and number theory.<br />
<br />
===December 4 (Wednesday): Steven Sam (Berkeley)===<br />
<br />
''Free Resolutions and Symmetry''<br />
<br />
This talk is about the use of symmetry in the study of modules and free resolutions in commutative algebra and algebraic geometry, and specifically how it clarifies, organizes, and rigidifies calculations, and how it enables us to find finiteness in situations where it a priori does not seem to exist. I will begin the talk with an example coming from classical invariant theory and determinantal ideals using just some basic notions from linear algebra. Then I will explain some of my own work which builds on this setting in several directions. Finally, I'll discuss a recent program on twisted commutative algebras, developed jointly with Andrew Snowden, which formalizes the synthesis of representation theory and commutative algebra and leads to new finiteness results in seemingly infinite settings.<br />
<br />
===December 6: Paul Hand (MIT)===<br />
<br />
''Simplifications of the Lifting Approach for Quadratic Signal Recovery Problems''<br />
<br />
Many signal recovery problems are quadratic in nature, such as phase<br />
retrieval and sparse principal component analysis. Such problems in<br />
R^n can be convexified by introducing n^2 variables corresponding to<br />
each quadratic combination of unknowns. This approach often gives<br />
rise to an n x n matrix recovery problem that is convex and has<br />
provable recovery guarantees. Because the dimensionality has been<br />
squared, it is an important task to find simplifications that make<br />
computation more tractable. We will discuss two examples where the<br />
lifting approach can be simplified while retaining recovery<br />
guarantees. These examples will be the phase retrieval problem and a<br />
special case of sparse principal component analysis.<br />
<br />
===December 9 (Monday): Jacob Bedrossian (Courant Institute)===<br />
<br />
''Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations''<br />
<br />
We prove asymptotic stability of shear flows close to the<br />
planar, periodic Couette flow in the 2D incompressible Euler equations.<br />
That is, given an initial perturbation of the Couette flow small in a<br />
suitable regularity class, specifically Gevrey space of class smaller than<br />
2, the velocity converges strongly in L2 to a shear flow which is also<br />
close to the Couette flow. The vorticity is asymptotically mixed to small<br />
scales by an almost linear evolution and in general enstrophy is lost in<br />
the weak limit. The strong convergence of the velocity field is sometimes<br />
referred to as inviscid damping, due to the relationship with Landau<br />
damping in the Vlasov equations. Joint work with Nader Masmoudi.<br />
<br />
===Wednesday, Dec 11: Lu Wang (Johns Hopkins)===<br />
<br />
''Rigidity of Self-shrinkers of Mean Curvature Flow''<br />
<br />
The study of mean curvature flow not only is fundamental in geometry, topology and analysis, but also has important applications in applied mathematics, for instance, image processing. One of the most important problems in mean curvature flow is to understand the possible singularities of the flow and self-shrinkers, i.e., self-shrinking solutions of the flow, provide the singularity models.<br />
<br />
In this talk, I will describe the rigidity of asymptotic structures of self-shrinkers. First, I show the uniqueness of properly embedded self-shrinkers asymptotic to any given regular cone. Next, I give a partial affirmative answer to a conjecture of Ilmanen under an infinite order asymptotic assumption, which asserts that the only two-dimensional properly embedded self-shrinker asymptotic to a cylinder along some end is itself the cylinder. The feature of our results is that no completeness of self-shrinkers is required.<br />
<br />
The key ingredients in the proof are a novel reduction of unique continuation for elliptic operators to backwards uniqueness for parabolic operators and the Carleman type techniques. If time permits, I will discuss some applications of our approach to shrinking solitons of Ricci flow.<br />
<br />
===Friday, Dec 13: Chanwoo Kim (Cambridge)===<br />
<br />
''Regularity of the Boltzmann equation in convex domains''<br />
<br />
A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the Boltzmann equation in a strictly convex domain with the specular, bounce-back and diffuse boundary condition. With the aid of a distance function toward the grazing set, we construct weighted classical <math>C^{1}</math> solutions away from the grazing set for all boundary conditions. For the diffuse boundary condition, we construct <math>W^{1,p}</math> solutions for 1< p<2 and weighted <math>W^{1,p}</math> solutions for <math>2\leq p\leq \infty</math> as well. On the other hand, we show second derivatives do not exist up to the boundary in general by constructing counterexamples for all boundary conditions. This is a joint work with Guo, Tonon, Trescases.<br />
<br />
===December 17: Perla Sousi (Cambridge)===<br />
<br />
''The effect of drift on the volume of the Wiener sausage''<br />
<br />
The Wiener sausage at time t is the algebraic sum of a Brownian path on [0,t] and a ball. Does the expected volume of the Wiener sausage increase when we add drift?<br />
How do you compare the expected volume of the usual Wiener sausage to one defined as the algebraic sum of the Brownian path and a square (in 2D) or a cube (in higher dimensions)? We will answer these questions using their relation to the detection problem for Poisson Brownian motions, and rearrangement inequalities on the sphere (with Y. Peres). We will also discuss generalisations of this to Levy processes (with A. Drewitz and R. Sun) as well as an adversarial detection problem and its connections to Kakeya sets (with Babichenko, Peres, Peretz and Winkler).<br />
<br />
<br />
===December 18: Dustin Cartwright (Yale)===<br />
<br />
''Tropical Complexes''<br />
<br />
Tropical geometry is a way of understanding algebraic varieties by the limiting behavior of their degenerations. Through tropicalization, algebraic operations are replaced with combinatorial constructions and piecewise linear functions. I will introduce tropical complexes, which a way of understanding the geometry of algebraic varieties through combinatorics. Tropical complexes are Delta-complexes together with additional integral data, for which one has parallels and concrete comparisons with the behavior of algebraic varieties. <br />
<br />
===January 6: Aaron Lauda (USC)===<br />
<br />
''An introduction to diagrammatic categorification''<br />
<br />
Categorification seeks to reveal a hidden layer in mathematical<br />
structures. Often the resulting structures can be combinatorially<br />
complex objects making them difficult to study. One method of<br />
overcoming this difficulty, that has proven very successful, is to<br />
encode the categorification into a diagrammatic calculus that makes<br />
computations simple and intuitive.<br />
<br />
In this talk I will review some of the original considerations that<br />
led to the categorification philosophy. We will examine how the<br />
diagrammatic perspective has helped to produce new categorifications<br />
having profound applications to algebra, representation theory, and<br />
low-dimensional topology.<br />
<br />
===January 8: Karin Melnick (Maryland)===<br />
<br />
''Normal forms for local flows on parabolic geometries''<br />
<br />
The exponential map in Riemannian geometry conjugates the differential of an isometry at a point with the action of the isometry near the point. It thus provides a linear normal form for all isometries fixing a point. Conformal transformations are not linearizable in general. I will discuss a suite of normal forms theorems in conformal geometry and, more generally, for parabolic geometries, a rich family of geometric structures of which conformal, projective, and CR structures are examples.<br />
<br />
===January 10, 4PM: Yen Do (Yale)===<br />
<br />
''Convergence of Fourier series and multilinear analysis''<br />
<br />
Almost everywhere convergence of the Fourier series of square <br />
integrable functions was first proved by Lennart Carleson in 1966, and <br />
the proof has lead to deep developments in various multilinear settings. <br />
In this talk I would like to introduce a brief history of the subject <br />
and sketch some recent developments, some of these involve my joint <br />
works with collaborators.<br />
<br />
===Mon, January 13: Yi Wang (Stanford)===<br />
<br />
''Isoperimetric Inequality and Q-curvature''<br />
<br />
A well-known question in differential geometry is to prove the<br />
isoperimetric inequality under intrinsic curvature conditions. In<br />
dimension 2, the isoperimetric inequality is controlled by the integral of<br />
the positive part of the Gaussian curvature. In my recent work, I prove<br />
that on simply connected conformally flat manifolds of higher dimensions,<br />
the role of the Gaussian curvature can be replaced by the Branson's<br />
Q-curvature. The isoperimetric inequality is valid if the integral of the<br />
Q-curvature is below a sharp threshold. Moreover, the isoperimetric<br />
constant depends only on the integrals of the Q-curvature. The proof<br />
relies on the theory of $A_p$ weights in harmonic analysis.<br />
<br />
===January 15: Wei Xiang (University of Oxford)===<br />
<br />
''Conservation Laws and Shock Waves''<br />
<br />
The study of continuum physics gave birth to the theory of quasilinear<br />
systems in divergence form, commonly called conservation laws. In this<br />
talk, conservation laws, the Euler equations, and the definition of the<br />
corresponding weak solutions will be introduced first. Then a short history<br />
of the studying of conservation laws and shock waves will be given. Finally<br />
I would like to present two of our current research projects. One is on the<br />
mathematical analysis of shock diffraction by convex cornered wedges, and<br />
the other one is on the validation of weakly nonlinear geometric optics for<br />
entropy solutions of nonlinear hyperbolic systems of conservation laws.<br />
<br />
Fri, Jan 17, 2:25PM, VV901 Adrianna Gillman (Dartmouth) Fast direct solvers for linear partial differential equations<br />
<br />
===Fri, Jan 17: Adrianna Gillman (Dartmouth) ===<br />
''Fast direct solvers for linear partial differential equations''<br />
<br />
The cost of solving a large linear system often determines what can and cannot be modeled computationally in many areas of science and engineering. Unlike Gaussian elimination which scales cubically with the respect to the number of unknowns, fast direct solvers construct an inverse of a linear in system with a cost that scales linearly or nearly linearly. The fast direct solvers presented in this talk are designed for the linear systems arising from the discretization of linear partial differential equations. These methods are more robust, versatile and stable than iterative schemes. Since an inverse is computed, additional right-hand sides can be processed rapidly. The talk will give the audience a brief introduction to the core ideas, an overview of recent advancements, and it will conclude with a sampling of challenging application examples including the scattering of waves.<br />
<br />
===Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) ===<br />
''Intertwinings, wave equations and growth models''<br />
<br />
We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to hyperbolic partial differential equations, symmetric polynomials and the corresponding random growth models. The talk will be devoted to these recent developments which also shed new light on some beautiful old examples of intertwinings. Based on joint works with Vadim Gorin and Soumik Pal. <br />
<br />
<br />
===Jan 24: Yaniv Plan (Michigan) ===<br />
''Low-dimensionality in mathematical signal processing''<br />
<br />
Natural images tend to be compressible, i.e., the amount of information needed to encode an image is small. This conciseness of information -- in other words, low dimensionality of the signal -- is found throughout a plethora of applications ranging from MRI to quantum state tomography. It is natural to ask: can the number of measurements needed to determine a signal be comparable with the information content? We explore this question under modern models of low-dimensionality and measurement acquisition.<br />
<br />
===Thur, Jan 30: Urbashi Mitra (USC) ===<br />
''Underwater Networks: A Convergence of Communications, Control and Sensing''<br />
<br />
The oceans cover 71% of the earth’s surface and represent one of the least explored frontiers, yet the oceans are integral to climate regulation, nutrient production, oil retrieval and transportation. Future scientific and technological efforts to achieve better understanding of oceans and water-related applications will rely heavily on our ability to communicate reliably between instruments, vehicles (manned and unmanned), human operators, platforms and sensors of all types. Underwater acoustic communication techniques have not reached the same maturity as those for terrestrial radio communications and present some unique opportunities for new developments in information and communication theories. Key features of underwater acoustic communication channels are examined: slow speed of propagation, significant delay spreads, sparse multi-path, time-variation and range-dependent available bandwidth. Another unique feature of underwater networks is that the cost of communication, sensing and control are often comparable resulting in new tradeoffs between these activities. We examine some new results (with implications wider than underwater systems) in channel identifiability, communicating over channels with state and cooperative game theory motivated by the underwater network application.<br />
<br />
<br />
===Feb 14: Alexander Karp (Columbia Teacher's College) ===<br />
''History of Mathematics Education as a Research Field and as Magistra Vitae''<br />
<br />
The presentation will be based on the experience of putting together and editing the Handbook<br />
on the History of Mathematics Education, which will be published by Springer in the near future. <br />
This volume, which was prepared by a large group of researchers from different countries, <br />
contains the first systematic account of the history of the development of mathematics education <br />
in the whole world (and not just in some particular country or region). The editing of such a <br />
book gave rise to thoughts about the methodology of research in this field, and also about what <br />
constitutes an object of such research. These are the thoughts that the presenter intends to share <br />
with his audience. From them, it is natural to pass to an analysis of the current situation and how <br />
it might develop.<br />
<br />
<br />
<br />
===March 28: Michael Lacey (GA Tech) ===<br />
''The Two Weight Inequality for the Hilbert Transform''<br />
<br />
The individual two weight inequality for the Hilbert transform <br />
asks for a real variable characterization of those pairs of weights <br />
(u,v) for which the Hilbert transform H maps L^2(u) to L^2(v). <br />
This question arises naturally in different settings, most famously <br />
in work of Sarason. Answering in the positive a deep <br />
conjecture of Nazarov-Treil-Volberg, the mapping property <br />
of the Hilbert transform is characterized by a triple of conditions, <br />
the first being a two-weight Poisson A2 on the pair of weights, <br />
with a pair of so-called testing inequalities, uniform over all <br />
intervals. This is the first result of this type for a singular <br />
integral operator. (Joint work with Sawyer, C.-Y. Shen and Uriate-Tuero)<br />
<br />
== Past talks ==<br />
<br />
Last year's schedule: [[Colloquia 2012-2013]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=6388Colloquia/Fall182014-01-19T22:08:30Z<p>Shamgar: /* Spring 2014 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Fall 2013 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
|[http://people.math.gatech.edu/~mbaker/ Matt Baker] (Georgia Institute of Technology)<br />
|Riemann-Roch for Graphs and Applications<br />
|Ellenberg<br />
|-<br />
|Sept 13<br />
|[http://math.wisc.edu/~andrews/ Uri Andrews] (University of Wisconsin)<br />
|A hop, skip, and a jump through the degrees of relative provability<br />
|<br />
|-<br />
|Sept 20<br />
|[http://www.math.neu.edu/people/profile/valerio-toledano-laredo Valerio Toledano Laredo] (Northeastern)<br />
|Flat connections and quantum groups<br />
|Gurevich<br />
|-<br />
|'''Wed, Sept 25, 2:30PM in B139'''<br />
|[http://mypage.iu.edu/~alindens/ Ayelet Lindenstrauss] (Indiana University)<br />
|Taylor Series in Homotopy Theory<br />
|Meyer<br />
|-<br />
|'''Wed, Sept 25''' (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication-Avoiding Algorithms for Linear Algebra and Beyond<br />
|Gurevich<br />
|-<br />
|'''Thurs, Sept 26''' (LAA lecture, Joint with Applied Algebra Seminar)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Implementing Communication-Avoiding Algorithms<br />
|Gurevich<br />
|-<br />
|Sept 27 (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays<br />
|Gurevich<br />
|-<br />
|Oct 4<br />
|[http://www.math.tamu.edu/~sottile/ Frank Sottile] (Texas A&M)<br />
|Galois groups of Schubert problems<br />
|Caldararu<br />
|-<br />
|Oct 11<br />
|[http://math.uchicago.edu/~wilkinso/ Amie Wilkinson] (Chicago)<br />
|[[Colloquia#October 11: Amie Wilkinson (Chicago) | Robust mechanisms for chaos]]<br />
|WIMAW (Cladek)<br />
|-<br />
|'''Tues, Oct 15, 4PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability I]]<br />
|Valko<br />
|-<br />
|'''Wed, Oct 16, 2:30PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability II]]<br />
|Valko<br />
|-<br />
|<strike>Oct 18</strike><br />
|No colloquium due to the distinguished lecture<br />
|<br />
|<br />
|-<br />
|Oct 25<br />
|[http://www.math.umn.edu/~garrett/ Paul Garrett] (Minnesota)<br />
|[[Colloquia#October 25: Paul Garrett (Minnesota) | Boundary-value problems, generalized functions, and zeros of zeta functions]]<br />
|Gurevich<br />
|<br />
|<br />
|-<br />
|Nov 1<br />
|[http://www.cs.columbia.edu/~alewko/ Allison Lewko] (Columbia University)<br />
|On sets of large doubling, Lambda(4) sets, and error-correcting codes<br />
|Stovall<br />
|-<br />
|Nov 8<br />
|[http://www.math.cornell.edu/~riley/ Tim Riley] (Cornell)<br />
|[[Colloquia#November 8: Tim Riley (Cornell) | Hydra groups]]<br />
|Dymarz<br />
|-<br />
|Nov 15 and later<br />
|Reserved<br />
|<br />
|Street<br />
|-<br />
|Nov 22<br />
|[http://www.math.uchicago.edu/~tj/ Tianling Jin] (University of Chicago)<br />
|Solutions of some Monge-Ampere equations with degeneracy or singularities.<br />
|Bolotin<br />
|-<br />
|'''Mon, Nov 25, 4PM'''<br />
|[https://web.math.princeton.edu/~linlin/ Lin Lin] (Lawrence Berkeley National Lab)<br />
|Fast algorithms for electronic structure analysis<br />
|Jin<br />
|-<br />
|'''Tue, Nov 26, 4PM, B139'''<br />
|[http://www.math.cornell.edu/m/People/Faculty/conley Clinton Conley] (Cornell)<br />
|[[Colloquia#November 26 (Tuesday): Clinton Conley (Cornell) | Descriptive set-theoretic graph theory]]<br />
|Lempp<br />
|-<br />
|'''Mon, Dec 2, 4PM'''<br />
|[http://www.math.northwestern.edu/~slm/ Simon Marshall] (Northwestern)<br />
|[[Colloquia#December 2 (Monday): Simon Marshall (Northwestern) | Semiclassical estimates for eigenfunctions on locally symmetric spaces]]<br />
|Denissov<br />
|-<br />
|'''Wed, Dec 4, 4PM'''<br />
|[http://math.berkeley.edu/~svs/ Steven Sam] (Berkeley)<br />
|Free Resolutions and Symmetry<br />
|Boston <br />
|-<br />
|'''Fri, Dec 6'''<br />
|[http://math.mit.edu/~hand/ Paul Hand] (MIT)<br />
|[[Colloquia#December 6: Paul Hand (MIT) | Simplifications of the lifting approach for quadratic signal recovery problems]]<br />
|Thiffeault<br />
|-<br />
|'''Fri, Dec. 6 and Sat Dec. 7'''<br />
|<br />
|[http://www.math.umn.edu/~stant001/askey80 Conference in honor of Dick Askey]<br />
|<br />
|-<br />
|'''Mon, Dec. 9, 4pm, VV B239'''<br />
|[http://www.cims.nyu.edu/~jacob/ Jacob Bedrossian] (Courant Institute)<br />
|Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations<br />
|Bolotin<br />
|-<br />
|'''Wed, Dec 11, 4PM'''<br />
|[http://math.jhu.edu/~lwang/ Lu Wang] (Johns Hopkins)<br />
|Rigidity of Self-shrinkers of Mean Curvature Flow<br />
|Viaclovsky <br />
|-<br />
|'''Fri, Dec. 13, 2:25pm, VV 901'''<br />
|[http://chanwookim.wordpress.com/ Chanwoo Kim] (Cambridge)<br />
|Regularity of the Boltzmann equation in convex domains<br />
|Bolotin<br />
|-<br />
|'''Tues, Dec 17, 4PM'''<br />
|[http://www.statslab.cam.ac.uk/~ps422/ Perla Sousi] (Cambridge)<br />
|[[Colloquia#December 17: Perla Sousi (Cambridge) | The effect of drift on the volume of the Wiener sausage]]<br />
|Seppalainen <br />
|-<br />
|'''Wed, Dec 18, 4PM'''<br />
|[http://users.math.yale.edu/~dc597/ Dustin Cartwright] (Yale)<br />
|[[Colloquia#December 18: Dustin Cartwright (Yale) | Tropical Complexes]]<br />
|Gurevich<br />
|}<br />
<br />
== Spring 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Mon, Jan 6, 4PM'''<br />
|[http://www-bcf.usc.edu/~lauda/Aaron_Laudas_Page/Home.html Aaron Lauda] (USC) <br />
|[[Colloquia#January 6: Aaron Lauda (USC) | An introduction to diagrammatic categorification]]<br />
|Caldararu<br />
|-<br />
|'''Wed, Jan 8, 4PM'''<br />
|[http://www2.math.umd.edu/~kmelnick/ Karin Melnick] (Maryland) <br />
|[[Colloquia#January 8: Karin Melnick (Maryland) | Normal forms for local flows on parabolic geometries]]<br />
|Kent<br />
|-<br />
|Jan 10, 4PM<br />
|[http://users.math.yale.edu/~yd82/ Yen Do] (Yale) <br />
|Convergence of Fourier series and multilinear analysis<br />
|Denissov<br />
|-<br />
|'''Mon, Jan 13, 4pm'''<br />
|[http://math.stanford.edu/~wangyi/ Yi Wang] (Stanford)<br />
|Isoperimetric Inequality and Q-curvature<br />
|Viaclovsky<br />
|-<br />
|'''Wen, Jan 15, 4pm'''<br />
|[http://www.maths.ox.ac.uk/people/profiles/wei.xiang Wei Xiang] (University of Oxford)<br />
|[[Colloquia#January 15: Wei Xiang (University of Oxford) |Conservation Laws and Shock Waves]]<br />
|Bolotin<br />
|-<br />
|'''Fri, Jan 17, 2:25PM, VV901'''<br />
|[http://www.math.dartmouth.edu/~gillmana/ Adrianna Gillman] (Dartmouth) <br />
|Fast direct solvers for linear partial differential equations<br />
|Thiffeault<br />
|-<br />
|'''Thu, Jan 23, 2:25, VV901'''<br />
|[http://www.stat.berkeley.edu/~mshkolni/ Mykhaylo Shkolnikov] (Berkeley)<br />
|[[Colloquia#Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) | Intertwinings, wave equations and growth models]]<br />
|Seppalainen<br />
|-<br />
|Jan 24<br />
|[http://www.yanivplan.com/ Yaniv Plan] (Michigan)<br />
|Low-dimensionality in mathematical signal processing<br />
|Thiffeault<br />
|-<br />
|Jan 31<br />
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)<br />
|Underwater Networks: A Convergence of Communications, Control and Sensing<br />
|Gurevich<br />
|-<br />
|Feb 7<br />
|David Treumann (Boston College)<br />
|<br />
|Street<br />
|-<br />
|Feb 14<br />
|[http://www.tc.columbia.edu/academics/index.htm?facid=apk16 Alexander Karp] (Columbia Teacher's College)<br />
|History of Mathematics Education as a Research Field and as Magistra Vitae<br />
|Kiselev<br />
|-<br />
|Feb 21<br />
|<br />
|<br />
|<br />
|-<br />
|Feb 28<br />
|[http://math.nyu.edu/faculty/shelley/ Michael Shelley] (Courant)<br />
|<br />
|Spagnolie<br />
|-<br />
|March 7<br />
|[http://www.math.northwestern.edu/people/facultyProfiles/steve.zelditch.html Steve Zelditch] (Northwestern)<br />
|<br />
|Seeger<br />
|-<br />
|March 14<br />
|[https://www.math.ucdavis.edu/~strohmer Thomas Strohmer] (Davis)<br />
|<br />
|Gurevich<br />
|- <br />
|<strike>March 21</strike><br />
|'''Spring Break'''<br />
|No Colloquium<br />
|<br />
|-<br />
|March 28<br />
|[http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)<br />
|The Two Weight Inequality for the Hilbert Transform<br />
|Street<br />
|-<br />
|April 4<br />
|[http://www.math.brown.edu/~res/ Richard Schwartz] (Brown)<br />
|<br />
|Mari-Beffa<br />
|-<br />
|April 11<br />
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)<br />
|<br />
|Gurevich<br />
|-<br />
|April 18 (Wasow Lecture)<br />
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)<br />
|<br />
|Seeger<br />
|-<br />
|April 25<br />
|[http://www.charlesdoran.net Charles Doran](University of Alberta)<br />
|<br />
|Song<br />
|-<br />
|'''Monday, April 28''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|A mystery concerning algebraic plane curves<br />
|Maxim<br />
|-<br />
|'''Tuesday, April 29''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Matrix factorizations old and new<br />
|Maxim<br />
|-<br />
|'''Wednesday, April 30''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Easy solution of polynomial equations over finite fields<br />
|Maxim<br />
|-<br />
|May 2<br />
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)<br />
|<br />
|Boston<br />
|-<br />
|May 9<br />
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)<br />
|<br />
|WIMAW<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sep 6: Matt Baker (GA Tech) ===<br />
''Riemann-Roch for Graphs and Applications''<br />
<br />
We will begin by formulating the Riemann-Roch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a Riemann-Roch theorem for tropical curves, proved by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof of the Brill-Noether theorem in algebraic geometry (work of by Cools-Draisma-Payne-Robeva), a "volume-theoretic proof" of Kirchhoff's Matrix-Tree Theorem (work of An, Kuperberg, Shokrieh, and the speaker), and a new Chabauty-Coleman style bound for the number of rational points on an algebraic curve over the rationals (work of Katz and Zureick-Brown).<br />
<br />
===Sep 13: Uri Andrews (UW-Madison) ===<br />
''A hop, skip, and a jump through the degrees of relative provability''<br />
<br />
The topic of this talk arises from two directions. On the one hand, Gödel's incompleteness theorem tell us that given any sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic, there is a statement that is true but not provable in T. On the other hand, over the past seventy years, a number of researchers studying witnessing functions for various combinatorial statements have realized the importance of fast-growing functions and the fact that their totality is often not provable over a given sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic (e.g. the Paris-Harrington and the Kirby-Paris theorems).<br />
<br />
I will talk about the structure induced by giving the order (for a fixed T) of relative provability for totality of algorithms. That is, for algorithms describing functions f and g, we say f ≤ g if T along with the totality of g suffices to prove the totality of f. It turns out that this structure is rich, and encodes many facets of the nature of provability over sufficiently strong, consistent, effectively axiomatizable theories for first-order arithmetic. (Work joint with Mingzhong Cai, David Diamondstone, Steffen Lempp, and Joseph S. Miller.)<br />
<br />
===Sep 20: Valerio Toledano Laredo (Northeastern)===<br />
''Flat connections and quantum groups''<br />
<br />
Quantum groups are natural deformations of the Lie algebra of<br />
nxn matrices, and more generally of semisimple Lie algebras.<br />
They first arose in the mid eighties in the study of solvable<br />
models in statistical mechanics.<br />
<br />
I will explain how these algebraic objects can serve as natural<br />
receptacles for the (transcendental) monodromy of flat connections<br />
arising from representation theory.<br />
<br />
These connections exist in rational, trigonometric and elliptic<br />
forms, and lead to quantum groups of increasing interest and<br />
complexity.<br />
<br />
===Wed, Sept 25, 2:30PM Ayelet Lindenstrauss (Indiana University)===<br />
''Taylor Series in Homotopy Theory''<br />
<br />
I will discuss Goodwillie's calculus of functors on topological spaces. To mimic the set-up in real analysis, topological spaces are considered small if their nontrivial homotopy groups start only in higher dimensions. They can be considered close only in relation to a map between them, but a map allows us to construct the difference between two spaces, and two spaces are close if the difference between them is small. Spaces can be summed (in different ways) by taking twisted products of them. It is straightforward to construct the analogs of constant, linear, and higher degree homogenous functors, and they can be assembled into "polynomials" and "infinite sums". There are notions of differentiability and higher derivatives, of Taylor towers, and of analytic functions.<br />
<br />
What might look like a game of analogies is an extremely useful tool because when one looks at functors that map topological spaces not into the category of topological spaces, but into the category of spectra (the stabilized version of the category of spaces, which will be explained), many of them are, in fact, analytic, so they can be constructed from the homogenous functors of different degrees. And we can use appropriate analogs of calculus theorems to understand them better. I will conclude with some recent work of Randy McCarthy and myself, applying Goodwillie's calculus to algebraic K-theory calculations.<br />
<br />
===Sep 25: Jim Demmel (Berkeley) ===<br />
''Communication Avoiding Algorithms for Linear Algebra and Beyond''<br />
<br />
Algorithm have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present algorithms that attain provable lower bounds on communication, and show large speedups compared to their conventional counterparts. These algorithms are for direct and iterative linear algebra, for dense and sparse matrices, as well as direct n-body simulations. Several of these algorithms exhibit perfect strong scaling, in both time and energy: run time (resp. energy) for a fixed problem size drops proportionally to the number of processors p (resp. is independent of p). Finally, we describe extensions to algorithms involving arbitrary loop nests and array accesses, assuming only that array subscripts are affine functions of the loop indices. <br />
<br />
===Sep 26: Jim Demmel (Berkeley) ===<br />
''Implementing Communication Avoiding Algorithms''<br />
<br />
Designing algorithms that avoiding communication, attaining<br />
lower bounds if possible, is critical for algorithms to minimize runtime and<br />
energy on current and future architectures. These new algorithms can have <br />
new numerical stability properties, new ways to encode answers, and new data<br />
structures, not just depend on loop transformations (we need those too!).<br />
We will illustrate with a variety of examples including direct linear algebra<br />
(eg new ways to perform pivoting, new deterministic and randomized<br />
eigenvalue algorithms), iterative linear algebra (eg new ways to reorganize<br />
Krylov subspace methods) and direct n-body algorithms, on architectures<br />
ranging from multicore to distributed memory to heterogeneous.<br />
The theory describing communication avoiding algorithms can give us a large<br />
design space of possible implementations, so we use autotuning to find<br />
the fastest one automatically. Finally, on parallel architectures one can<br />
frequently not expect to get bitwise identical results from multiple runs,<br />
because of dynamic scheduling and floating point nonassociativity; <br />
this can be a problem for reasons from debugging to correctness.<br />
We discuss some techniques to get reproducible results at modest cost.<br />
<br />
===Sep 27: Jim Demmel (Berkeley) ===<br />
''Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays''<br />
<br />
Our goal is to minimize communication, i.e. moving data, since it increasingly<br />
dominates the cost of arithmetic in algorithms. Motivated by this, attainable<br />
communication lower bounds have been established by many authors for a <br />
variety of algorithms including matrix computations.<br />
<br />
The lower bound approach used initially by Irony, Tiskin and Toledo <br />
for O(n^3) matrix multiplication, and later by Ballard et al <br />
for many other linear algebra algorithms, depends on a geometric result by <br />
Loomis and Whitney: this result bounds the volume of a 3D set <br />
(representing multiply-adds done in the inner loop of the algorithm) <br />
using the product of the areas of certain 2D projections of this set <br />
(representing the matrix entries available locally, i.e., without communication).<br />
<br />
Using a recent generalization of Loomis' and Whitney's result, we generalize <br />
this lower bound approach to a much larger class of algorithms, <br />
that may have arbitrary numbers of loops and arrays with arbitrary dimensions, <br />
as long as the index expressions are affine combinations of loop variables.<br />
In other words, the algorithm can do arbitrary operations on any number of <br />
variables like A(i1,i2,i2-2*i1,3-4*i3+7*i_4,…).<br />
Moreover, the result applies to recursive programs, irregular iteration spaces, <br />
sparse matrices, and other data structures as long as the computation can be<br />
logically mapped to loops and indexed data structure accesses. <br />
<br />
We also discuss when optimal algorithms exist that attain the lower bounds; <br />
this leads to new asymptotically faster algorithms for several problems.<br />
<br />
===October 4: Frank Sottile (Texas A&M) ===<br />
''Galois groups of Schubert problems''<br />
<br />
Work of Jordan from 1870 showed how Galois theory<br />
can be applied to enumerative geometry. Hermite earlier<br />
showed the equivalence of Galois groups with geometric <br />
monodromy groups, and in 1979 Harris used this to study <br />
Galois groups of many enumerative problems. Vakil gave <br />
a geometric-combinatorial criterion that implies a Galois <br />
group contains the alternating group. With Brooks and <br />
Martin del Campo, we used Vakil's criterion to show that <br />
all Schubert problems involving lines have at least <br />
alternating Galois group. White and I have given a new <br />
proof of this based on 2-transitivity.<br />
<br />
My talk will describe this background and sketch a <br />
current project to systematically determine Galois groups <br />
of all Schubert problems of moderate size on all small <br />
classical flag manifolds, investigating at least several <br />
million problems. This will use supercomputers employing <br />
several overlapping methods, including combinatorial <br />
criteria, symbolic computation, and numerical homotopy <br />
continuation, and require the development of new <br />
algorithms and software.<br />
<br />
===October 11: Amie Wilkinson (Chicago) ===<br />
<br />
''Robust mechanisms for chaos''<br />
<br />
What are the underlying mechanisms for robustly chaotic behavior in smooth dynamics?<br />
<br />
In addressing this question, I'll focus on the study of diffeomorphisms of a compact manifold, where "chaotic" means "mixing" and and "robustly" means "stable under smooth perturbations." I'll describe recent advances in constructing and using tools called "blenders" to produce stably chaotic behavior with arbitrarily little effort.<br />
<br />
===October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) ===<br />
<br />
''Integrable probability I and II''<br />
<br />
The goal of the talks is to describe the emerging field of integrable<br />
probability, whose goal is to identify and analyze exactly solvable<br />
probabilistic models. The models and results are often easy to describe,<br />
yet difficult to find, and they carry essential information about broad<br />
universality classes of stochastic processes.<br />
<br />
<br />
===October 25: Paul Garrett (Minnesota)=== <br />
<br />
''Boundary-value problems, generalized functions, and zeros of zeta functions''<br />
<br />
Modern analysis (Beppo Levi, Sobolev, Friedrichs, Schwartz) illuminates work of D. Hejhal and Y. Colin de Verdiere from 30 years<br />
ago, clarifying, as in P. Cartier's letter to A. Weil, "how the Riemann Hypothesis was not proven". (Joint with E. Bombieri.)<br />
<br />
===November 1: Allison Lewko (Columbia University) ===<br />
<br />
''On sets of large doubling, Lambda(4) sets, and error-correcting codes''<br />
<br />
We investigate the structure of finite sets A of integers such that A+A is large, presenting a counterexample to natural conjectures in the pursuit of an "anti-Freiman" theory in additive combinatorics. We will begin with a brief history of the problem and its connection to the study of Lambda(4) sets in harmonic analysis, and then we will discuss our counterexample and its construction from error-correcting codes. We will conclude by describing some related open problems.<br />
This is joint work with Mark Lewko.<br />
<br />
===November 8: Tim Riley (Cornell)===<br />
<br />
''Hydra groups''<br />
<br />
A few years ago Will Dison and I constructed a family of<br />
finitely generated groups whose workings include a string-rewriting<br />
phenomenon of extraordinary duration which is reminiscent of Hercules'<br />
battle with the hydra. I will describe this and the investigations it<br />
spurred in hyperbolic geometry, combinatorial group theory, and a<br />
problem of how to calculate efficiently with hugely compressed<br />
representations of integers.<br />
<br />
===November 22: Tianling Jin (University of Chicago)===<br />
<br />
''Solutions of some Monge-Ampere equations with degeneracy or singularities''<br />
<br />
We will first give a new proof of a celebrated theorem of<br />
Jorgens which states that every classical convex solution of det(Hess<br />
u)=1 in R^2 has to be a second order polynomial. Our arguments do not use<br />
complex analysis, and will be applied to establish such Liouville type<br />
theorems for solutions some degenerate Monge-Ampere equations. We will<br />
also discuss some results on existence, regularity, classification, and<br />
asymptotic behavior of solutions of some Monge-Ampere equations with<br />
isolated and line singularities. This is joint work with J. Xiong.<br />
<br />
===Monday, Nov 25: Lin Lin (Lawrence Berkeley National Lab)===<br />
<br />
''Fast algorithms for electronic structure analysis''<br />
<br />
Kohn-Sham density functional theory (KSDFT) is the most widely used<br />
electronic structure theory for molecules and condensed matter systems. For<br />
a system with N electrons, the standard method for solving KSDFT requires<br />
solving N eigenvectors for an O(N) * O(N) Kohn-Sham Hamiltonian matrix.<br />
The computational cost for such procedure is expensive and scales as<br />
O(N^3). We have developed pole expansion plus selected inversion (PEXSI)<br />
method, in which KSDFT is solved by evaluating the selected elements of the<br />
inverse of a series of sparse symmetric matrices, and the overall algorithm<br />
scales at most O(N^2) for all materials including insulators,<br />
semiconductors and metals. The PEXSI method can be used with orthogonal or<br />
nonorthogonal basis set, and the physical quantities including electron<br />
density, energy, atomic force, density of states, and local density of<br />
states are calculated accurately without using the eigenvalues and<br />
eigenvectors. The recently developed massively parallel PEXSI method has<br />
been implemented in SIESTA, one of the most popular electronic structure<br />
software using atomic orbital basis set. The resulting method can allow<br />
accurate treatment of electronic structure in a unprecedented scale. We<br />
demonstrate the application of the method for solving graphene-like<br />
structures with more than 20,000 atoms, and the method can be efficiently<br />
parallelized 10,000 - 100,000 processors on Department of Energy (DOE) high<br />
performance machines.<br />
<br />
===November 26 (Tuesday): Clinton Conley (Cornell)===<br />
<br />
''Descriptive set-theoretic graph theory''<br />
<br />
Familiar graph-theoretic problems (for example, vertex coloring) exhibit a<br />
stark change of character when measurability constraints are placed on the<br />
structures and functions involved. While discussing some ramifications in<br />
descriptive set theory, we also pay special attention to interactions with<br />
probability (concerning random colorings of Cayley graphs) and ergodic<br />
theory (characterizing various dynamical properties of groups). The talk<br />
will include joint work with Alexander Kechris, Andrew Marks, Benjamin<br />
Miller, and Robin Tucker-Drob.<br />
<br />
<br />
===December 2 (Monday): Simon Marshall (Northwestern)===<br />
<br />
''Semiclassical estimates for eigenfunctions on locally symmetric spaces''<br />
<br />
Let M be a compact Riemannian manifold, and f an L^2-normalised Laplace<br />
eigenfunction on M. If p > 2, a theorem of Sogge tells us how large the L^p<br />
norm of f can be in terms of its Laplace eigenvalue. For instance, when p<br />
is infinity this is asking how large the peaks of f can be. I will present<br />
an analogue of Sogge's theorem for eigenfunctions of the full ring of<br />
invariant differential operators on a locally symmetric space, and discuss<br />
some links between this result and number theory.<br />
<br />
===December 4 (Wednesday): Steven Sam (Berkeley)===<br />
<br />
''Free Resolutions and Symmetry''<br />
<br />
This talk is about the use of symmetry in the study of modules and free resolutions in commutative algebra and algebraic geometry, and specifically how it clarifies, organizes, and rigidifies calculations, and how it enables us to find finiteness in situations where it a priori does not seem to exist. I will begin the talk with an example coming from classical invariant theory and determinantal ideals using just some basic notions from linear algebra. Then I will explain some of my own work which builds on this setting in several directions. Finally, I'll discuss a recent program on twisted commutative algebras, developed jointly with Andrew Snowden, which formalizes the synthesis of representation theory and commutative algebra and leads to new finiteness results in seemingly infinite settings.<br />
<br />
===December 6: Paul Hand (MIT)===<br />
<br />
''Simplifications of the Lifting Approach for Quadratic Signal Recovery Problems''<br />
<br />
Many signal recovery problems are quadratic in nature, such as phase<br />
retrieval and sparse principal component analysis. Such problems in<br />
R^n can be convexified by introducing n^2 variables corresponding to<br />
each quadratic combination of unknowns. This approach often gives<br />
rise to an n x n matrix recovery problem that is convex and has<br />
provable recovery guarantees. Because the dimensionality has been<br />
squared, it is an important task to find simplifications that make<br />
computation more tractable. We will discuss two examples where the<br />
lifting approach can be simplified while retaining recovery<br />
guarantees. These examples will be the phase retrieval problem and a<br />
special case of sparse principal component analysis.<br />
<br />
===December 9 (Monday): Jacob Bedrossian (Courant Institute)===<br />
<br />
''Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations''<br />
<br />
We prove asymptotic stability of shear flows close to the<br />
planar, periodic Couette flow in the 2D incompressible Euler equations.<br />
That is, given an initial perturbation of the Couette flow small in a<br />
suitable regularity class, specifically Gevrey space of class smaller than<br />
2, the velocity converges strongly in L2 to a shear flow which is also<br />
close to the Couette flow. The vorticity is asymptotically mixed to small<br />
scales by an almost linear evolution and in general enstrophy is lost in<br />
the weak limit. The strong convergence of the velocity field is sometimes<br />
referred to as inviscid damping, due to the relationship with Landau<br />
damping in the Vlasov equations. Joint work with Nader Masmoudi.<br />
<br />
===Wednesday, Dec 11: Lu Wang (Johns Hopkins)===<br />
<br />
''Rigidity of Self-shrinkers of Mean Curvature Flow''<br />
<br />
The study of mean curvature flow not only is fundamental in geometry, topology and analysis, but also has important applications in applied mathematics, for instance, image processing. One of the most important problems in mean curvature flow is to understand the possible singularities of the flow and self-shrinkers, i.e., self-shrinking solutions of the flow, provide the singularity models.<br />
<br />
In this talk, I will describe the rigidity of asymptotic structures of self-shrinkers. First, I show the uniqueness of properly embedded self-shrinkers asymptotic to any given regular cone. Next, I give a partial affirmative answer to a conjecture of Ilmanen under an infinite order asymptotic assumption, which asserts that the only two-dimensional properly embedded self-shrinker asymptotic to a cylinder along some end is itself the cylinder. The feature of our results is that no completeness of self-shrinkers is required.<br />
<br />
The key ingredients in the proof are a novel reduction of unique continuation for elliptic operators to backwards uniqueness for parabolic operators and the Carleman type techniques. If time permits, I will discuss some applications of our approach to shrinking solitons of Ricci flow.<br />
<br />
===Friday, Dec 13: Chanwoo Kim (Cambridge)===<br />
<br />
''Regularity of the Boltzmann equation in convex domains''<br />
<br />
A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the Boltzmann equation in a strictly convex domain with the specular, bounce-back and diffuse boundary condition. With the aid of a distance function toward the grazing set, we construct weighted classical <math>C^{1}</math> solutions away from the grazing set for all boundary conditions. For the diffuse boundary condition, we construct <math>W^{1,p}</math> solutions for 1< p<2 and weighted <math>W^{1,p}</math> solutions for <math>2\leq p\leq \infty</math> as well. On the other hand, we show second derivatives do not exist up to the boundary in general by constructing counterexamples for all boundary conditions. This is a joint work with Guo, Tonon, Trescases.<br />
<br />
===December 17: Perla Sousi (Cambridge)===<br />
<br />
''The effect of drift on the volume of the Wiener sausage''<br />
<br />
The Wiener sausage at time t is the algebraic sum of a Brownian path on [0,t] and a ball. Does the expected volume of the Wiener sausage increase when we add drift?<br />
How do you compare the expected volume of the usual Wiener sausage to one defined as the algebraic sum of the Brownian path and a square (in 2D) or a cube (in higher dimensions)? We will answer these questions using their relation to the detection problem for Poisson Brownian motions, and rearrangement inequalities on the sphere (with Y. Peres). We will also discuss generalisations of this to Levy processes (with A. Drewitz and R. Sun) as well as an adversarial detection problem and its connections to Kakeya sets (with Babichenko, Peres, Peretz and Winkler).<br />
<br />
<br />
===December 18: Dustin Cartwright (Yale)===<br />
<br />
''Tropical Complexes''<br />
<br />
Tropical geometry is a way of understanding algebraic varieties by the limiting behavior of their degenerations. Through tropicalization, algebraic operations are replaced with combinatorial constructions and piecewise linear functions. I will introduce tropical complexes, which a way of understanding the geometry of algebraic varieties through combinatorics. Tropical complexes are Delta-complexes together with additional integral data, for which one has parallels and concrete comparisons with the behavior of algebraic varieties. <br />
<br />
===January 6: Aaron Lauda (USC)===<br />
<br />
''An introduction to diagrammatic categorification''<br />
<br />
Categorification seeks to reveal a hidden layer in mathematical<br />
structures. Often the resulting structures can be combinatorially<br />
complex objects making them difficult to study. One method of<br />
overcoming this difficulty, that has proven very successful, is to<br />
encode the categorification into a diagrammatic calculus that makes<br />
computations simple and intuitive.<br />
<br />
In this talk I will review some of the original considerations that<br />
led to the categorification philosophy. We will examine how the<br />
diagrammatic perspective has helped to produce new categorifications<br />
having profound applications to algebra, representation theory, and<br />
low-dimensional topology.<br />
<br />
===January 8: Karin Melnick (Maryland)===<br />
<br />
''Normal forms for local flows on parabolic geometries''<br />
<br />
The exponential map in Riemannian geometry conjugates the differential of an isometry at a point with the action of the isometry near the point. It thus provides a linear normal form for all isometries fixing a point. Conformal transformations are not linearizable in general. I will discuss a suite of normal forms theorems in conformal geometry and, more generally, for parabolic geometries, a rich family of geometric structures of which conformal, projective, and CR structures are examples.<br />
<br />
===January 10, 4PM: Yen Do (Yale)===<br />
<br />
''Convergence of Fourier series and multilinear analysis''<br />
<br />
Almost everywhere convergence of the Fourier series of square <br />
integrable functions was first proved by Lennart Carleson in 1966, and <br />
the proof has lead to deep developments in various multilinear settings. <br />
In this talk I would like to introduce a brief history of the subject <br />
and sketch some recent developments, some of these involve my joint <br />
works with collaborators.<br />
<br />
===Mon, January 13: Yi Wang (Stanford)===<br />
<br />
''Isoperimetric Inequality and Q-curvature''<br />
<br />
A well-known question in differential geometry is to prove the<br />
isoperimetric inequality under intrinsic curvature conditions. In<br />
dimension 2, the isoperimetric inequality is controlled by the integral of<br />
the positive part of the Gaussian curvature. In my recent work, I prove<br />
that on simply connected conformally flat manifolds of higher dimensions,<br />
the role of the Gaussian curvature can be replaced by the Branson's<br />
Q-curvature. The isoperimetric inequality is valid if the integral of the<br />
Q-curvature is below a sharp threshold. Moreover, the isoperimetric<br />
constant depends only on the integrals of the Q-curvature. The proof<br />
relies on the theory of $A_p$ weights in harmonic analysis.<br />
<br />
===January 15: Wei Xiang (University of Oxford)===<br />
<br />
''Conservation Laws and Shock Waves''<br />
<br />
The study of continuum physics gave birth to the theory of quasilinear<br />
systems in divergence form, commonly called conservation laws. In this<br />
talk, conservation laws, the Euler equations, and the definition of the<br />
corresponding weak solutions will be introduced first. Then a short history<br />
of the studying of conservation laws and shock waves will be given. Finally<br />
I would like to present two of our current research projects. One is on the<br />
mathematical analysis of shock diffraction by convex cornered wedges, and<br />
the other one is on the validation of weakly nonlinear geometric optics for<br />
entropy solutions of nonlinear hyperbolic systems of conservation laws.<br />
<br />
Fri, Jan 17, 2:25PM, VV901 Adrianna Gillman (Dartmouth) Fast direct solvers for linear partial differential equations<br />
<br />
===Fri, Jan 17: Adrianna Gillman (Dartmouth) ===<br />
''Fast direct solvers for linear partial differential equations''<br />
<br />
The cost of solving a large linear system often determines what can and cannot be modeled computationally in many areas of science and engineering. Unlike Gaussian elimination which scales cubically with the respect to the number of unknowns, fast direct solvers construct an inverse of a linear in system with a cost that scales linearly or nearly linearly. The fast direct solvers presented in this talk are designed for the linear systems arising from the discretization of linear partial differential equations. These methods are more robust, versatile and stable than iterative schemes. Since an inverse is computed, additional right-hand sides can be processed rapidly. The talk will give the audience a brief introduction to the core ideas, an overview of recent advancements, and it will conclude with a sampling of challenging application examples including the scattering of waves.<br />
<br />
===Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) ===<br />
''Intertwinings, wave equations and growth models''<br />
<br />
We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to hyperbolic partial differential equations, symmetric polynomials and the corresponding random growth models. The talk will be devoted to these recent developments which also shed new light on some beautiful old examples of intertwinings. Based on joint works with Vadim Gorin and Soumik Pal. <br />
<br />
<br />
===Jan 24: Yaniv Plan (Michigan) ===<br />
''Low-dimensionality in mathematical signal processing''<br />
<br />
Natural images tend to be compressible, i.e., the amount of information needed to encode an image is small. This conciseness of information -- in other words, low dimensionality of the signal -- is found throughout a plethora of applications ranging from MRI to quantum state tomography. It is natural to ask: can the number of measurements needed to determine a signal be comparable with the information content? We explore this question under modern models of low-dimensionality and measurement acquisition.<br />
<br />
===Thur, Jan 30: Urbashi Mitra (USC) ===<br />
''Underwater Networks: A Convergence of Communications, Control and Sensing''<br />
<br />
The oceans cover 71% of the earth’s surface and represent one of the least explored frontiers, yet the oceans are integral to climate regulation, nutrient production, oil retrieval and transportation. Future scientific and technological efforts to achieve better understanding of oceans and water-related applications will rely heavily on our ability to communicate reliably between instruments, vehicles (manned and unmanned), human operators, platforms and sensors of all types. Underwater acoustic communication techniques have not reached the same maturity as those for terrestrial radio communications and present some unique opportunities for new developments in information and communication theories. Key features of underwater acoustic communication channels are examined: slow speed of propagation, significant delay spreads, sparse multi-path, time-variation and range-dependent available bandwidth. Another unique feature of underwater networks is that the cost of communication, sensing and control are often comparable resulting in new tradeoffs between these activities. We examine some new results (with implications wider than underwater systems) in channel identifiability, communicating over channels with state and cooperative game theory motivated by the underwater network application.<br />
<br />
<br />
===Feb 14: Alexander Karp (Columbia Teacher's College) ===<br />
''History of Mathematics Education as a Research Field and as Magistra Vitae''<br />
<br />
The presentation will be based on the experience of putting together and editing the Handbook<br />
on the History of Mathematics Education, which will be published by Springer in the near future. <br />
This volume, which was prepared by a large group of researchers from different countries, <br />
contains the first systematic account of the history of the development of mathematics education <br />
in the whole world (and not just in some particular country or region). The editing of such a <br />
book gave rise to thoughts about the methodology of research in this field, and also about what <br />
constitutes an object of such research. These are the thoughts that the presenter intends to share <br />
with his audience. From them, it is natural to pass to an analysis of the current situation and how <br />
it might develop.<br />
<br />
<br />
<br />
===March 28: Michael Lacey (GA Tech) ===<br />
''The Two Weight Inequality for the Hilbert Transform''<br />
<br />
The individual two weight inequality for the Hilbert transform <br />
asks for a real variable characterization of those pairs of weights <br />
(u,v) for which the Hilbert transform H maps L^2(u) to L^2(v). <br />
This question arises naturally in different settings, most famously <br />
in work of Sarason. Answering in the positive a deep <br />
conjecture of Nazarov-Treil-Volberg, the mapping property <br />
of the Hilbert transform is characterized by a triple of conditions, <br />
the first being a two-weight Poisson A2 on the pair of weights, <br />
with a pair of so-called testing inequalities, uniform over all <br />
intervals. This is the first result of this type for a singular <br />
integral operator. (Joint work with Sawyer, C.-Y. Shen and Uriate-Tuero)<br />
<br />
== Past talks ==<br />
<br />
Last year's schedule: [[Colloquia 2012-2013]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=6387Colloquia/Fall182014-01-19T22:02:51Z<p>Shamgar: /* Abstracts */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Fall 2013 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
|[http://people.math.gatech.edu/~mbaker/ Matt Baker] (Georgia Institute of Technology)<br />
|Riemann-Roch for Graphs and Applications<br />
|Ellenberg<br />
|-<br />
|Sept 13<br />
|[http://math.wisc.edu/~andrews/ Uri Andrews] (University of Wisconsin)<br />
|A hop, skip, and a jump through the degrees of relative provability<br />
|<br />
|-<br />
|Sept 20<br />
|[http://www.math.neu.edu/people/profile/valerio-toledano-laredo Valerio Toledano Laredo] (Northeastern)<br />
|Flat connections and quantum groups<br />
|Gurevich<br />
|-<br />
|'''Wed, Sept 25, 2:30PM in B139'''<br />
|[http://mypage.iu.edu/~alindens/ Ayelet Lindenstrauss] (Indiana University)<br />
|Taylor Series in Homotopy Theory<br />
|Meyer<br />
|-<br />
|'''Wed, Sept 25''' (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication-Avoiding Algorithms for Linear Algebra and Beyond<br />
|Gurevich<br />
|-<br />
|'''Thurs, Sept 26''' (LAA lecture, Joint with Applied Algebra Seminar)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Implementing Communication-Avoiding Algorithms<br />
|Gurevich<br />
|-<br />
|Sept 27 (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays<br />
|Gurevich<br />
|-<br />
|Oct 4<br />
|[http://www.math.tamu.edu/~sottile/ Frank Sottile] (Texas A&M)<br />
|Galois groups of Schubert problems<br />
|Caldararu<br />
|-<br />
|Oct 11<br />
|[http://math.uchicago.edu/~wilkinso/ Amie Wilkinson] (Chicago)<br />
|[[Colloquia#October 11: Amie Wilkinson (Chicago) | Robust mechanisms for chaos]]<br />
|WIMAW (Cladek)<br />
|-<br />
|'''Tues, Oct 15, 4PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability I]]<br />
|Valko<br />
|-<br />
|'''Wed, Oct 16, 2:30PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability II]]<br />
|Valko<br />
|-<br />
|<strike>Oct 18</strike><br />
|No colloquium due to the distinguished lecture<br />
|<br />
|<br />
|-<br />
|Oct 25<br />
|[http://www.math.umn.edu/~garrett/ Paul Garrett] (Minnesota)<br />
|[[Colloquia#October 25: Paul Garrett (Minnesota) | Boundary-value problems, generalized functions, and zeros of zeta functions]]<br />
|Gurevich<br />
|<br />
|<br />
|-<br />
|Nov 1<br />
|[http://www.cs.columbia.edu/~alewko/ Allison Lewko] (Columbia University)<br />
|On sets of large doubling, Lambda(4) sets, and error-correcting codes<br />
|Stovall<br />
|-<br />
|Nov 8<br />
|[http://www.math.cornell.edu/~riley/ Tim Riley] (Cornell)<br />
|[[Colloquia#November 8: Tim Riley (Cornell) | Hydra groups]]<br />
|Dymarz<br />
|-<br />
|Nov 15 and later<br />
|Reserved<br />
|<br />
|Street<br />
|-<br />
|Nov 22<br />
|[http://www.math.uchicago.edu/~tj/ Tianling Jin] (University of Chicago)<br />
|Solutions of some Monge-Ampere equations with degeneracy or singularities.<br />
|Bolotin<br />
|-<br />
|'''Mon, Nov 25, 4PM'''<br />
|[https://web.math.princeton.edu/~linlin/ Lin Lin] (Lawrence Berkeley National Lab)<br />
|Fast algorithms for electronic structure analysis<br />
|Jin<br />
|-<br />
|'''Tue, Nov 26, 4PM, B139'''<br />
|[http://www.math.cornell.edu/m/People/Faculty/conley Clinton Conley] (Cornell)<br />
|[[Colloquia#November 26 (Tuesday): Clinton Conley (Cornell) | Descriptive set-theoretic graph theory]]<br />
|Lempp<br />
|-<br />
|'''Mon, Dec 2, 4PM'''<br />
|[http://www.math.northwestern.edu/~slm/ Simon Marshall] (Northwestern)<br />
|[[Colloquia#December 2 (Monday): Simon Marshall (Northwestern) | Semiclassical estimates for eigenfunctions on locally symmetric spaces]]<br />
|Denissov<br />
|-<br />
|'''Wed, Dec 4, 4PM'''<br />
|[http://math.berkeley.edu/~svs/ Steven Sam] (Berkeley)<br />
|Free Resolutions and Symmetry<br />
|Boston <br />
|-<br />
|'''Fri, Dec 6'''<br />
|[http://math.mit.edu/~hand/ Paul Hand] (MIT)<br />
|[[Colloquia#December 6: Paul Hand (MIT) | Simplifications of the lifting approach for quadratic signal recovery problems]]<br />
|Thiffeault<br />
|-<br />
|'''Fri, Dec. 6 and Sat Dec. 7'''<br />
|<br />
|[http://www.math.umn.edu/~stant001/askey80 Conference in honor of Dick Askey]<br />
|<br />
|-<br />
|'''Mon, Dec. 9, 4pm, VV B239'''<br />
|[http://www.cims.nyu.edu/~jacob/ Jacob Bedrossian] (Courant Institute)<br />
|Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations<br />
|Bolotin<br />
|-<br />
|'''Wed, Dec 11, 4PM'''<br />
|[http://math.jhu.edu/~lwang/ Lu Wang] (Johns Hopkins)<br />
|Rigidity of Self-shrinkers of Mean Curvature Flow<br />
|Viaclovsky <br />
|-<br />
|'''Fri, Dec. 13, 2:25pm, VV 901'''<br />
|[http://chanwookim.wordpress.com/ Chanwoo Kim] (Cambridge)<br />
|Regularity of the Boltzmann equation in convex domains<br />
|Bolotin<br />
|-<br />
|'''Tues, Dec 17, 4PM'''<br />
|[http://www.statslab.cam.ac.uk/~ps422/ Perla Sousi] (Cambridge)<br />
|[[Colloquia#December 17: Perla Sousi (Cambridge) | The effect of drift on the volume of the Wiener sausage]]<br />
|Seppalainen <br />
|-<br />
|'''Wed, Dec 18, 4PM'''<br />
|[http://users.math.yale.edu/~dc597/ Dustin Cartwright] (Yale)<br />
|[[Colloquia#December 18: Dustin Cartwright (Yale) | Tropical Complexes]]<br />
|Gurevich<br />
|}<br />
<br />
== Spring 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Mon, Jan 6, 4PM'''<br />
|[http://www-bcf.usc.edu/~lauda/Aaron_Laudas_Page/Home.html Aaron Lauda] (USC) <br />
|[[Colloquia#January 6: Aaron Lauda (USC) | An introduction to diagrammatic categorification]]<br />
|Caldararu<br />
|-<br />
|'''Wed, Jan 8, 4PM'''<br />
|[http://www2.math.umd.edu/~kmelnick/ Karin Melnick] (Maryland) <br />
|[[Colloquia#January 8: Karin Melnick (Maryland) | Normal forms for local flows on parabolic geometries]]<br />
|Kent<br />
|-<br />
|Jan 10, 4PM<br />
|[http://users.math.yale.edu/~yd82/ Yen Do] (Yale) <br />
|Convergence of Fourier series and multilinear analysis<br />
|Denissov<br />
|-<br />
|'''Mon, Jan 13, 4pm'''<br />
|[http://math.stanford.edu/~wangyi/ Yi Wang] (Stanford)<br />
|Isoperimetric Inequality and Q-curvature<br />
|Viaclovsky<br />
|-<br />
|'''Wen, Jan 15, 4pm'''<br />
|[http://www.maths.ox.ac.uk/people/profiles/wei.xiang Wei Xiang] (University of Oxford)<br />
|[[Colloquia#January 15: Wei Xiang (University of Oxford) |Conservation Laws and Shock Waves]]<br />
|Bolotin<br />
|-<br />
|'''Fri, Jan 17, 2:25PM, VV901'''<br />
|[http://www.math.dartmouth.edu/~gillmana/ Adrianna Gillman] (Dartmouth) <br />
|Fast direct solvers for linear partial differential equations<br />
|Thiffeault<br />
|-<br />
|'''Thu, Jan 23, 2:25, VV901'''<br />
|[http://www.stat.berkeley.edu/~mshkolni/ Mykhaylo Shkolnikov] (Berkeley)<br />
|[[Colloquia#Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) | Intertwinings, wave equations and growth models]]<br />
|Seppalainen<br />
|-<br />
|Jan 24<br />
|[http://www.yanivplan.com/ Yaniv Plan] (Michigan)<br />
|Low-dimensionality in mathematical signal processing<br />
|Thiffeault<br />
|-<br />
|Jan 31<br />
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)<br />
|[[Colloquia#Fri, Jan 31: Urbashi Mitra] (USC)| Underwater Networks: A Convergence of Communications, Control and Sensing]]<br />
|Gurevich<br />
|-<br />
|Feb 7<br />
|David Treumann (Boston College)<br />
|<br />
|Street<br />
|-<br />
|Feb 14<br />
|[http://www.tc.columbia.edu/academics/index.htm?facid=apk16 Alexander Karp] (Columbia Teacher's College)<br />
|History of Mathematics Education as a Research Field and as Magistra Vitae<br />
|Kiselev<br />
|-<br />
|Feb 21<br />
|<br />
|<br />
|<br />
|-<br />
|Feb 28<br />
|[http://math.nyu.edu/faculty/shelley/ Michael Shelley] (Courant)<br />
|<br />
|Spagnolie<br />
|-<br />
|March 7<br />
|[http://www.math.northwestern.edu/people/facultyProfiles/steve.zelditch.html Steve Zelditch] (Northwestern)<br />
|<br />
|Seeger<br />
|-<br />
|March 14<br />
|[https://www.math.ucdavis.edu/~strohmer Thomas Strohmer] (Davis)<br />
|<br />
|Gurevich<br />
|- <br />
|<strike>March 21</strike><br />
|'''Spring Break'''<br />
|No Colloquium<br />
|<br />
|-<br />
|March 28<br />
|[http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)<br />
|The Two Weight Inequality for the Hilbert Transform<br />
|Street<br />
|-<br />
|April 4<br />
|[http://www.math.brown.edu/~res/ Richard Schwartz] (Brown)<br />
|<br />
|Mari-Beffa<br />
|-<br />
|April 11<br />
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)<br />
|<br />
|Gurevich<br />
|-<br />
|April 18 (Wasow Lecture)<br />
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)<br />
|<br />
|Seeger<br />
|-<br />
|April 25<br />
|[http://www.charlesdoran.net Charles Doran](University of Alberta)<br />
|<br />
|Song<br />
|-<br />
|'''Monday, April 28''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|A mystery concerning algebraic plane curves<br />
|Maxim<br />
|-<br />
|'''Tuesday, April 29''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Matrix factorizations old and new<br />
|Maxim<br />
|-<br />
|'''Wednesday, April 30''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Easy solution of polynomial equations over finite fields<br />
|Maxim<br />
|-<br />
|May 2<br />
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)<br />
|<br />
|Boston<br />
|-<br />
|May 9<br />
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)<br />
|<br />
|WIMAW<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sep 6: Matt Baker (GA Tech) ===<br />
''Riemann-Roch for Graphs and Applications''<br />
<br />
We will begin by formulating the Riemann-Roch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a Riemann-Roch theorem for tropical curves, proved by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof of the Brill-Noether theorem in algebraic geometry (work of by Cools-Draisma-Payne-Robeva), a "volume-theoretic proof" of Kirchhoff's Matrix-Tree Theorem (work of An, Kuperberg, Shokrieh, and the speaker), and a new Chabauty-Coleman style bound for the number of rational points on an algebraic curve over the rationals (work of Katz and Zureick-Brown).<br />
<br />
===Sep 13: Uri Andrews (UW-Madison) ===<br />
''A hop, skip, and a jump through the degrees of relative provability''<br />
<br />
The topic of this talk arises from two directions. On the one hand, Gödel's incompleteness theorem tell us that given any sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic, there is a statement that is true but not provable in T. On the other hand, over the past seventy years, a number of researchers studying witnessing functions for various combinatorial statements have realized the importance of fast-growing functions and the fact that their totality is often not provable over a given sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic (e.g. the Paris-Harrington and the Kirby-Paris theorems).<br />
<br />
I will talk about the structure induced by giving the order (for a fixed T) of relative provability for totality of algorithms. That is, for algorithms describing functions f and g, we say f ≤ g if T along with the totality of g suffices to prove the totality of f. It turns out that this structure is rich, and encodes many facets of the nature of provability over sufficiently strong, consistent, effectively axiomatizable theories for first-order arithmetic. (Work joint with Mingzhong Cai, David Diamondstone, Steffen Lempp, and Joseph S. Miller.)<br />
<br />
===Sep 20: Valerio Toledano Laredo (Northeastern)===<br />
''Flat connections and quantum groups''<br />
<br />
Quantum groups are natural deformations of the Lie algebra of<br />
nxn matrices, and more generally of semisimple Lie algebras.<br />
They first arose in the mid eighties in the study of solvable<br />
models in statistical mechanics.<br />
<br />
I will explain how these algebraic objects can serve as natural<br />
receptacles for the (transcendental) monodromy of flat connections<br />
arising from representation theory.<br />
<br />
These connections exist in rational, trigonometric and elliptic<br />
forms, and lead to quantum groups of increasing interest and<br />
complexity.<br />
<br />
===Wed, Sept 25, 2:30PM Ayelet Lindenstrauss (Indiana University)===<br />
''Taylor Series in Homotopy Theory''<br />
<br />
I will discuss Goodwillie's calculus of functors on topological spaces. To mimic the set-up in real analysis, topological spaces are considered small if their nontrivial homotopy groups start only in higher dimensions. They can be considered close only in relation to a map between them, but a map allows us to construct the difference between two spaces, and two spaces are close if the difference between them is small. Spaces can be summed (in different ways) by taking twisted products of them. It is straightforward to construct the analogs of constant, linear, and higher degree homogenous functors, and they can be assembled into "polynomials" and "infinite sums". There are notions of differentiability and higher derivatives, of Taylor towers, and of analytic functions.<br />
<br />
What might look like a game of analogies is an extremely useful tool because when one looks at functors that map topological spaces not into the category of topological spaces, but into the category of spectra (the stabilized version of the category of spaces, which will be explained), many of them are, in fact, analytic, so they can be constructed from the homogenous functors of different degrees. And we can use appropriate analogs of calculus theorems to understand them better. I will conclude with some recent work of Randy McCarthy and myself, applying Goodwillie's calculus to algebraic K-theory calculations.<br />
<br />
===Sep 25: Jim Demmel (Berkeley) ===<br />
''Communication Avoiding Algorithms for Linear Algebra and Beyond''<br />
<br />
Algorithm have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present algorithms that attain provable lower bounds on communication, and show large speedups compared to their conventional counterparts. These algorithms are for direct and iterative linear algebra, for dense and sparse matrices, as well as direct n-body simulations. Several of these algorithms exhibit perfect strong scaling, in both time and energy: run time (resp. energy) for a fixed problem size drops proportionally to the number of processors p (resp. is independent of p). Finally, we describe extensions to algorithms involving arbitrary loop nests and array accesses, assuming only that array subscripts are affine functions of the loop indices. <br />
<br />
===Sep 26: Jim Demmel (Berkeley) ===<br />
''Implementing Communication Avoiding Algorithms''<br />
<br />
Designing algorithms that avoiding communication, attaining<br />
lower bounds if possible, is critical for algorithms to minimize runtime and<br />
energy on current and future architectures. These new algorithms can have <br />
new numerical stability properties, new ways to encode answers, and new data<br />
structures, not just depend on loop transformations (we need those too!).<br />
We will illustrate with a variety of examples including direct linear algebra<br />
(eg new ways to perform pivoting, new deterministic and randomized<br />
eigenvalue algorithms), iterative linear algebra (eg new ways to reorganize<br />
Krylov subspace methods) and direct n-body algorithms, on architectures<br />
ranging from multicore to distributed memory to heterogeneous.<br />
The theory describing communication avoiding algorithms can give us a large<br />
design space of possible implementations, so we use autotuning to find<br />
the fastest one automatically. Finally, on parallel architectures one can<br />
frequently not expect to get bitwise identical results from multiple runs,<br />
because of dynamic scheduling and floating point nonassociativity; <br />
this can be a problem for reasons from debugging to correctness.<br />
We discuss some techniques to get reproducible results at modest cost.<br />
<br />
===Sep 27: Jim Demmel (Berkeley) ===<br />
''Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays''<br />
<br />
Our goal is to minimize communication, i.e. moving data, since it increasingly<br />
dominates the cost of arithmetic in algorithms. Motivated by this, attainable<br />
communication lower bounds have been established by many authors for a <br />
variety of algorithms including matrix computations.<br />
<br />
The lower bound approach used initially by Irony, Tiskin and Toledo <br />
for O(n^3) matrix multiplication, and later by Ballard et al <br />
for many other linear algebra algorithms, depends on a geometric result by <br />
Loomis and Whitney: this result bounds the volume of a 3D set <br />
(representing multiply-adds done in the inner loop of the algorithm) <br />
using the product of the areas of certain 2D projections of this set <br />
(representing the matrix entries available locally, i.e., without communication).<br />
<br />
Using a recent generalization of Loomis' and Whitney's result, we generalize <br />
this lower bound approach to a much larger class of algorithms, <br />
that may have arbitrary numbers of loops and arrays with arbitrary dimensions, <br />
as long as the index expressions are affine combinations of loop variables.<br />
In other words, the algorithm can do arbitrary operations on any number of <br />
variables like A(i1,i2,i2-2*i1,3-4*i3+7*i_4,…).<br />
Moreover, the result applies to recursive programs, irregular iteration spaces, <br />
sparse matrices, and other data structures as long as the computation can be<br />
logically mapped to loops and indexed data structure accesses. <br />
<br />
We also discuss when optimal algorithms exist that attain the lower bounds; <br />
this leads to new asymptotically faster algorithms for several problems.<br />
<br />
===October 4: Frank Sottile (Texas A&M) ===<br />
''Galois groups of Schubert problems''<br />
<br />
Work of Jordan from 1870 showed how Galois theory<br />
can be applied to enumerative geometry. Hermite earlier<br />
showed the equivalence of Galois groups with geometric <br />
monodromy groups, and in 1979 Harris used this to study <br />
Galois groups of many enumerative problems. Vakil gave <br />
a geometric-combinatorial criterion that implies a Galois <br />
group contains the alternating group. With Brooks and <br />
Martin del Campo, we used Vakil's criterion to show that <br />
all Schubert problems involving lines have at least <br />
alternating Galois group. White and I have given a new <br />
proof of this based on 2-transitivity.<br />
<br />
My talk will describe this background and sketch a <br />
current project to systematically determine Galois groups <br />
of all Schubert problems of moderate size on all small <br />
classical flag manifolds, investigating at least several <br />
million problems. This will use supercomputers employing <br />
several overlapping methods, including combinatorial <br />
criteria, symbolic computation, and numerical homotopy <br />
continuation, and require the development of new <br />
algorithms and software.<br />
<br />
===October 11: Amie Wilkinson (Chicago) ===<br />
<br />
''Robust mechanisms for chaos''<br />
<br />
What are the underlying mechanisms for robustly chaotic behavior in smooth dynamics?<br />
<br />
In addressing this question, I'll focus on the study of diffeomorphisms of a compact manifold, where "chaotic" means "mixing" and and "robustly" means "stable under smooth perturbations." I'll describe recent advances in constructing and using tools called "blenders" to produce stably chaotic behavior with arbitrarily little effort.<br />
<br />
===October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) ===<br />
<br />
''Integrable probability I and II''<br />
<br />
The goal of the talks is to describe the emerging field of integrable<br />
probability, whose goal is to identify and analyze exactly solvable<br />
probabilistic models. The models and results are often easy to describe,<br />
yet difficult to find, and they carry essential information about broad<br />
universality classes of stochastic processes.<br />
<br />
<br />
===October 25: Paul Garrett (Minnesota)=== <br />
<br />
''Boundary-value problems, generalized functions, and zeros of zeta functions''<br />
<br />
Modern analysis (Beppo Levi, Sobolev, Friedrichs, Schwartz) illuminates work of D. Hejhal and Y. Colin de Verdiere from 30 years<br />
ago, clarifying, as in P. Cartier's letter to A. Weil, "how the Riemann Hypothesis was not proven". (Joint with E. Bombieri.)<br />
<br />
===November 1: Allison Lewko (Columbia University) ===<br />
<br />
''On sets of large doubling, Lambda(4) sets, and error-correcting codes''<br />
<br />
We investigate the structure of finite sets A of integers such that A+A is large, presenting a counterexample to natural conjectures in the pursuit of an "anti-Freiman" theory in additive combinatorics. We will begin with a brief history of the problem and its connection to the study of Lambda(4) sets in harmonic analysis, and then we will discuss our counterexample and its construction from error-correcting codes. We will conclude by describing some related open problems.<br />
This is joint work with Mark Lewko.<br />
<br />
===November 8: Tim Riley (Cornell)===<br />
<br />
''Hydra groups''<br />
<br />
A few years ago Will Dison and I constructed a family of<br />
finitely generated groups whose workings include a string-rewriting<br />
phenomenon of extraordinary duration which is reminiscent of Hercules'<br />
battle with the hydra. I will describe this and the investigations it<br />
spurred in hyperbolic geometry, combinatorial group theory, and a<br />
problem of how to calculate efficiently with hugely compressed<br />
representations of integers.<br />
<br />
===November 22: Tianling Jin (University of Chicago)===<br />
<br />
''Solutions of some Monge-Ampere equations with degeneracy or singularities''<br />
<br />
We will first give a new proof of a celebrated theorem of<br />
Jorgens which states that every classical convex solution of det(Hess<br />
u)=1 in R^2 has to be a second order polynomial. Our arguments do not use<br />
complex analysis, and will be applied to establish such Liouville type<br />
theorems for solutions some degenerate Monge-Ampere equations. We will<br />
also discuss some results on existence, regularity, classification, and<br />
asymptotic behavior of solutions of some Monge-Ampere equations with<br />
isolated and line singularities. This is joint work with J. Xiong.<br />
<br />
===Monday, Nov 25: Lin Lin (Lawrence Berkeley National Lab)===<br />
<br />
''Fast algorithms for electronic structure analysis''<br />
<br />
Kohn-Sham density functional theory (KSDFT) is the most widely used<br />
electronic structure theory for molecules and condensed matter systems. For<br />
a system with N electrons, the standard method for solving KSDFT requires<br />
solving N eigenvectors for an O(N) * O(N) Kohn-Sham Hamiltonian matrix.<br />
The computational cost for such procedure is expensive and scales as<br />
O(N^3). We have developed pole expansion plus selected inversion (PEXSI)<br />
method, in which KSDFT is solved by evaluating the selected elements of the<br />
inverse of a series of sparse symmetric matrices, and the overall algorithm<br />
scales at most O(N^2) for all materials including insulators,<br />
semiconductors and metals. The PEXSI method can be used with orthogonal or<br />
nonorthogonal basis set, and the physical quantities including electron<br />
density, energy, atomic force, density of states, and local density of<br />
states are calculated accurately without using the eigenvalues and<br />
eigenvectors. The recently developed massively parallel PEXSI method has<br />
been implemented in SIESTA, one of the most popular electronic structure<br />
software using atomic orbital basis set. The resulting method can allow<br />
accurate treatment of electronic structure in a unprecedented scale. We<br />
demonstrate the application of the method for solving graphene-like<br />
structures with more than 20,000 atoms, and the method can be efficiently<br />
parallelized 10,000 - 100,000 processors on Department of Energy (DOE) high<br />
performance machines.<br />
<br />
===November 26 (Tuesday): Clinton Conley (Cornell)===<br />
<br />
''Descriptive set-theoretic graph theory''<br />
<br />
Familiar graph-theoretic problems (for example, vertex coloring) exhibit a<br />
stark change of character when measurability constraints are placed on the<br />
structures and functions involved. While discussing some ramifications in<br />
descriptive set theory, we also pay special attention to interactions with<br />
probability (concerning random colorings of Cayley graphs) and ergodic<br />
theory (characterizing various dynamical properties of groups). The talk<br />
will include joint work with Alexander Kechris, Andrew Marks, Benjamin<br />
Miller, and Robin Tucker-Drob.<br />
<br />
<br />
===December 2 (Monday): Simon Marshall (Northwestern)===<br />
<br />
''Semiclassical estimates for eigenfunctions on locally symmetric spaces''<br />
<br />
Let M be a compact Riemannian manifold, and f an L^2-normalised Laplace<br />
eigenfunction on M. If p > 2, a theorem of Sogge tells us how large the L^p<br />
norm of f can be in terms of its Laplace eigenvalue. For instance, when p<br />
is infinity this is asking how large the peaks of f can be. I will present<br />
an analogue of Sogge's theorem for eigenfunctions of the full ring of<br />
invariant differential operators on a locally symmetric space, and discuss<br />
some links between this result and number theory.<br />
<br />
===December 4 (Wednesday): Steven Sam (Berkeley)===<br />
<br />
''Free Resolutions and Symmetry''<br />
<br />
This talk is about the use of symmetry in the study of modules and free resolutions in commutative algebra and algebraic geometry, and specifically how it clarifies, organizes, and rigidifies calculations, and how it enables us to find finiteness in situations where it a priori does not seem to exist. I will begin the talk with an example coming from classical invariant theory and determinantal ideals using just some basic notions from linear algebra. Then I will explain some of my own work which builds on this setting in several directions. Finally, I'll discuss a recent program on twisted commutative algebras, developed jointly with Andrew Snowden, which formalizes the synthesis of representation theory and commutative algebra and leads to new finiteness results in seemingly infinite settings.<br />
<br />
===December 6: Paul Hand (MIT)===<br />
<br />
''Simplifications of the Lifting Approach for Quadratic Signal Recovery Problems''<br />
<br />
Many signal recovery problems are quadratic in nature, such as phase<br />
retrieval and sparse principal component analysis. Such problems in<br />
R^n can be convexified by introducing n^2 variables corresponding to<br />
each quadratic combination of unknowns. This approach often gives<br />
rise to an n x n matrix recovery problem that is convex and has<br />
provable recovery guarantees. Because the dimensionality has been<br />
squared, it is an important task to find simplifications that make<br />
computation more tractable. We will discuss two examples where the<br />
lifting approach can be simplified while retaining recovery<br />
guarantees. These examples will be the phase retrieval problem and a<br />
special case of sparse principal component analysis.<br />
<br />
===December 9 (Monday): Jacob Bedrossian (Courant Institute)===<br />
<br />
''Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations''<br />
<br />
We prove asymptotic stability of shear flows close to the<br />
planar, periodic Couette flow in the 2D incompressible Euler equations.<br />
That is, given an initial perturbation of the Couette flow small in a<br />
suitable regularity class, specifically Gevrey space of class smaller than<br />
2, the velocity converges strongly in L2 to a shear flow which is also<br />
close to the Couette flow. The vorticity is asymptotically mixed to small<br />
scales by an almost linear evolution and in general enstrophy is lost in<br />
the weak limit. The strong convergence of the velocity field is sometimes<br />
referred to as inviscid damping, due to the relationship with Landau<br />
damping in the Vlasov equations. Joint work with Nader Masmoudi.<br />
<br />
===Wednesday, Dec 11: Lu Wang (Johns Hopkins)===<br />
<br />
''Rigidity of Self-shrinkers of Mean Curvature Flow''<br />
<br />
The study of mean curvature flow not only is fundamental in geometry, topology and analysis, but also has important applications in applied mathematics, for instance, image processing. One of the most important problems in mean curvature flow is to understand the possible singularities of the flow and self-shrinkers, i.e., self-shrinking solutions of the flow, provide the singularity models.<br />
<br />
In this talk, I will describe the rigidity of asymptotic structures of self-shrinkers. First, I show the uniqueness of properly embedded self-shrinkers asymptotic to any given regular cone. Next, I give a partial affirmative answer to a conjecture of Ilmanen under an infinite order asymptotic assumption, which asserts that the only two-dimensional properly embedded self-shrinker asymptotic to a cylinder along some end is itself the cylinder. The feature of our results is that no completeness of self-shrinkers is required.<br />
<br />
The key ingredients in the proof are a novel reduction of unique continuation for elliptic operators to backwards uniqueness for parabolic operators and the Carleman type techniques. If time permits, I will discuss some applications of our approach to shrinking solitons of Ricci flow.<br />
<br />
===Friday, Dec 13: Chanwoo Kim (Cambridge)===<br />
<br />
''Regularity of the Boltzmann equation in convex domains''<br />
<br />
A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the Boltzmann equation in a strictly convex domain with the specular, bounce-back and diffuse boundary condition. With the aid of a distance function toward the grazing set, we construct weighted classical <math>C^{1}</math> solutions away from the grazing set for all boundary conditions. For the diffuse boundary condition, we construct <math>W^{1,p}</math> solutions for 1< p<2 and weighted <math>W^{1,p}</math> solutions for <math>2\leq p\leq \infty</math> as well. On the other hand, we show second derivatives do not exist up to the boundary in general by constructing counterexamples for all boundary conditions. This is a joint work with Guo, Tonon, Trescases.<br />
<br />
===December 17: Perla Sousi (Cambridge)===<br />
<br />
''The effect of drift on the volume of the Wiener sausage''<br />
<br />
The Wiener sausage at time t is the algebraic sum of a Brownian path on [0,t] and a ball. Does the expected volume of the Wiener sausage increase when we add drift?<br />
How do you compare the expected volume of the usual Wiener sausage to one defined as the algebraic sum of the Brownian path and a square (in 2D) or a cube (in higher dimensions)? We will answer these questions using their relation to the detection problem for Poisson Brownian motions, and rearrangement inequalities on the sphere (with Y. Peres). We will also discuss generalisations of this to Levy processes (with A. Drewitz and R. Sun) as well as an adversarial detection problem and its connections to Kakeya sets (with Babichenko, Peres, Peretz and Winkler).<br />
<br />
<br />
===December 18: Dustin Cartwright (Yale)===<br />
<br />
''Tropical Complexes''<br />
<br />
Tropical geometry is a way of understanding algebraic varieties by the limiting behavior of their degenerations. Through tropicalization, algebraic operations are replaced with combinatorial constructions and piecewise linear functions. I will introduce tropical complexes, which a way of understanding the geometry of algebraic varieties through combinatorics. Tropical complexes are Delta-complexes together with additional integral data, for which one has parallels and concrete comparisons with the behavior of algebraic varieties. <br />
<br />
===January 6: Aaron Lauda (USC)===<br />
<br />
''An introduction to diagrammatic categorification''<br />
<br />
Categorification seeks to reveal a hidden layer in mathematical<br />
structures. Often the resulting structures can be combinatorially<br />
complex objects making them difficult to study. One method of<br />
overcoming this difficulty, that has proven very successful, is to<br />
encode the categorification into a diagrammatic calculus that makes<br />
computations simple and intuitive.<br />
<br />
In this talk I will review some of the original considerations that<br />
led to the categorification philosophy. We will examine how the<br />
diagrammatic perspective has helped to produce new categorifications<br />
having profound applications to algebra, representation theory, and<br />
low-dimensional topology.<br />
<br />
===January 8: Karin Melnick (Maryland)===<br />
<br />
''Normal forms for local flows on parabolic geometries''<br />
<br />
The exponential map in Riemannian geometry conjugates the differential of an isometry at a point with the action of the isometry near the point. It thus provides a linear normal form for all isometries fixing a point. Conformal transformations are not linearizable in general. I will discuss a suite of normal forms theorems in conformal geometry and, more generally, for parabolic geometries, a rich family of geometric structures of which conformal, projective, and CR structures are examples.<br />
<br />
===January 10, 4PM: Yen Do (Yale)===<br />
<br />
''Convergence of Fourier series and multilinear analysis''<br />
<br />
Almost everywhere convergence of the Fourier series of square <br />
integrable functions was first proved by Lennart Carleson in 1966, and <br />
the proof has lead to deep developments in various multilinear settings. <br />
In this talk I would like to introduce a brief history of the subject <br />
and sketch some recent developments, some of these involve my joint <br />
works with collaborators.<br />
<br />
===Mon, January 13: Yi Wang (Stanford)===<br />
<br />
''Isoperimetric Inequality and Q-curvature''<br />
<br />
A well-known question in differential geometry is to prove the<br />
isoperimetric inequality under intrinsic curvature conditions. In<br />
dimension 2, the isoperimetric inequality is controlled by the integral of<br />
the positive part of the Gaussian curvature. In my recent work, I prove<br />
that on simply connected conformally flat manifolds of higher dimensions,<br />
the role of the Gaussian curvature can be replaced by the Branson's<br />
Q-curvature. The isoperimetric inequality is valid if the integral of the<br />
Q-curvature is below a sharp threshold. Moreover, the isoperimetric<br />
constant depends only on the integrals of the Q-curvature. The proof<br />
relies on the theory of $A_p$ weights in harmonic analysis.<br />
<br />
===January 15: Wei Xiang (University of Oxford)===<br />
<br />
''Conservation Laws and Shock Waves''<br />
<br />
The study of continuum physics gave birth to the theory of quasilinear<br />
systems in divergence form, commonly called conservation laws. In this<br />
talk, conservation laws, the Euler equations, and the definition of the<br />
corresponding weak solutions will be introduced first. Then a short history<br />
of the studying of conservation laws and shock waves will be given. Finally<br />
I would like to present two of our current research projects. One is on the<br />
mathematical analysis of shock diffraction by convex cornered wedges, and<br />
the other one is on the validation of weakly nonlinear geometric optics for<br />
entropy solutions of nonlinear hyperbolic systems of conservation laws.<br />
<br />
Fri, Jan 17, 2:25PM, VV901 Adrianna Gillman (Dartmouth) Fast direct solvers for linear partial differential equations<br />
<br />
===Fri, Jan 17: Adrianna Gillman (Dartmouth) ===<br />
''Fast direct solvers for linear partial differential equations''<br />
<br />
The cost of solving a large linear system often determines what can and cannot be modeled computationally in many areas of science and engineering. Unlike Gaussian elimination which scales cubically with the respect to the number of unknowns, fast direct solvers construct an inverse of a linear in system with a cost that scales linearly or nearly linearly. The fast direct solvers presented in this talk are designed for the linear systems arising from the discretization of linear partial differential equations. These methods are more robust, versatile and stable than iterative schemes. Since an inverse is computed, additional right-hand sides can be processed rapidly. The talk will give the audience a brief introduction to the core ideas, an overview of recent advancements, and it will conclude with a sampling of challenging application examples including the scattering of waves.<br />
<br />
===Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) ===<br />
''Intertwinings, wave equations and growth models''<br />
<br />
We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to hyperbolic partial differential equations, symmetric polynomials and the corresponding random growth models. The talk will be devoted to these recent developments which also shed new light on some beautiful old examples of intertwinings. Based on joint works with Vadim Gorin and Soumik Pal. <br />
<br />
<br />
===Jan 24: Yaniv Plan (Michigan) ===<br />
''Low-dimensionality in mathematical signal processing''<br />
<br />
Natural images tend to be compressible, i.e., the amount of information needed to encode an image is small. This conciseness of information -- in other words, low dimensionality of the signal -- is found throughout a plethora of applications ranging from MRI to quantum state tomography. It is natural to ask: can the number of measurements needed to determine a signal be comparable with the information content? We explore this question under modern models of low-dimensionality and measurement acquisition.<br />
<br />
===Thur, Jan 30: Urbashi Mitra (USC) ===<br />
''Underwater Networks: A Convergence of Communications, Control and Sensing''<br />
<br />
The oceans cover 71% of the earth’s surface and represent one of the least explored frontiers, yet the oceans are integral to climate regulation, nutrient production, oil retrieval and transportation. Future scientific and technological efforts to achieve better understanding of oceans and water-related applications will rely heavily on our ability to communicate reliably between instruments, vehicles (manned and unmanned), human operators, platforms and sensors of all types. Underwater acoustic communication techniques have not reached the same maturity as those for terrestrial radio communications and present some unique opportunities for new developments in information and communication theories. Key features of underwater acoustic communication channels are examined: slow speed of propagation, significant delay spreads, sparse multi-path, time-variation and range-dependent available bandwidth. Another unique feature of underwater networks is that the cost of communication, sensing and control are often comparable resulting in new tradeoffs between these activities. We examine some new results (with implications wider than underwater systems) in channel identifiability, communicating over channels with state and cooperative game theory motivated by the underwater network application.<br />
<br />
<br />
===Feb 14: Alexander Karp (Columbia Teacher's College) ===<br />
''History of Mathematics Education as a Research Field and as Magistra Vitae''<br />
<br />
The presentation will be based on the experience of putting together and editing the Handbook<br />
on the History of Mathematics Education, which will be published by Springer in the near future. <br />
This volume, which was prepared by a large group of researchers from different countries, <br />
contains the first systematic account of the history of the development of mathematics education <br />
in the whole world (and not just in some particular country or region). The editing of such a <br />
book gave rise to thoughts about the methodology of research in this field, and also about what <br />
constitutes an object of such research. These are the thoughts that the presenter intends to share <br />
with his audience. From them, it is natural to pass to an analysis of the current situation and how <br />
it might develop.<br />
<br />
<br />
<br />
===March 28: Michael Lacey (GA Tech) ===<br />
''The Two Weight Inequality for the Hilbert Transform''<br />
<br />
The individual two weight inequality for the Hilbert transform <br />
asks for a real variable characterization of those pairs of weights <br />
(u,v) for which the Hilbert transform H maps L^2(u) to L^2(v). <br />
This question arises naturally in different settings, most famously <br />
in work of Sarason. Answering in the positive a deep <br />
conjecture of Nazarov-Treil-Volberg, the mapping property <br />
of the Hilbert transform is characterized by a triple of conditions, <br />
the first being a two-weight Poisson A2 on the pair of weights, <br />
with a pair of so-called testing inequalities, uniform over all <br />
intervals. This is the first result of this type for a singular <br />
integral operator. (Joint work with Sawyer, C.-Y. Shen and Uriate-Tuero)<br />
<br />
== Past talks ==<br />
<br />
Last year's schedule: [[Colloquia 2012-2013]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=6386Colloquia/Fall182014-01-19T21:54:54Z<p>Shamgar: /* Spring 2014 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Fall 2013 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
|[http://people.math.gatech.edu/~mbaker/ Matt Baker] (Georgia Institute of Technology)<br />
|Riemann-Roch for Graphs and Applications<br />
|Ellenberg<br />
|-<br />
|Sept 13<br />
|[http://math.wisc.edu/~andrews/ Uri Andrews] (University of Wisconsin)<br />
|A hop, skip, and a jump through the degrees of relative provability<br />
|<br />
|-<br />
|Sept 20<br />
|[http://www.math.neu.edu/people/profile/valerio-toledano-laredo Valerio Toledano Laredo] (Northeastern)<br />
|Flat connections and quantum groups<br />
|Gurevich<br />
|-<br />
|'''Wed, Sept 25, 2:30PM in B139'''<br />
|[http://mypage.iu.edu/~alindens/ Ayelet Lindenstrauss] (Indiana University)<br />
|Taylor Series in Homotopy Theory<br />
|Meyer<br />
|-<br />
|'''Wed, Sept 25''' (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication-Avoiding Algorithms for Linear Algebra and Beyond<br />
|Gurevich<br />
|-<br />
|'''Thurs, Sept 26''' (LAA lecture, Joint with Applied Algebra Seminar)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Implementing Communication-Avoiding Algorithms<br />
|Gurevich<br />
|-<br />
|Sept 27 (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays<br />
|Gurevich<br />
|-<br />
|Oct 4<br />
|[http://www.math.tamu.edu/~sottile/ Frank Sottile] (Texas A&M)<br />
|Galois groups of Schubert problems<br />
|Caldararu<br />
|-<br />
|Oct 11<br />
|[http://math.uchicago.edu/~wilkinso/ Amie Wilkinson] (Chicago)<br />
|[[Colloquia#October 11: Amie Wilkinson (Chicago) | Robust mechanisms for chaos]]<br />
|WIMAW (Cladek)<br />
|-<br />
|'''Tues, Oct 15, 4PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability I]]<br />
|Valko<br />
|-<br />
|'''Wed, Oct 16, 2:30PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability II]]<br />
|Valko<br />
|-<br />
|<strike>Oct 18</strike><br />
|No colloquium due to the distinguished lecture<br />
|<br />
|<br />
|-<br />
|Oct 25<br />
|[http://www.math.umn.edu/~garrett/ Paul Garrett] (Minnesota)<br />
|[[Colloquia#October 25: Paul Garrett (Minnesota) | Boundary-value problems, generalized functions, and zeros of zeta functions]]<br />
|Gurevich<br />
|<br />
|<br />
|-<br />
|Nov 1<br />
|[http://www.cs.columbia.edu/~alewko/ Allison Lewko] (Columbia University)<br />
|On sets of large doubling, Lambda(4) sets, and error-correcting codes<br />
|Stovall<br />
|-<br />
|Nov 8<br />
|[http://www.math.cornell.edu/~riley/ Tim Riley] (Cornell)<br />
|[[Colloquia#November 8: Tim Riley (Cornell) | Hydra groups]]<br />
|Dymarz<br />
|-<br />
|Nov 15 and later<br />
|Reserved<br />
|<br />
|Street<br />
|-<br />
|Nov 22<br />
|[http://www.math.uchicago.edu/~tj/ Tianling Jin] (University of Chicago)<br />
|Solutions of some Monge-Ampere equations with degeneracy or singularities.<br />
|Bolotin<br />
|-<br />
|'''Mon, Nov 25, 4PM'''<br />
|[https://web.math.princeton.edu/~linlin/ Lin Lin] (Lawrence Berkeley National Lab)<br />
|Fast algorithms for electronic structure analysis<br />
|Jin<br />
|-<br />
|'''Tue, Nov 26, 4PM, B139'''<br />
|[http://www.math.cornell.edu/m/People/Faculty/conley Clinton Conley] (Cornell)<br />
|[[Colloquia#November 26 (Tuesday): Clinton Conley (Cornell) | Descriptive set-theoretic graph theory]]<br />
|Lempp<br />
|-<br />
|'''Mon, Dec 2, 4PM'''<br />
|[http://www.math.northwestern.edu/~slm/ Simon Marshall] (Northwestern)<br />
|[[Colloquia#December 2 (Monday): Simon Marshall (Northwestern) | Semiclassical estimates for eigenfunctions on locally symmetric spaces]]<br />
|Denissov<br />
|-<br />
|'''Wed, Dec 4, 4PM'''<br />
|[http://math.berkeley.edu/~svs/ Steven Sam] (Berkeley)<br />
|Free Resolutions and Symmetry<br />
|Boston <br />
|-<br />
|'''Fri, Dec 6'''<br />
|[http://math.mit.edu/~hand/ Paul Hand] (MIT)<br />
|[[Colloquia#December 6: Paul Hand (MIT) | Simplifications of the lifting approach for quadratic signal recovery problems]]<br />
|Thiffeault<br />
|-<br />
|'''Fri, Dec. 6 and Sat Dec. 7'''<br />
|<br />
|[http://www.math.umn.edu/~stant001/askey80 Conference in honor of Dick Askey]<br />
|<br />
|-<br />
|'''Mon, Dec. 9, 4pm, VV B239'''<br />
|[http://www.cims.nyu.edu/~jacob/ Jacob Bedrossian] (Courant Institute)<br />
|Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations<br />
|Bolotin<br />
|-<br />
|'''Wed, Dec 11, 4PM'''<br />
|[http://math.jhu.edu/~lwang/ Lu Wang] (Johns Hopkins)<br />
|Rigidity of Self-shrinkers of Mean Curvature Flow<br />
|Viaclovsky <br />
|-<br />
|'''Fri, Dec. 13, 2:25pm, VV 901'''<br />
|[http://chanwookim.wordpress.com/ Chanwoo Kim] (Cambridge)<br />
|Regularity of the Boltzmann equation in convex domains<br />
|Bolotin<br />
|-<br />
|'''Tues, Dec 17, 4PM'''<br />
|[http://www.statslab.cam.ac.uk/~ps422/ Perla Sousi] (Cambridge)<br />
|[[Colloquia#December 17: Perla Sousi (Cambridge) | The effect of drift on the volume of the Wiener sausage]]<br />
|Seppalainen <br />
|-<br />
|'''Wed, Dec 18, 4PM'''<br />
|[http://users.math.yale.edu/~dc597/ Dustin Cartwright] (Yale)<br />
|[[Colloquia#December 18: Dustin Cartwright (Yale) | Tropical Complexes]]<br />
|Gurevich<br />
|}<br />
<br />
== Spring 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Mon, Jan 6, 4PM'''<br />
|[http://www-bcf.usc.edu/~lauda/Aaron_Laudas_Page/Home.html Aaron Lauda] (USC) <br />
|[[Colloquia#January 6: Aaron Lauda (USC) | An introduction to diagrammatic categorification]]<br />
|Caldararu<br />
|-<br />
|'''Wed, Jan 8, 4PM'''<br />
|[http://www2.math.umd.edu/~kmelnick/ Karin Melnick] (Maryland) <br />
|[[Colloquia#January 8: Karin Melnick (Maryland) | Normal forms for local flows on parabolic geometries]]<br />
|Kent<br />
|-<br />
|Jan 10, 4PM<br />
|[http://users.math.yale.edu/~yd82/ Yen Do] (Yale) <br />
|Convergence of Fourier series and multilinear analysis<br />
|Denissov<br />
|-<br />
|'''Mon, Jan 13, 4pm'''<br />
|[http://math.stanford.edu/~wangyi/ Yi Wang] (Stanford)<br />
|Isoperimetric Inequality and Q-curvature<br />
|Viaclovsky<br />
|-<br />
|'''Wen, Jan 15, 4pm'''<br />
|[http://www.maths.ox.ac.uk/people/profiles/wei.xiang Wei Xiang] (University of Oxford)<br />
|[[Colloquia#January 15: Wei Xiang (University of Oxford) |Conservation Laws and Shock Waves]]<br />
|Bolotin<br />
|-<br />
|'''Fri, Jan 17, 2:25PM, VV901'''<br />
|[http://www.math.dartmouth.edu/~gillmana/ Adrianna Gillman] (Dartmouth) <br />
|Fast direct solvers for linear partial differential equations<br />
|Thiffeault<br />
|-<br />
|'''Thu, Jan 23, 2:25, VV901'''<br />
|[http://www.stat.berkeley.edu/~mshkolni/ Mykhaylo Shkolnikov] (Berkeley)<br />
|[[Colloquia#Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) | Intertwinings, wave equations and growth models]]<br />
|Seppalainen<br />
|-<br />
|Jan 24<br />
|[http://www.yanivplan.com/ Yaniv Plan] (Michigan)<br />
|Low-dimensionality in mathematical signal processing<br />
|Thiffeault<br />
|-<br />
|Jan 31<br />
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)<br />
|[[Colloquia#Fri, Jan 31: Urbashi Mitra] (USC)| Underwater Networks: A Convergence of Communications, Control and Sensing]]<br />
|Gurevich<br />
|-<br />
|Feb 7<br />
|David Treumann (Boston College)<br />
|<br />
|Street<br />
|-<br />
|Feb 14<br />
|[http://www.tc.columbia.edu/academics/index.htm?facid=apk16 Alexander Karp] (Columbia Teacher's College)<br />
|History of Mathematics Education as a Research Field and as Magistra Vitae<br />
|Kiselev<br />
|-<br />
|Feb 21<br />
|<br />
|<br />
|<br />
|-<br />
|Feb 28<br />
|[http://math.nyu.edu/faculty/shelley/ Michael Shelley] (Courant)<br />
|<br />
|Spagnolie<br />
|-<br />
|March 7<br />
|[http://www.math.northwestern.edu/people/facultyProfiles/steve.zelditch.html Steve Zelditch] (Northwestern)<br />
|<br />
|Seeger<br />
|-<br />
|March 14<br />
|[https://www.math.ucdavis.edu/~strohmer Thomas Strohmer] (Davis)<br />
|<br />
|Gurevich<br />
|- <br />
|<strike>March 21</strike><br />
|'''Spring Break'''<br />
|No Colloquium<br />
|<br />
|-<br />
|March 28<br />
|[http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)<br />
|The Two Weight Inequality for the Hilbert Transform<br />
|Street<br />
|-<br />
|April 4<br />
|[http://www.math.brown.edu/~res/ Richard Schwartz] (Brown)<br />
|<br />
|Mari-Beffa<br />
|-<br />
|April 11<br />
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)<br />
|<br />
|Gurevich<br />
|-<br />
|April 18 (Wasow Lecture)<br />
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)<br />
|<br />
|Seeger<br />
|-<br />
|April 25<br />
|[http://www.charlesdoran.net Charles Doran](University of Alberta)<br />
|<br />
|Song<br />
|-<br />
|'''Monday, April 28''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|A mystery concerning algebraic plane curves<br />
|Maxim<br />
|-<br />
|'''Tuesday, April 29''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Matrix factorizations old and new<br />
|Maxim<br />
|-<br />
|'''Wednesday, April 30''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Easy solution of polynomial equations over finite fields<br />
|Maxim<br />
|-<br />
|May 2<br />
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)<br />
|<br />
|Boston<br />
|-<br />
|May 9<br />
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)<br />
|<br />
|WIMAW<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sep 6: Matt Baker (GA Tech) ===<br />
''Riemann-Roch for Graphs and Applications''<br />
<br />
We will begin by formulating the Riemann-Roch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a Riemann-Roch theorem for tropical curves, proved by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof of the Brill-Noether theorem in algebraic geometry (work of by Cools-Draisma-Payne-Robeva), a "volume-theoretic proof" of Kirchhoff's Matrix-Tree Theorem (work of An, Kuperberg, Shokrieh, and the speaker), and a new Chabauty-Coleman style bound for the number of rational points on an algebraic curve over the rationals (work of Katz and Zureick-Brown).<br />
<br />
===Sep 13: Uri Andrews (UW-Madison) ===<br />
''A hop, skip, and a jump through the degrees of relative provability''<br />
<br />
The topic of this talk arises from two directions. On the one hand, Gödel's incompleteness theorem tell us that given any sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic, there is a statement that is true but not provable in T. On the other hand, over the past seventy years, a number of researchers studying witnessing functions for various combinatorial statements have realized the importance of fast-growing functions and the fact that their totality is often not provable over a given sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic (e.g. the Paris-Harrington and the Kirby-Paris theorems).<br />
<br />
I will talk about the structure induced by giving the order (for a fixed T) of relative provability for totality of algorithms. That is, for algorithms describing functions f and g, we say f ≤ g if T along with the totality of g suffices to prove the totality of f. It turns out that this structure is rich, and encodes many facets of the nature of provability over sufficiently strong, consistent, effectively axiomatizable theories for first-order arithmetic. (Work joint with Mingzhong Cai, David Diamondstone, Steffen Lempp, and Joseph S. Miller.)<br />
<br />
===Sep 20: Valerio Toledano Laredo (Northeastern)===<br />
''Flat connections and quantum groups''<br />
<br />
Quantum groups are natural deformations of the Lie algebra of<br />
nxn matrices, and more generally of semisimple Lie algebras.<br />
They first arose in the mid eighties in the study of solvable<br />
models in statistical mechanics.<br />
<br />
I will explain how these algebraic objects can serve as natural<br />
receptacles for the (transcendental) monodromy of flat connections<br />
arising from representation theory.<br />
<br />
These connections exist in rational, trigonometric and elliptic<br />
forms, and lead to quantum groups of increasing interest and<br />
complexity.<br />
<br />
===Wed, Sept 25, 2:30PM Ayelet Lindenstrauss (Indiana University)===<br />
''Taylor Series in Homotopy Theory''<br />
<br />
I will discuss Goodwillie's calculus of functors on topological spaces. To mimic the set-up in real analysis, topological spaces are considered small if their nontrivial homotopy groups start only in higher dimensions. They can be considered close only in relation to a map between them, but a map allows us to construct the difference between two spaces, and two spaces are close if the difference between them is small. Spaces can be summed (in different ways) by taking twisted products of them. It is straightforward to construct the analogs of constant, linear, and higher degree homogenous functors, and they can be assembled into "polynomials" and "infinite sums". There are notions of differentiability and higher derivatives, of Taylor towers, and of analytic functions.<br />
<br />
What might look like a game of analogies is an extremely useful tool because when one looks at functors that map topological spaces not into the category of topological spaces, but into the category of spectra (the stabilized version of the category of spaces, which will be explained), many of them are, in fact, analytic, so they can be constructed from the homogenous functors of different degrees. And we can use appropriate analogs of calculus theorems to understand them better. I will conclude with some recent work of Randy McCarthy and myself, applying Goodwillie's calculus to algebraic K-theory calculations.<br />
<br />
===Sep 25: Jim Demmel (Berkeley) ===<br />
''Communication Avoiding Algorithms for Linear Algebra and Beyond''<br />
<br />
Algorithm have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present algorithms that attain provable lower bounds on communication, and show large speedups compared to their conventional counterparts. These algorithms are for direct and iterative linear algebra, for dense and sparse matrices, as well as direct n-body simulations. Several of these algorithms exhibit perfect strong scaling, in both time and energy: run time (resp. energy) for a fixed problem size drops proportionally to the number of processors p (resp. is independent of p). Finally, we describe extensions to algorithms involving arbitrary loop nests and array accesses, assuming only that array subscripts are affine functions of the loop indices. <br />
<br />
===Sep 26: Jim Demmel (Berkeley) ===<br />
''Implementing Communication Avoiding Algorithms''<br />
<br />
Designing algorithms that avoiding communication, attaining<br />
lower bounds if possible, is critical for algorithms to minimize runtime and<br />
energy on current and future architectures. These new algorithms can have <br />
new numerical stability properties, new ways to encode answers, and new data<br />
structures, not just depend on loop transformations (we need those too!).<br />
We will illustrate with a variety of examples including direct linear algebra<br />
(eg new ways to perform pivoting, new deterministic and randomized<br />
eigenvalue algorithms), iterative linear algebra (eg new ways to reorganize<br />
Krylov subspace methods) and direct n-body algorithms, on architectures<br />
ranging from multicore to distributed memory to heterogeneous.<br />
The theory describing communication avoiding algorithms can give us a large<br />
design space of possible implementations, so we use autotuning to find<br />
the fastest one automatically. Finally, on parallel architectures one can<br />
frequently not expect to get bitwise identical results from multiple runs,<br />
because of dynamic scheduling and floating point nonassociativity; <br />
this can be a problem for reasons from debugging to correctness.<br />
We discuss some techniques to get reproducible results at modest cost.<br />
<br />
===Sep 27: Jim Demmel (Berkeley) ===<br />
''Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays''<br />
<br />
Our goal is to minimize communication, i.e. moving data, since it increasingly<br />
dominates the cost of arithmetic in algorithms. Motivated by this, attainable<br />
communication lower bounds have been established by many authors for a <br />
variety of algorithms including matrix computations.<br />
<br />
The lower bound approach used initially by Irony, Tiskin and Toledo <br />
for O(n^3) matrix multiplication, and later by Ballard et al <br />
for many other linear algebra algorithms, depends on a geometric result by <br />
Loomis and Whitney: this result bounds the volume of a 3D set <br />
(representing multiply-adds done in the inner loop of the algorithm) <br />
using the product of the areas of certain 2D projections of this set <br />
(representing the matrix entries available locally, i.e., without communication).<br />
<br />
Using a recent generalization of Loomis' and Whitney's result, we generalize <br />
this lower bound approach to a much larger class of algorithms, <br />
that may have arbitrary numbers of loops and arrays with arbitrary dimensions, <br />
as long as the index expressions are affine combinations of loop variables.<br />
In other words, the algorithm can do arbitrary operations on any number of <br />
variables like A(i1,i2,i2-2*i1,3-4*i3+7*i_4,…).<br />
Moreover, the result applies to recursive programs, irregular iteration spaces, <br />
sparse matrices, and other data structures as long as the computation can be<br />
logically mapped to loops and indexed data structure accesses. <br />
<br />
We also discuss when optimal algorithms exist that attain the lower bounds; <br />
this leads to new asymptotically faster algorithms for several problems.<br />
<br />
===October 4: Frank Sottile (Texas A&M) ===<br />
''Galois groups of Schubert problems''<br />
<br />
Work of Jordan from 1870 showed how Galois theory<br />
can be applied to enumerative geometry. Hermite earlier<br />
showed the equivalence of Galois groups with geometric <br />
monodromy groups, and in 1979 Harris used this to study <br />
Galois groups of many enumerative problems. Vakil gave <br />
a geometric-combinatorial criterion that implies a Galois <br />
group contains the alternating group. With Brooks and <br />
Martin del Campo, we used Vakil's criterion to show that <br />
all Schubert problems involving lines have at least <br />
alternating Galois group. White and I have given a new <br />
proof of this based on 2-transitivity.<br />
<br />
My talk will describe this background and sketch a <br />
current project to systematically determine Galois groups <br />
of all Schubert problems of moderate size on all small <br />
classical flag manifolds, investigating at least several <br />
million problems. This will use supercomputers employing <br />
several overlapping methods, including combinatorial <br />
criteria, symbolic computation, and numerical homotopy <br />
continuation, and require the development of new <br />
algorithms and software.<br />
<br />
===October 11: Amie Wilkinson (Chicago) ===<br />
<br />
''Robust mechanisms for chaos''<br />
<br />
What are the underlying mechanisms for robustly chaotic behavior in smooth dynamics?<br />
<br />
In addressing this question, I'll focus on the study of diffeomorphisms of a compact manifold, where "chaotic" means "mixing" and and "robustly" means "stable under smooth perturbations." I'll describe recent advances in constructing and using tools called "blenders" to produce stably chaotic behavior with arbitrarily little effort.<br />
<br />
===October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) ===<br />
<br />
''Integrable probability I and II''<br />
<br />
The goal of the talks is to describe the emerging field of integrable<br />
probability, whose goal is to identify and analyze exactly solvable<br />
probabilistic models. The models and results are often easy to describe,<br />
yet difficult to find, and they carry essential information about broad<br />
universality classes of stochastic processes.<br />
<br />
<br />
===October 25: Paul Garrett (Minnesota)=== <br />
<br />
''Boundary-value problems, generalized functions, and zeros of zeta functions''<br />
<br />
Modern analysis (Beppo Levi, Sobolev, Friedrichs, Schwartz) illuminates work of D. Hejhal and Y. Colin de Verdiere from 30 years<br />
ago, clarifying, as in P. Cartier's letter to A. Weil, "how the Riemann Hypothesis was not proven". (Joint with E. Bombieri.)<br />
<br />
===November 1: Allison Lewko (Columbia University) ===<br />
<br />
''On sets of large doubling, Lambda(4) sets, and error-correcting codes''<br />
<br />
We investigate the structure of finite sets A of integers such that A+A is large, presenting a counterexample to natural conjectures in the pursuit of an "anti-Freiman" theory in additive combinatorics. We will begin with a brief history of the problem and its connection to the study of Lambda(4) sets in harmonic analysis, and then we will discuss our counterexample and its construction from error-correcting codes. We will conclude by describing some related open problems.<br />
This is joint work with Mark Lewko.<br />
<br />
===November 8: Tim Riley (Cornell)===<br />
<br />
''Hydra groups''<br />
<br />
A few years ago Will Dison and I constructed a family of<br />
finitely generated groups whose workings include a string-rewriting<br />
phenomenon of extraordinary duration which is reminiscent of Hercules'<br />
battle with the hydra. I will describe this and the investigations it<br />
spurred in hyperbolic geometry, combinatorial group theory, and a<br />
problem of how to calculate efficiently with hugely compressed<br />
representations of integers.<br />
<br />
===November 22: Tianling Jin (University of Chicago)===<br />
<br />
''Solutions of some Monge-Ampere equations with degeneracy or singularities''<br />
<br />
We will first give a new proof of a celebrated theorem of<br />
Jorgens which states that every classical convex solution of det(Hess<br />
u)=1 in R^2 has to be a second order polynomial. Our arguments do not use<br />
complex analysis, and will be applied to establish such Liouville type<br />
theorems for solutions some degenerate Monge-Ampere equations. We will<br />
also discuss some results on existence, regularity, classification, and<br />
asymptotic behavior of solutions of some Monge-Ampere equations with<br />
isolated and line singularities. This is joint work with J. Xiong.<br />
<br />
===Monday, Nov 25: Lin Lin (Lawrence Berkeley National Lab)===<br />
<br />
''Fast algorithms for electronic structure analysis''<br />
<br />
Kohn-Sham density functional theory (KSDFT) is the most widely used<br />
electronic structure theory for molecules and condensed matter systems. For<br />
a system with N electrons, the standard method for solving KSDFT requires<br />
solving N eigenvectors for an O(N) * O(N) Kohn-Sham Hamiltonian matrix.<br />
The computational cost for such procedure is expensive and scales as<br />
O(N^3). We have developed pole expansion plus selected inversion (PEXSI)<br />
method, in which KSDFT is solved by evaluating the selected elements of the<br />
inverse of a series of sparse symmetric matrices, and the overall algorithm<br />
scales at most O(N^2) for all materials including insulators,<br />
semiconductors and metals. The PEXSI method can be used with orthogonal or<br />
nonorthogonal basis set, and the physical quantities including electron<br />
density, energy, atomic force, density of states, and local density of<br />
states are calculated accurately without using the eigenvalues and<br />
eigenvectors. The recently developed massively parallel PEXSI method has<br />
been implemented in SIESTA, one of the most popular electronic structure<br />
software using atomic orbital basis set. The resulting method can allow<br />
accurate treatment of electronic structure in a unprecedented scale. We<br />
demonstrate the application of the method for solving graphene-like<br />
structures with more than 20,000 atoms, and the method can be efficiently<br />
parallelized 10,000 - 100,000 processors on Department of Energy (DOE) high<br />
performance machines.<br />
<br />
===November 26 (Tuesday): Clinton Conley (Cornell)===<br />
<br />
''Descriptive set-theoretic graph theory''<br />
<br />
Familiar graph-theoretic problems (for example, vertex coloring) exhibit a<br />
stark change of character when measurability constraints are placed on the<br />
structures and functions involved. While discussing some ramifications in<br />
descriptive set theory, we also pay special attention to interactions with<br />
probability (concerning random colorings of Cayley graphs) and ergodic<br />
theory (characterizing various dynamical properties of groups). The talk<br />
will include joint work with Alexander Kechris, Andrew Marks, Benjamin<br />
Miller, and Robin Tucker-Drob.<br />
<br />
<br />
===December 2 (Monday): Simon Marshall (Northwestern)===<br />
<br />
''Semiclassical estimates for eigenfunctions on locally symmetric spaces''<br />
<br />
Let M be a compact Riemannian manifold, and f an L^2-normalised Laplace<br />
eigenfunction on M. If p > 2, a theorem of Sogge tells us how large the L^p<br />
norm of f can be in terms of its Laplace eigenvalue. For instance, when p<br />
is infinity this is asking how large the peaks of f can be. I will present<br />
an analogue of Sogge's theorem for eigenfunctions of the full ring of<br />
invariant differential operators on a locally symmetric space, and discuss<br />
some links between this result and number theory.<br />
<br />
===December 4 (Wednesday): Steven Sam (Berkeley)===<br />
<br />
''Free Resolutions and Symmetry''<br />
<br />
This talk is about the use of symmetry in the study of modules and free resolutions in commutative algebra and algebraic geometry, and specifically how it clarifies, organizes, and rigidifies calculations, and how it enables us to find finiteness in situations where it a priori does not seem to exist. I will begin the talk with an example coming from classical invariant theory and determinantal ideals using just some basic notions from linear algebra. Then I will explain some of my own work which builds on this setting in several directions. Finally, I'll discuss a recent program on twisted commutative algebras, developed jointly with Andrew Snowden, which formalizes the synthesis of representation theory and commutative algebra and leads to new finiteness results in seemingly infinite settings.<br />
<br />
===December 6: Paul Hand (MIT)===<br />
<br />
''Simplifications of the Lifting Approach for Quadratic Signal Recovery Problems''<br />
<br />
Many signal recovery problems are quadratic in nature, such as phase<br />
retrieval and sparse principal component analysis. Such problems in<br />
R^n can be convexified by introducing n^2 variables corresponding to<br />
each quadratic combination of unknowns. This approach often gives<br />
rise to an n x n matrix recovery problem that is convex and has<br />
provable recovery guarantees. Because the dimensionality has been<br />
squared, it is an important task to find simplifications that make<br />
computation more tractable. We will discuss two examples where the<br />
lifting approach can be simplified while retaining recovery<br />
guarantees. These examples will be the phase retrieval problem and a<br />
special case of sparse principal component analysis.<br />
<br />
===December 9 (Monday): Jacob Bedrossian (Courant Institute)===<br />
<br />
''Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations''<br />
<br />
We prove asymptotic stability of shear flows close to the<br />
planar, periodic Couette flow in the 2D incompressible Euler equations.<br />
That is, given an initial perturbation of the Couette flow small in a<br />
suitable regularity class, specifically Gevrey space of class smaller than<br />
2, the velocity converges strongly in L2 to a shear flow which is also<br />
close to the Couette flow. The vorticity is asymptotically mixed to small<br />
scales by an almost linear evolution and in general enstrophy is lost in<br />
the weak limit. The strong convergence of the velocity field is sometimes<br />
referred to as inviscid damping, due to the relationship with Landau<br />
damping in the Vlasov equations. Joint work with Nader Masmoudi.<br />
<br />
===Wednesday, Dec 11: Lu Wang (Johns Hopkins)===<br />
<br />
''Rigidity of Self-shrinkers of Mean Curvature Flow''<br />
<br />
The study of mean curvature flow not only is fundamental in geometry, topology and analysis, but also has important applications in applied mathematics, for instance, image processing. One of the most important problems in mean curvature flow is to understand the possible singularities of the flow and self-shrinkers, i.e., self-shrinking solutions of the flow, provide the singularity models.<br />
<br />
In this talk, I will describe the rigidity of asymptotic structures of self-shrinkers. First, I show the uniqueness of properly embedded self-shrinkers asymptotic to any given regular cone. Next, I give a partial affirmative answer to a conjecture of Ilmanen under an infinite order asymptotic assumption, which asserts that the only two-dimensional properly embedded self-shrinker asymptotic to a cylinder along some end is itself the cylinder. The feature of our results is that no completeness of self-shrinkers is required.<br />
<br />
The key ingredients in the proof are a novel reduction of unique continuation for elliptic operators to backwards uniqueness for parabolic operators and the Carleman type techniques. If time permits, I will discuss some applications of our approach to shrinking solitons of Ricci flow.<br />
<br />
===Friday, Dec 13: Chanwoo Kim (Cambridge)===<br />
<br />
''Regularity of the Boltzmann equation in convex domains''<br />
<br />
A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the Boltzmann equation in a strictly convex domain with the specular, bounce-back and diffuse boundary condition. With the aid of a distance function toward the grazing set, we construct weighted classical <math>C^{1}</math> solutions away from the grazing set for all boundary conditions. For the diffuse boundary condition, we construct <math>W^{1,p}</math> solutions for 1< p<2 and weighted <math>W^{1,p}</math> solutions for <math>2\leq p\leq \infty</math> as well. On the other hand, we show second derivatives do not exist up to the boundary in general by constructing counterexamples for all boundary conditions. This is a joint work with Guo, Tonon, Trescases.<br />
<br />
===December 17: Perla Sousi (Cambridge)===<br />
<br />
''The effect of drift on the volume of the Wiener sausage''<br />
<br />
The Wiener sausage at time t is the algebraic sum of a Brownian path on [0,t] and a ball. Does the expected volume of the Wiener sausage increase when we add drift?<br />
How do you compare the expected volume of the usual Wiener sausage to one defined as the algebraic sum of the Brownian path and a square (in 2D) or a cube (in higher dimensions)? We will answer these questions using their relation to the detection problem for Poisson Brownian motions, and rearrangement inequalities on the sphere (with Y. Peres). We will also discuss generalisations of this to Levy processes (with A. Drewitz and R. Sun) as well as an adversarial detection problem and its connections to Kakeya sets (with Babichenko, Peres, Peretz and Winkler).<br />
<br />
<br />
===December 18: Dustin Cartwright (Yale)===<br />
<br />
''Tropical Complexes''<br />
<br />
Tropical geometry is a way of understanding algebraic varieties by the limiting behavior of their degenerations. Through tropicalization, algebraic operations are replaced with combinatorial constructions and piecewise linear functions. I will introduce tropical complexes, which a way of understanding the geometry of algebraic varieties through combinatorics. Tropical complexes are Delta-complexes together with additional integral data, for which one has parallels and concrete comparisons with the behavior of algebraic varieties. <br />
<br />
===January 6: Aaron Lauda (USC)===<br />
<br />
''An introduction to diagrammatic categorification''<br />
<br />
Categorification seeks to reveal a hidden layer in mathematical<br />
structures. Often the resulting structures can be combinatorially<br />
complex objects making them difficult to study. One method of<br />
overcoming this difficulty, that has proven very successful, is to<br />
encode the categorification into a diagrammatic calculus that makes<br />
computations simple and intuitive.<br />
<br />
In this talk I will review some of the original considerations that<br />
led to the categorification philosophy. We will examine how the<br />
diagrammatic perspective has helped to produce new categorifications<br />
having profound applications to algebra, representation theory, and<br />
low-dimensional topology.<br />
<br />
===January 8: Karin Melnick (Maryland)===<br />
<br />
''Normal forms for local flows on parabolic geometries''<br />
<br />
The exponential map in Riemannian geometry conjugates the differential of an isometry at a point with the action of the isometry near the point. It thus provides a linear normal form for all isometries fixing a point. Conformal transformations are not linearizable in general. I will discuss a suite of normal forms theorems in conformal geometry and, more generally, for parabolic geometries, a rich family of geometric structures of which conformal, projective, and CR structures are examples.<br />
<br />
===January 10, 4PM: Yen Do (Yale)===<br />
<br />
''Convergence of Fourier series and multilinear analysis''<br />
<br />
Almost everywhere convergence of the Fourier series of square <br />
integrable functions was first proved by Lennart Carleson in 1966, and <br />
the proof has lead to deep developments in various multilinear settings. <br />
In this talk I would like to introduce a brief history of the subject <br />
and sketch some recent developments, some of these involve my joint <br />
works with collaborators.<br />
<br />
===Mon, January 13: Yi Wang (Stanford)===<br />
<br />
''Isoperimetric Inequality and Q-curvature''<br />
<br />
A well-known question in differential geometry is to prove the<br />
isoperimetric inequality under intrinsic curvature conditions. In<br />
dimension 2, the isoperimetric inequality is controlled by the integral of<br />
the positive part of the Gaussian curvature. In my recent work, I prove<br />
that on simply connected conformally flat manifolds of higher dimensions,<br />
the role of the Gaussian curvature can be replaced by the Branson's<br />
Q-curvature. The isoperimetric inequality is valid if the integral of the<br />
Q-curvature is below a sharp threshold. Moreover, the isoperimetric<br />
constant depends only on the integrals of the Q-curvature. The proof<br />
relies on the theory of $A_p$ weights in harmonic analysis.<br />
<br />
===January 15: Wei Xiang (University of Oxford)===<br />
<br />
''Conservation Laws and Shock Waves''<br />
<br />
The study of continuum physics gave birth to the theory of quasilinear<br />
systems in divergence form, commonly called conservation laws. In this<br />
talk, conservation laws, the Euler equations, and the definition of the<br />
corresponding weak solutions will be introduced first. Then a short history<br />
of the studying of conservation laws and shock waves will be given. Finally<br />
I would like to present two of our current research projects. One is on the<br />
mathematical analysis of shock diffraction by convex cornered wedges, and<br />
the other one is on the validation of weakly nonlinear geometric optics for<br />
entropy solutions of nonlinear hyperbolic systems of conservation laws.<br />
<br />
Fri, Jan 17, 2:25PM, VV901 Adrianna Gillman (Dartmouth) Fast direct solvers for linear partial differential equations<br />
<br />
===Fri, Jan 17: Adrianna Gillman (Dartmouth) ===<br />
''Fast direct solvers for linear partial differential equations''<br />
<br />
The cost of solving a large linear system often determines what can and cannot be modeled computationally in many areas of science and engineering. Unlike Gaussian elimination which scales cubically with the respect to the number of unknowns, fast direct solvers construct an inverse of a linear in system with a cost that scales linearly or nearly linearly. The fast direct solvers presented in this talk are designed for the linear systems arising from the discretization of linear partial differential equations. These methods are more robust, versatile and stable than iterative schemes. Since an inverse is computed, additional right-hand sides can be processed rapidly. The talk will give the audience a brief introduction to the core ideas, an overview of recent advancements, and it will conclude with a sampling of challenging application examples including the scattering of waves.<br />
<br />
===Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) ===<br />
''Intertwinings, wave equations and growth models''<br />
<br />
We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to hyperbolic partial differential equations, symmetric polynomials and the corresponding random growth models. The talk will be devoted to these recent developments which also shed new light on some beautiful old examples of intertwinings. Based on joint works with Vadim Gorin and Soumik Pal. <br />
<br />
<br />
===Jan 24: Yaniv Plan (Michigan) ===<br />
''Low-dimensionality in mathematical signal processing''<br />
<br />
Natural images tend to be compressible, i.e., the amount of information needed to encode an image is small. This conciseness of information -- in other words, low dimensionality of the signal -- is found throughout a plethora of applications ranging from MRI to quantum state tomography. It is natural to ask: can the number of measurements needed to determine a signal be comparable with the information content? We explore this question under modern models of low-dimensionality and measurement acquisition.<br />
<br />
===Feb 14: Alexander Karp (Columbia Teacher's College) ===<br />
''History of Mathematics Education as a Research Field and as Magistra Vitae''<br />
<br />
The presentation will be based on the experience of putting together and editing the Handbook<br />
on the History of Mathematics Education, which will be published by Springer in the near future. <br />
This volume, which was prepared by a large group of researchers from different countries, <br />
contains the first systematic account of the history of the development of mathematics education <br />
in the whole world (and not just in some particular country or region). The editing of such a <br />
book gave rise to thoughts about the methodology of research in this field, and also about what <br />
constitutes an object of such research. These are the thoughts that the presenter intends to share <br />
with his audience. From them, it is natural to pass to an analysis of the current situation and how <br />
it might develop.<br />
<br />
<br />
<br />
===March 28: Michael Lacey (GA Tech) ===<br />
''The Two Weight Inequality for the Hilbert Transform''<br />
<br />
The individual two weight inequality for the Hilbert transform <br />
asks for a real variable characterization of those pairs of weights <br />
(u,v) for which the Hilbert transform H maps L^2(u) to L^2(v). <br />
This question arises naturally in different settings, most famously <br />
in work of Sarason. Answering in the positive a deep <br />
conjecture of Nazarov-Treil-Volberg, the mapping property <br />
of the Hilbert transform is characterized by a triple of conditions, <br />
the first being a two-weight Poisson A2 on the pair of weights, <br />
with a pair of so-called testing inequalities, uniform over all <br />
intervals. This is the first result of this type for a singular <br />
integral operator. (Joint work with Sawyer, C.-Y. Shen and Uriate-Tuero)<br />
<br />
== Past talks ==<br />
<br />
Last year's schedule: [[Colloquia 2012-2013]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=6385Colloquia/Fall182014-01-19T21:09:04Z<p>Shamgar: /* Spring 2014 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Fall 2013 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
|[http://people.math.gatech.edu/~mbaker/ Matt Baker] (Georgia Institute of Technology)<br />
|Riemann-Roch for Graphs and Applications<br />
|Ellenberg<br />
|-<br />
|Sept 13<br />
|[http://math.wisc.edu/~andrews/ Uri Andrews] (University of Wisconsin)<br />
|A hop, skip, and a jump through the degrees of relative provability<br />
|<br />
|-<br />
|Sept 20<br />
|[http://www.math.neu.edu/people/profile/valerio-toledano-laredo Valerio Toledano Laredo] (Northeastern)<br />
|Flat connections and quantum groups<br />
|Gurevich<br />
|-<br />
|'''Wed, Sept 25, 2:30PM in B139'''<br />
|[http://mypage.iu.edu/~alindens/ Ayelet Lindenstrauss] (Indiana University)<br />
|Taylor Series in Homotopy Theory<br />
|Meyer<br />
|-<br />
|'''Wed, Sept 25''' (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication-Avoiding Algorithms for Linear Algebra and Beyond<br />
|Gurevich<br />
|-<br />
|'''Thurs, Sept 26''' (LAA lecture, Joint with Applied Algebra Seminar)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Implementing Communication-Avoiding Algorithms<br />
|Gurevich<br />
|-<br />
|Sept 27 (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays<br />
|Gurevich<br />
|-<br />
|Oct 4<br />
|[http://www.math.tamu.edu/~sottile/ Frank Sottile] (Texas A&M)<br />
|Galois groups of Schubert problems<br />
|Caldararu<br />
|-<br />
|Oct 11<br />
|[http://math.uchicago.edu/~wilkinso/ Amie Wilkinson] (Chicago)<br />
|[[Colloquia#October 11: Amie Wilkinson (Chicago) | Robust mechanisms for chaos]]<br />
|WIMAW (Cladek)<br />
|-<br />
|'''Tues, Oct 15, 4PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability I]]<br />
|Valko<br />
|-<br />
|'''Wed, Oct 16, 2:30PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability II]]<br />
|Valko<br />
|-<br />
|<strike>Oct 18</strike><br />
|No colloquium due to the distinguished lecture<br />
|<br />
|<br />
|-<br />
|Oct 25<br />
|[http://www.math.umn.edu/~garrett/ Paul Garrett] (Minnesota)<br />
|[[Colloquia#October 25: Paul Garrett (Minnesota) | Boundary-value problems, generalized functions, and zeros of zeta functions]]<br />
|Gurevich<br />
|<br />
|<br />
|-<br />
|Nov 1<br />
|[http://www.cs.columbia.edu/~alewko/ Allison Lewko] (Columbia University)<br />
|On sets of large doubling, Lambda(4) sets, and error-correcting codes<br />
|Stovall<br />
|-<br />
|Nov 8<br />
|[http://www.math.cornell.edu/~riley/ Tim Riley] (Cornell)<br />
|[[Colloquia#November 8: Tim Riley (Cornell) | Hydra groups]]<br />
|Dymarz<br />
|-<br />
|Nov 15 and later<br />
|Reserved<br />
|<br />
|Street<br />
|-<br />
|Nov 22<br />
|[http://www.math.uchicago.edu/~tj/ Tianling Jin] (University of Chicago)<br />
|Solutions of some Monge-Ampere equations with degeneracy or singularities.<br />
|Bolotin<br />
|-<br />
|'''Mon, Nov 25, 4PM'''<br />
|[https://web.math.princeton.edu/~linlin/ Lin Lin] (Lawrence Berkeley National Lab)<br />
|Fast algorithms for electronic structure analysis<br />
|Jin<br />
|-<br />
|'''Tue, Nov 26, 4PM, B139'''<br />
|[http://www.math.cornell.edu/m/People/Faculty/conley Clinton Conley] (Cornell)<br />
|[[Colloquia#November 26 (Tuesday): Clinton Conley (Cornell) | Descriptive set-theoretic graph theory]]<br />
|Lempp<br />
|-<br />
|'''Mon, Dec 2, 4PM'''<br />
|[http://www.math.northwestern.edu/~slm/ Simon Marshall] (Northwestern)<br />
|[[Colloquia#December 2 (Monday): Simon Marshall (Northwestern) | Semiclassical estimates for eigenfunctions on locally symmetric spaces]]<br />
|Denissov<br />
|-<br />
|'''Wed, Dec 4, 4PM'''<br />
|[http://math.berkeley.edu/~svs/ Steven Sam] (Berkeley)<br />
|Free Resolutions and Symmetry<br />
|Boston <br />
|-<br />
|'''Fri, Dec 6'''<br />
|[http://math.mit.edu/~hand/ Paul Hand] (MIT)<br />
|[[Colloquia#December 6: Paul Hand (MIT) | Simplifications of the lifting approach for quadratic signal recovery problems]]<br />
|Thiffeault<br />
|-<br />
|'''Fri, Dec. 6 and Sat Dec. 7'''<br />
|<br />
|[http://www.math.umn.edu/~stant001/askey80 Conference in honor of Dick Askey]<br />
|<br />
|-<br />
|'''Mon, Dec. 9, 4pm, VV B239'''<br />
|[http://www.cims.nyu.edu/~jacob/ Jacob Bedrossian] (Courant Institute)<br />
|Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations<br />
|Bolotin<br />
|-<br />
|'''Wed, Dec 11, 4PM'''<br />
|[http://math.jhu.edu/~lwang/ Lu Wang] (Johns Hopkins)<br />
|Rigidity of Self-shrinkers of Mean Curvature Flow<br />
|Viaclovsky <br />
|-<br />
|'''Fri, Dec. 13, 2:25pm, VV 901'''<br />
|[http://chanwookim.wordpress.com/ Chanwoo Kim] (Cambridge)<br />
|Regularity of the Boltzmann equation in convex domains<br />
|Bolotin<br />
|-<br />
|'''Tues, Dec 17, 4PM'''<br />
|[http://www.statslab.cam.ac.uk/~ps422/ Perla Sousi] (Cambridge)<br />
|[[Colloquia#December 17: Perla Sousi (Cambridge) | The effect of drift on the volume of the Wiener sausage]]<br />
|Seppalainen <br />
|-<br />
|'''Wed, Dec 18, 4PM'''<br />
|[http://users.math.yale.edu/~dc597/ Dustin Cartwright] (Yale)<br />
|[[Colloquia#December 18: Dustin Cartwright (Yale) | Tropical Complexes]]<br />
|Gurevich<br />
|}<br />
<br />
== Spring 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Mon, Jan 6, 4PM'''<br />
|[http://www-bcf.usc.edu/~lauda/Aaron_Laudas_Page/Home.html Aaron Lauda] (USC) <br />
|[[Colloquia#January 6: Aaron Lauda (USC) | An introduction to diagrammatic categorification]]<br />
|Caldararu<br />
|-<br />
|'''Wed, Jan 8, 4PM'''<br />
|[http://www2.math.umd.edu/~kmelnick/ Karin Melnick] (Maryland) <br />
|[[Colloquia#January 8: Karin Melnick (Maryland) | Normal forms for local flows on parabolic geometries]]<br />
|Kent<br />
|-<br />
|Jan 10, 4PM<br />
|[http://users.math.yale.edu/~yd82/ Yen Do] (Yale) <br />
|Convergence of Fourier series and multilinear analysis<br />
|Denissov<br />
|-<br />
|'''Mon, Jan 13, 4pm'''<br />
|[http://math.stanford.edu/~wangyi/ Yi Wang] (Stanford)<br />
|Isoperimetric Inequality and Q-curvature<br />
|Viaclovsky<br />
|-<br />
|'''Wen, Jan 15, 4pm'''<br />
|[http://www.maths.ox.ac.uk/people/profiles/wei.xiang Wei Xiang] (University of Oxford)<br />
|[[Colloquia#January 15: Wei Xiang (University of Oxford) |Conservation Laws and Shock Waves]]<br />
|Bolotin<br />
|-<br />
|'''Fri, Jan 17, 2:25PM, VV901'''<br />
|[http://www.math.dartmouth.edu/~gillmana/ Adrianna Gillman] (Dartmouth) <br />
|Fast direct solvers for linear partial differential equations<br />
|Thiffeault<br />
|-<br />
|'''Thu, Jan 23, 2:25, VV901'''<br />
|[http://www.stat.berkeley.edu/~mshkolni/ Mykhaylo Shkolnikov] (Berkeley)<br />
|[[Colloquia#Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) | Intertwinings, wave equations and growth models]]<br />
|Seppalainen<br />
|-<br />
|Jan 24<br />
|[http://www.yanivplan.com/ Yaniv Plan] (Michigan)<br />
|Low-dimensionality in mathematical signal processing<br />
|Thiffeault<br />
|-<br />
|Jan 31<br />
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)<br />
|<br />
|Gurevich<br />
|-<br />
|Feb 7<br />
|David Treumann (Boston College)<br />
|<br />
|Street<br />
|-<br />
|Feb 14<br />
|[http://www.tc.columbia.edu/academics/index.htm?facid=apk16 Alexander Karp] (Columbia Teacher's College)<br />
|History of Mathematics Education as a Research Field and as Magistra Vitae<br />
|Kiselev<br />
|-<br />
|Feb 21<br />
|<br />
|<br />
|<br />
|-<br />
|Feb 28<br />
|[http://math.nyu.edu/faculty/shelley/ Michael Shelley] (Courant)<br />
|<br />
|Spagnolie<br />
|-<br />
|March 7<br />
|[http://www.math.northwestern.edu/people/facultyProfiles/steve.zelditch.html Steve Zelditch] (Northwestern)<br />
|<br />
|Seeger<br />
|-<br />
|March 14<br />
|[https://www.math.ucdavis.edu/~strohmer Thomas Strohmer] (Davis)<br />
|<br />
|Gurevich<br />
|- <br />
|<strike>March 21</strike><br />
|'''Spring Break'''<br />
|No Colloquium<br />
|<br />
|-<br />
|March 28<br />
|[http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)<br />
|The Two Weight Inequality for the Hilbert Transform<br />
|Street<br />
|-<br />
|April 4<br />
|[http://www.math.brown.edu/~res/ Richard Schwartz] (Brown)<br />
|<br />
|Mari-Beffa<br />
|-<br />
|April 11<br />
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)<br />
|<br />
|Gurevich<br />
|-<br />
|April 18 (Wasow Lecture)<br />
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)<br />
|<br />
|Seeger<br />
|-<br />
|April 25<br />
|[http://www.charlesdoran.net Charles Doran](University of Alberta)<br />
|<br />
|Song<br />
|-<br />
|'''Monday, April 28''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|A mystery concerning algebraic plane curves<br />
|Maxim<br />
|-<br />
|'''Tuesday, April 29''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Matrix factorizations old and new<br />
|Maxim<br />
|-<br />
|'''Wednesday, April 30''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Easy solution of polynomial equations over finite fields<br />
|Maxim<br />
|-<br />
|May 2<br />
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)<br />
|<br />
|Boston<br />
|-<br />
|May 9<br />
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)<br />
|<br />
|WIMAW<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sep 6: Matt Baker (GA Tech) ===<br />
''Riemann-Roch for Graphs and Applications''<br />
<br />
We will begin by formulating the Riemann-Roch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a Riemann-Roch theorem for tropical curves, proved by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof of the Brill-Noether theorem in algebraic geometry (work of by Cools-Draisma-Payne-Robeva), a "volume-theoretic proof" of Kirchhoff's Matrix-Tree Theorem (work of An, Kuperberg, Shokrieh, and the speaker), and a new Chabauty-Coleman style bound for the number of rational points on an algebraic curve over the rationals (work of Katz and Zureick-Brown).<br />
<br />
===Sep 13: Uri Andrews (UW-Madison) ===<br />
''A hop, skip, and a jump through the degrees of relative provability''<br />
<br />
The topic of this talk arises from two directions. On the one hand, Gödel's incompleteness theorem tell us that given any sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic, there is a statement that is true but not provable in T. On the other hand, over the past seventy years, a number of researchers studying witnessing functions for various combinatorial statements have realized the importance of fast-growing functions and the fact that their totality is often not provable over a given sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic (e.g. the Paris-Harrington and the Kirby-Paris theorems).<br />
<br />
I will talk about the structure induced by giving the order (for a fixed T) of relative provability for totality of algorithms. That is, for algorithms describing functions f and g, we say f ≤ g if T along with the totality of g suffices to prove the totality of f. It turns out that this structure is rich, and encodes many facets of the nature of provability over sufficiently strong, consistent, effectively axiomatizable theories for first-order arithmetic. (Work joint with Mingzhong Cai, David Diamondstone, Steffen Lempp, and Joseph S. Miller.)<br />
<br />
===Sep 20: Valerio Toledano Laredo (Northeastern)===<br />
''Flat connections and quantum groups''<br />
<br />
Quantum groups are natural deformations of the Lie algebra of<br />
nxn matrices, and more generally of semisimple Lie algebras.<br />
They first arose in the mid eighties in the study of solvable<br />
models in statistical mechanics.<br />
<br />
I will explain how these algebraic objects can serve as natural<br />
receptacles for the (transcendental) monodromy of flat connections<br />
arising from representation theory.<br />
<br />
These connections exist in rational, trigonometric and elliptic<br />
forms, and lead to quantum groups of increasing interest and<br />
complexity.<br />
<br />
===Wed, Sept 25, 2:30PM Ayelet Lindenstrauss (Indiana University)===<br />
''Taylor Series in Homotopy Theory''<br />
<br />
I will discuss Goodwillie's calculus of functors on topological spaces. To mimic the set-up in real analysis, topological spaces are considered small if their nontrivial homotopy groups start only in higher dimensions. They can be considered close only in relation to a map between them, but a map allows us to construct the difference between two spaces, and two spaces are close if the difference between them is small. Spaces can be summed (in different ways) by taking twisted products of them. It is straightforward to construct the analogs of constant, linear, and higher degree homogenous functors, and they can be assembled into "polynomials" and "infinite sums". There are notions of differentiability and higher derivatives, of Taylor towers, and of analytic functions.<br />
<br />
What might look like a game of analogies is an extremely useful tool because when one looks at functors that map topological spaces not into the category of topological spaces, but into the category of spectra (the stabilized version of the category of spaces, which will be explained), many of them are, in fact, analytic, so they can be constructed from the homogenous functors of different degrees. And we can use appropriate analogs of calculus theorems to understand them better. I will conclude with some recent work of Randy McCarthy and myself, applying Goodwillie's calculus to algebraic K-theory calculations.<br />
<br />
===Sep 25: Jim Demmel (Berkeley) ===<br />
''Communication Avoiding Algorithms for Linear Algebra and Beyond''<br />
<br />
Algorithm have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present algorithms that attain provable lower bounds on communication, and show large speedups compared to their conventional counterparts. These algorithms are for direct and iterative linear algebra, for dense and sparse matrices, as well as direct n-body simulations. Several of these algorithms exhibit perfect strong scaling, in both time and energy: run time (resp. energy) for a fixed problem size drops proportionally to the number of processors p (resp. is independent of p). Finally, we describe extensions to algorithms involving arbitrary loop nests and array accesses, assuming only that array subscripts are affine functions of the loop indices. <br />
<br />
===Sep 26: Jim Demmel (Berkeley) ===<br />
''Implementing Communication Avoiding Algorithms''<br />
<br />
Designing algorithms that avoiding communication, attaining<br />
lower bounds if possible, is critical for algorithms to minimize runtime and<br />
energy on current and future architectures. These new algorithms can have <br />
new numerical stability properties, new ways to encode answers, and new data<br />
structures, not just depend on loop transformations (we need those too!).<br />
We will illustrate with a variety of examples including direct linear algebra<br />
(eg new ways to perform pivoting, new deterministic and randomized<br />
eigenvalue algorithms), iterative linear algebra (eg new ways to reorganize<br />
Krylov subspace methods) and direct n-body algorithms, on architectures<br />
ranging from multicore to distributed memory to heterogeneous.<br />
The theory describing communication avoiding algorithms can give us a large<br />
design space of possible implementations, so we use autotuning to find<br />
the fastest one automatically. Finally, on parallel architectures one can<br />
frequently not expect to get bitwise identical results from multiple runs,<br />
because of dynamic scheduling and floating point nonassociativity; <br />
this can be a problem for reasons from debugging to correctness.<br />
We discuss some techniques to get reproducible results at modest cost.<br />
<br />
===Sep 27: Jim Demmel (Berkeley) ===<br />
''Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays''<br />
<br />
Our goal is to minimize communication, i.e. moving data, since it increasingly<br />
dominates the cost of arithmetic in algorithms. Motivated by this, attainable<br />
communication lower bounds have been established by many authors for a <br />
variety of algorithms including matrix computations.<br />
<br />
The lower bound approach used initially by Irony, Tiskin and Toledo <br />
for O(n^3) matrix multiplication, and later by Ballard et al <br />
for many other linear algebra algorithms, depends on a geometric result by <br />
Loomis and Whitney: this result bounds the volume of a 3D set <br />
(representing multiply-adds done in the inner loop of the algorithm) <br />
using the product of the areas of certain 2D projections of this set <br />
(representing the matrix entries available locally, i.e., without communication).<br />
<br />
Using a recent generalization of Loomis' and Whitney's result, we generalize <br />
this lower bound approach to a much larger class of algorithms, <br />
that may have arbitrary numbers of loops and arrays with arbitrary dimensions, <br />
as long as the index expressions are affine combinations of loop variables.<br />
In other words, the algorithm can do arbitrary operations on any number of <br />
variables like A(i1,i2,i2-2*i1,3-4*i3+7*i_4,…).<br />
Moreover, the result applies to recursive programs, irregular iteration spaces, <br />
sparse matrices, and other data structures as long as the computation can be<br />
logically mapped to loops and indexed data structure accesses. <br />
<br />
We also discuss when optimal algorithms exist that attain the lower bounds; <br />
this leads to new asymptotically faster algorithms for several problems.<br />
<br />
===October 4: Frank Sottile (Texas A&M) ===<br />
''Galois groups of Schubert problems''<br />
<br />
Work of Jordan from 1870 showed how Galois theory<br />
can be applied to enumerative geometry. Hermite earlier<br />
showed the equivalence of Galois groups with geometric <br />
monodromy groups, and in 1979 Harris used this to study <br />
Galois groups of many enumerative problems. Vakil gave <br />
a geometric-combinatorial criterion that implies a Galois <br />
group contains the alternating group. With Brooks and <br />
Martin del Campo, we used Vakil's criterion to show that <br />
all Schubert problems involving lines have at least <br />
alternating Galois group. White and I have given a new <br />
proof of this based on 2-transitivity.<br />
<br />
My talk will describe this background and sketch a <br />
current project to systematically determine Galois groups <br />
of all Schubert problems of moderate size on all small <br />
classical flag manifolds, investigating at least several <br />
million problems. This will use supercomputers employing <br />
several overlapping methods, including combinatorial <br />
criteria, symbolic computation, and numerical homotopy <br />
continuation, and require the development of new <br />
algorithms and software.<br />
<br />
===October 11: Amie Wilkinson (Chicago) ===<br />
<br />
''Robust mechanisms for chaos''<br />
<br />
What are the underlying mechanisms for robustly chaotic behavior in smooth dynamics?<br />
<br />
In addressing this question, I'll focus on the study of diffeomorphisms of a compact manifold, where "chaotic" means "mixing" and and "robustly" means "stable under smooth perturbations." I'll describe recent advances in constructing and using tools called "blenders" to produce stably chaotic behavior with arbitrarily little effort.<br />
<br />
===October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) ===<br />
<br />
''Integrable probability I and II''<br />
<br />
The goal of the talks is to describe the emerging field of integrable<br />
probability, whose goal is to identify and analyze exactly solvable<br />
probabilistic models. The models and results are often easy to describe,<br />
yet difficult to find, and they carry essential information about broad<br />
universality classes of stochastic processes.<br />
<br />
<br />
===October 25: Paul Garrett (Minnesota)=== <br />
<br />
''Boundary-value problems, generalized functions, and zeros of zeta functions''<br />
<br />
Modern analysis (Beppo Levi, Sobolev, Friedrichs, Schwartz) illuminates work of D. Hejhal and Y. Colin de Verdiere from 30 years<br />
ago, clarifying, as in P. Cartier's letter to A. Weil, "how the Riemann Hypothesis was not proven". (Joint with E. Bombieri.)<br />
<br />
===November 1: Allison Lewko (Columbia University) ===<br />
<br />
''On sets of large doubling, Lambda(4) sets, and error-correcting codes''<br />
<br />
We investigate the structure of finite sets A of integers such that A+A is large, presenting a counterexample to natural conjectures in the pursuit of an "anti-Freiman" theory in additive combinatorics. We will begin with a brief history of the problem and its connection to the study of Lambda(4) sets in harmonic analysis, and then we will discuss our counterexample and its construction from error-correcting codes. We will conclude by describing some related open problems.<br />
This is joint work with Mark Lewko.<br />
<br />
===November 8: Tim Riley (Cornell)===<br />
<br />
''Hydra groups''<br />
<br />
A few years ago Will Dison and I constructed a family of<br />
finitely generated groups whose workings include a string-rewriting<br />
phenomenon of extraordinary duration which is reminiscent of Hercules'<br />
battle with the hydra. I will describe this and the investigations it<br />
spurred in hyperbolic geometry, combinatorial group theory, and a<br />
problem of how to calculate efficiently with hugely compressed<br />
representations of integers.<br />
<br />
===November 22: Tianling Jin (University of Chicago)===<br />
<br />
''Solutions of some Monge-Ampere equations with degeneracy or singularities''<br />
<br />
We will first give a new proof of a celebrated theorem of<br />
Jorgens which states that every classical convex solution of det(Hess<br />
u)=1 in R^2 has to be a second order polynomial. Our arguments do not use<br />
complex analysis, and will be applied to establish such Liouville type<br />
theorems for solutions some degenerate Monge-Ampere equations. We will<br />
also discuss some results on existence, regularity, classification, and<br />
asymptotic behavior of solutions of some Monge-Ampere equations with<br />
isolated and line singularities. This is joint work with J. Xiong.<br />
<br />
===Monday, Nov 25: Lin Lin (Lawrence Berkeley National Lab)===<br />
<br />
''Fast algorithms for electronic structure analysis''<br />
<br />
Kohn-Sham density functional theory (KSDFT) is the most widely used<br />
electronic structure theory for molecules and condensed matter systems. For<br />
a system with N electrons, the standard method for solving KSDFT requires<br />
solving N eigenvectors for an O(N) * O(N) Kohn-Sham Hamiltonian matrix.<br />
The computational cost for such procedure is expensive and scales as<br />
O(N^3). We have developed pole expansion plus selected inversion (PEXSI)<br />
method, in which KSDFT is solved by evaluating the selected elements of the<br />
inverse of a series of sparse symmetric matrices, and the overall algorithm<br />
scales at most O(N^2) for all materials including insulators,<br />
semiconductors and metals. The PEXSI method can be used with orthogonal or<br />
nonorthogonal basis set, and the physical quantities including electron<br />
density, energy, atomic force, density of states, and local density of<br />
states are calculated accurately without using the eigenvalues and<br />
eigenvectors. The recently developed massively parallel PEXSI method has<br />
been implemented in SIESTA, one of the most popular electronic structure<br />
software using atomic orbital basis set. The resulting method can allow<br />
accurate treatment of electronic structure in a unprecedented scale. We<br />
demonstrate the application of the method for solving graphene-like<br />
structures with more than 20,000 atoms, and the method can be efficiently<br />
parallelized 10,000 - 100,000 processors on Department of Energy (DOE) high<br />
performance machines.<br />
<br />
===November 26 (Tuesday): Clinton Conley (Cornell)===<br />
<br />
''Descriptive set-theoretic graph theory''<br />
<br />
Familiar graph-theoretic problems (for example, vertex coloring) exhibit a<br />
stark change of character when measurability constraints are placed on the<br />
structures and functions involved. While discussing some ramifications in<br />
descriptive set theory, we also pay special attention to interactions with<br />
probability (concerning random colorings of Cayley graphs) and ergodic<br />
theory (characterizing various dynamical properties of groups). The talk<br />
will include joint work with Alexander Kechris, Andrew Marks, Benjamin<br />
Miller, and Robin Tucker-Drob.<br />
<br />
<br />
===December 2 (Monday): Simon Marshall (Northwestern)===<br />
<br />
''Semiclassical estimates for eigenfunctions on locally symmetric spaces''<br />
<br />
Let M be a compact Riemannian manifold, and f an L^2-normalised Laplace<br />
eigenfunction on M. If p > 2, a theorem of Sogge tells us how large the L^p<br />
norm of f can be in terms of its Laplace eigenvalue. For instance, when p<br />
is infinity this is asking how large the peaks of f can be. I will present<br />
an analogue of Sogge's theorem for eigenfunctions of the full ring of<br />
invariant differential operators on a locally symmetric space, and discuss<br />
some links between this result and number theory.<br />
<br />
===December 4 (Wednesday): Steven Sam (Berkeley)===<br />
<br />
''Free Resolutions and Symmetry''<br />
<br />
This talk is about the use of symmetry in the study of modules and free resolutions in commutative algebra and algebraic geometry, and specifically how it clarifies, organizes, and rigidifies calculations, and how it enables us to find finiteness in situations where it a priori does not seem to exist. I will begin the talk with an example coming from classical invariant theory and determinantal ideals using just some basic notions from linear algebra. Then I will explain some of my own work which builds on this setting in several directions. Finally, I'll discuss a recent program on twisted commutative algebras, developed jointly with Andrew Snowden, which formalizes the synthesis of representation theory and commutative algebra and leads to new finiteness results in seemingly infinite settings.<br />
<br />
===December 6: Paul Hand (MIT)===<br />
<br />
''Simplifications of the Lifting Approach for Quadratic Signal Recovery Problems''<br />
<br />
Many signal recovery problems are quadratic in nature, such as phase<br />
retrieval and sparse principal component analysis. Such problems in<br />
R^n can be convexified by introducing n^2 variables corresponding to<br />
each quadratic combination of unknowns. This approach often gives<br />
rise to an n x n matrix recovery problem that is convex and has<br />
provable recovery guarantees. Because the dimensionality has been<br />
squared, it is an important task to find simplifications that make<br />
computation more tractable. We will discuss two examples where the<br />
lifting approach can be simplified while retaining recovery<br />
guarantees. These examples will be the phase retrieval problem and a<br />
special case of sparse principal component analysis.<br />
<br />
===December 9 (Monday): Jacob Bedrossian (Courant Institute)===<br />
<br />
''Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations''<br />
<br />
We prove asymptotic stability of shear flows close to the<br />
planar, periodic Couette flow in the 2D incompressible Euler equations.<br />
That is, given an initial perturbation of the Couette flow small in a<br />
suitable regularity class, specifically Gevrey space of class smaller than<br />
2, the velocity converges strongly in L2 to a shear flow which is also<br />
close to the Couette flow. The vorticity is asymptotically mixed to small<br />
scales by an almost linear evolution and in general enstrophy is lost in<br />
the weak limit. The strong convergence of the velocity field is sometimes<br />
referred to as inviscid damping, due to the relationship with Landau<br />
damping in the Vlasov equations. Joint work with Nader Masmoudi.<br />
<br />
===Wednesday, Dec 11: Lu Wang (Johns Hopkins)===<br />
<br />
''Rigidity of Self-shrinkers of Mean Curvature Flow''<br />
<br />
The study of mean curvature flow not only is fundamental in geometry, topology and analysis, but also has important applications in applied mathematics, for instance, image processing. One of the most important problems in mean curvature flow is to understand the possible singularities of the flow and self-shrinkers, i.e., self-shrinking solutions of the flow, provide the singularity models.<br />
<br />
In this talk, I will describe the rigidity of asymptotic structures of self-shrinkers. First, I show the uniqueness of properly embedded self-shrinkers asymptotic to any given regular cone. Next, I give a partial affirmative answer to a conjecture of Ilmanen under an infinite order asymptotic assumption, which asserts that the only two-dimensional properly embedded self-shrinker asymptotic to a cylinder along some end is itself the cylinder. The feature of our results is that no completeness of self-shrinkers is required.<br />
<br />
The key ingredients in the proof are a novel reduction of unique continuation for elliptic operators to backwards uniqueness for parabolic operators and the Carleman type techniques. If time permits, I will discuss some applications of our approach to shrinking solitons of Ricci flow.<br />
<br />
===Friday, Dec 13: Chanwoo Kim (Cambridge)===<br />
<br />
''Regularity of the Boltzmann equation in convex domains''<br />
<br />
A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the Boltzmann equation in a strictly convex domain with the specular, bounce-back and diffuse boundary condition. With the aid of a distance function toward the grazing set, we construct weighted classical <math>C^{1}</math> solutions away from the grazing set for all boundary conditions. For the diffuse boundary condition, we construct <math>W^{1,p}</math> solutions for 1< p<2 and weighted <math>W^{1,p}</math> solutions for <math>2\leq p\leq \infty</math> as well. On the other hand, we show second derivatives do not exist up to the boundary in general by constructing counterexamples for all boundary conditions. This is a joint work with Guo, Tonon, Trescases.<br />
<br />
===December 17: Perla Sousi (Cambridge)===<br />
<br />
''The effect of drift on the volume of the Wiener sausage''<br />
<br />
The Wiener sausage at time t is the algebraic sum of a Brownian path on [0,t] and a ball. Does the expected volume of the Wiener sausage increase when we add drift?<br />
How do you compare the expected volume of the usual Wiener sausage to one defined as the algebraic sum of the Brownian path and a square (in 2D) or a cube (in higher dimensions)? We will answer these questions using their relation to the detection problem for Poisson Brownian motions, and rearrangement inequalities on the sphere (with Y. Peres). We will also discuss generalisations of this to Levy processes (with A. Drewitz and R. Sun) as well as an adversarial detection problem and its connections to Kakeya sets (with Babichenko, Peres, Peretz and Winkler).<br />
<br />
<br />
===December 18: Dustin Cartwright (Yale)===<br />
<br />
''Tropical Complexes''<br />
<br />
Tropical geometry is a way of understanding algebraic varieties by the limiting behavior of their degenerations. Through tropicalization, algebraic operations are replaced with combinatorial constructions and piecewise linear functions. I will introduce tropical complexes, which a way of understanding the geometry of algebraic varieties through combinatorics. Tropical complexes are Delta-complexes together with additional integral data, for which one has parallels and concrete comparisons with the behavior of algebraic varieties. <br />
<br />
===January 6: Aaron Lauda (USC)===<br />
<br />
''An introduction to diagrammatic categorification''<br />
<br />
Categorification seeks to reveal a hidden layer in mathematical<br />
structures. Often the resulting structures can be combinatorially<br />
complex objects making them difficult to study. One method of<br />
overcoming this difficulty, that has proven very successful, is to<br />
encode the categorification into a diagrammatic calculus that makes<br />
computations simple and intuitive.<br />
<br />
In this talk I will review some of the original considerations that<br />
led to the categorification philosophy. We will examine how the<br />
diagrammatic perspective has helped to produce new categorifications<br />
having profound applications to algebra, representation theory, and<br />
low-dimensional topology.<br />
<br />
===January 8: Karin Melnick (Maryland)===<br />
<br />
''Normal forms for local flows on parabolic geometries''<br />
<br />
The exponential map in Riemannian geometry conjugates the differential of an isometry at a point with the action of the isometry near the point. It thus provides a linear normal form for all isometries fixing a point. Conformal transformations are not linearizable in general. I will discuss a suite of normal forms theorems in conformal geometry and, more generally, for parabolic geometries, a rich family of geometric structures of which conformal, projective, and CR structures are examples.<br />
<br />
===January 10, 4PM: Yen Do (Yale)===<br />
<br />
''Convergence of Fourier series and multilinear analysis''<br />
<br />
Almost everywhere convergence of the Fourier series of square <br />
integrable functions was first proved by Lennart Carleson in 1966, and <br />
the proof has lead to deep developments in various multilinear settings. <br />
In this talk I would like to introduce a brief history of the subject <br />
and sketch some recent developments, some of these involve my joint <br />
works with collaborators.<br />
<br />
===Mon, January 13: Yi Wang (Stanford)===<br />
<br />
''Isoperimetric Inequality and Q-curvature''<br />
<br />
A well-known question in differential geometry is to prove the<br />
isoperimetric inequality under intrinsic curvature conditions. In<br />
dimension 2, the isoperimetric inequality is controlled by the integral of<br />
the positive part of the Gaussian curvature. In my recent work, I prove<br />
that on simply connected conformally flat manifolds of higher dimensions,<br />
the role of the Gaussian curvature can be replaced by the Branson's<br />
Q-curvature. The isoperimetric inequality is valid if the integral of the<br />
Q-curvature is below a sharp threshold. Moreover, the isoperimetric<br />
constant depends only on the integrals of the Q-curvature. The proof<br />
relies on the theory of $A_p$ weights in harmonic analysis.<br />
<br />
===January 15: Wei Xiang (University of Oxford)===<br />
<br />
''Conservation Laws and Shock Waves''<br />
<br />
The study of continuum physics gave birth to the theory of quasilinear<br />
systems in divergence form, commonly called conservation laws. In this<br />
talk, conservation laws, the Euler equations, and the definition of the<br />
corresponding weak solutions will be introduced first. Then a short history<br />
of the studying of conservation laws and shock waves will be given. Finally<br />
I would like to present two of our current research projects. One is on the<br />
mathematical analysis of shock diffraction by convex cornered wedges, and<br />
the other one is on the validation of weakly nonlinear geometric optics for<br />
entropy solutions of nonlinear hyperbolic systems of conservation laws.<br />
<br />
Fri, Jan 17, 2:25PM, VV901 Adrianna Gillman (Dartmouth) Fast direct solvers for linear partial differential equations<br />
<br />
===Fri, Jan 17: Adrianna Gillman (Dartmouth) ===<br />
''Fast direct solvers for linear partial differential equations''<br />
<br />
The cost of solving a large linear system often determines what can and cannot be modeled computationally in many areas of science and engineering. Unlike Gaussian elimination which scales cubically with the respect to the number of unknowns, fast direct solvers construct an inverse of a linear in system with a cost that scales linearly or nearly linearly. The fast direct solvers presented in this talk are designed for the linear systems arising from the discretization of linear partial differential equations. These methods are more robust, versatile and stable than iterative schemes. Since an inverse is computed, additional right-hand sides can be processed rapidly. The talk will give the audience a brief introduction to the core ideas, an overview of recent advancements, and it will conclude with a sampling of challenging application examples including the scattering of waves.<br />
<br />
===Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) ===<br />
''Intertwinings, wave equations and growth models''<br />
<br />
We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to hyperbolic partial differential equations, symmetric polynomials and the corresponding random growth models. The talk will be devoted to these recent developments which also shed new light on some beautiful old examples of intertwinings. Based on joint works with Vadim Gorin and Soumik Pal. <br />
<br />
<br />
===Jan 24: Yaniv Plan (Michigan) ===<br />
''Low-dimensionality in mathematical signal processing''<br />
<br />
Natural images tend to be compressible, i.e., the amount of information needed to encode an image is small. This conciseness of information -- in other words, low dimensionality of the signal -- is found throughout a plethora of applications ranging from MRI to quantum state tomography. It is natural to ask: can the number of measurements needed to determine a signal be comparable with the information content? We explore this question under modern models of low-dimensionality and measurement acquisition.<br />
<br />
===Feb 14: Alexander Karp (Columbia Teacher's College) ===<br />
''History of Mathematics Education as a Research Field and as Magistra Vitae''<br />
<br />
The presentation will be based on the experience of putting together and editing the Handbook<br />
on the History of Mathematics Education, which will be published by Springer in the near future. <br />
This volume, which was prepared by a large group of researchers from different countries, <br />
contains the first systematic account of the history of the development of mathematics education <br />
in the whole world (and not just in some particular country or region). The editing of such a <br />
book gave rise to thoughts about the methodology of research in this field, and also about what <br />
constitutes an object of such research. These are the thoughts that the presenter intends to share <br />
with his audience. From them, it is natural to pass to an analysis of the current situation and how <br />
it might develop.<br />
<br />
<br />
<br />
===March 28: Michael Lacey (GA Tech) ===<br />
''The Two Weight Inequality for the Hilbert Transform''<br />
<br />
The individual two weight inequality for the Hilbert transform <br />
asks for a real variable characterization of those pairs of weights <br />
(u,v) for which the Hilbert transform H maps L^2(u) to L^2(v). <br />
This question arises naturally in different settings, most famously <br />
in work of Sarason. Answering in the positive a deep <br />
conjecture of Nazarov-Treil-Volberg, the mapping property <br />
of the Hilbert transform is characterized by a triple of conditions, <br />
the first being a two-weight Poisson A2 on the pair of weights, <br />
with a pair of so-called testing inequalities, uniform over all <br />
intervals. This is the first result of this type for a singular <br />
integral operator. (Joint work with Sawyer, C.-Y. Shen and Uriate-Tuero)<br />
<br />
== Past talks ==<br />
<br />
Last year's schedule: [[Colloquia 2012-2013]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=6384Colloquia/Fall182014-01-19T21:08:01Z<p>Shamgar: /* Spring 2014 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Fall 2013 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
|[http://people.math.gatech.edu/~mbaker/ Matt Baker] (Georgia Institute of Technology)<br />
|Riemann-Roch for Graphs and Applications<br />
|Ellenberg<br />
|-<br />
|Sept 13<br />
|[http://math.wisc.edu/~andrews/ Uri Andrews] (University of Wisconsin)<br />
|A hop, skip, and a jump through the degrees of relative provability<br />
|<br />
|-<br />
|Sept 20<br />
|[http://www.math.neu.edu/people/profile/valerio-toledano-laredo Valerio Toledano Laredo] (Northeastern)<br />
|Flat connections and quantum groups<br />
|Gurevich<br />
|-<br />
|'''Wed, Sept 25, 2:30PM in B139'''<br />
|[http://mypage.iu.edu/~alindens/ Ayelet Lindenstrauss] (Indiana University)<br />
|Taylor Series in Homotopy Theory<br />
|Meyer<br />
|-<br />
|'''Wed, Sept 25''' (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication-Avoiding Algorithms for Linear Algebra and Beyond<br />
|Gurevich<br />
|-<br />
|'''Thurs, Sept 26''' (LAA lecture, Joint with Applied Algebra Seminar)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Implementing Communication-Avoiding Algorithms<br />
|Gurevich<br />
|-<br />
|Sept 27 (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays<br />
|Gurevich<br />
|-<br />
|Oct 4<br />
|[http://www.math.tamu.edu/~sottile/ Frank Sottile] (Texas A&M)<br />
|Galois groups of Schubert problems<br />
|Caldararu<br />
|-<br />
|Oct 11<br />
|[http://math.uchicago.edu/~wilkinso/ Amie Wilkinson] (Chicago)<br />
|[[Colloquia#October 11: Amie Wilkinson (Chicago) | Robust mechanisms for chaos]]<br />
|WIMAW (Cladek)<br />
|-<br />
|'''Tues, Oct 15, 4PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability I]]<br />
|Valko<br />
|-<br />
|'''Wed, Oct 16, 2:30PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability II]]<br />
|Valko<br />
|-<br />
|<strike>Oct 18</strike><br />
|No colloquium due to the distinguished lecture<br />
|<br />
|<br />
|-<br />
|Oct 25<br />
|[http://www.math.umn.edu/~garrett/ Paul Garrett] (Minnesota)<br />
|[[Colloquia#October 25: Paul Garrett (Minnesota) | Boundary-value problems, generalized functions, and zeros of zeta functions]]<br />
|Gurevich<br />
|<br />
|<br />
|-<br />
|Nov 1<br />
|[http://www.cs.columbia.edu/~alewko/ Allison Lewko] (Columbia University)<br />
|On sets of large doubling, Lambda(4) sets, and error-correcting codes<br />
|Stovall<br />
|-<br />
|Nov 8<br />
|[http://www.math.cornell.edu/~riley/ Tim Riley] (Cornell)<br />
|[[Colloquia#November 8: Tim Riley (Cornell) | Hydra groups]]<br />
|Dymarz<br />
|-<br />
|Nov 15 and later<br />
|Reserved<br />
|<br />
|Street<br />
|-<br />
|Nov 22<br />
|[http://www.math.uchicago.edu/~tj/ Tianling Jin] (University of Chicago)<br />
|Solutions of some Monge-Ampere equations with degeneracy or singularities.<br />
|Bolotin<br />
|-<br />
|'''Mon, Nov 25, 4PM'''<br />
|[https://web.math.princeton.edu/~linlin/ Lin Lin] (Lawrence Berkeley National Lab)<br />
|Fast algorithms for electronic structure analysis<br />
|Jin<br />
|-<br />
|'''Tue, Nov 26, 4PM, B139'''<br />
|[http://www.math.cornell.edu/m/People/Faculty/conley Clinton Conley] (Cornell)<br />
|[[Colloquia#November 26 (Tuesday): Clinton Conley (Cornell) | Descriptive set-theoretic graph theory]]<br />
|Lempp<br />
|-<br />
|'''Mon, Dec 2, 4PM'''<br />
|[http://www.math.northwestern.edu/~slm/ Simon Marshall] (Northwestern)<br />
|[[Colloquia#December 2 (Monday): Simon Marshall (Northwestern) | Semiclassical estimates for eigenfunctions on locally symmetric spaces]]<br />
|Denissov<br />
|-<br />
|'''Wed, Dec 4, 4PM'''<br />
|[http://math.berkeley.edu/~svs/ Steven Sam] (Berkeley)<br />
|Free Resolutions and Symmetry<br />
|Boston <br />
|-<br />
|'''Fri, Dec 6'''<br />
|[http://math.mit.edu/~hand/ Paul Hand] (MIT)<br />
|[[Colloquia#December 6: Paul Hand (MIT) | Simplifications of the lifting approach for quadratic signal recovery problems]]<br />
|Thiffeault<br />
|-<br />
|'''Fri, Dec. 6 and Sat Dec. 7'''<br />
|<br />
|[http://www.math.umn.edu/~stant001/askey80 Conference in honor of Dick Askey]<br />
|<br />
|-<br />
|'''Mon, Dec. 9, 4pm, VV B239'''<br />
|[http://www.cims.nyu.edu/~jacob/ Jacob Bedrossian] (Courant Institute)<br />
|Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations<br />
|Bolotin<br />
|-<br />
|'''Wed, Dec 11, 4PM'''<br />
|[http://math.jhu.edu/~lwang/ Lu Wang] (Johns Hopkins)<br />
|Rigidity of Self-shrinkers of Mean Curvature Flow<br />
|Viaclovsky <br />
|-<br />
|'''Fri, Dec. 13, 2:25pm, VV 901'''<br />
|[http://chanwookim.wordpress.com/ Chanwoo Kim] (Cambridge)<br />
|Regularity of the Boltzmann equation in convex domains<br />
|Bolotin<br />
|-<br />
|'''Tues, Dec 17, 4PM'''<br />
|[http://www.statslab.cam.ac.uk/~ps422/ Perla Sousi] (Cambridge)<br />
|[[Colloquia#December 17: Perla Sousi (Cambridge) | The effect of drift on the volume of the Wiener sausage]]<br />
|Seppalainen <br />
|-<br />
|'''Wed, Dec 18, 4PM'''<br />
|[http://users.math.yale.edu/~dc597/ Dustin Cartwright] (Yale)<br />
|[[Colloquia#December 18: Dustin Cartwright (Yale) | Tropical Complexes]]<br />
|Gurevich<br />
|}<br />
<br />
== Spring 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Mon, Jan 6, 4PM'''<br />
|[http://www-bcf.usc.edu/~lauda/Aaron_Laudas_Page/Home.html Aaron Lauda] (USC) <br />
|[[Colloquia#January 6: Aaron Lauda (USC) | An introduction to diagrammatic categorification]]<br />
|Caldararu<br />
|-<br />
|'''Wed, Jan 8, 4PM'''<br />
|[http://www2.math.umd.edu/~kmelnick/ Karin Melnick] (Maryland) <br />
|[[Colloquia#January 8: Karin Melnick (Maryland) | Normal forms for local flows on parabolic geometries]]<br />
|Kent<br />
|-<br />
|Jan 10, 4PM<br />
|[http://users.math.yale.edu/~yd82/ Yen Do] (Yale) <br />
|Convergence of Fourier series and multilinear analysis<br />
|Denissov<br />
|-<br />
|'''Mon, Jan 13, 4pm'''<br />
|[http://math.stanford.edu/~wangyi/ Yi Wang] (Stanford)<br />
|Isoperimetric Inequality and Q-curvature<br />
|Viaclovsky<br />
|-<br />
|'''Wen, Jan 15, 4pm'''<br />
|[http://www.maths.ox.ac.uk/people/profiles/wei.xiang Wei Xiang] (University of Oxford)<br />
|[[Colloquia#January 15: Wei Xiang (University of Oxford) |Conservation Laws and Shock Waves]]<br />
|Bolotin<br />
|-<br />
|'''Fri, Jan 17, 2:25PM, VV901'''<br />
|[http://www.math.dartmouth.edu/~gillmana/ Adrianna Gillman] (Dartmouth) <br />
|Fast direct solvers for linear partial differential equations<br />
|Thiffeault<br />
|-<br />
|'''Thu, Jan 23, 2:25, VV901'''<br />
|[http://www.stat.berkeley.edu/~mshkolni/ Mykhaylo Shkolnikov] (Berkeley)<br />
|[[Colloquia#Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) | Intertwinings, wave equations and growth models]]<br />
|Seppalainen<br />
|-<br />
|Jan 24<br />
|[http://www.yanivplan.com/ Yaniv Plan] (Michigan)<br />
|Low-dimensionality in mathematical signal processing<br />
|Thiffeault<br />
|-<br />
|Jan 31<br />
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)<br />
|<br />
|Gurevich<br />
|-<br />
|Feb 7<br />
|David Treumann (Boston College)<br />
|<br />
|Street<br />
|-<br />
|Feb 14<br />
|[http://www.tc.columbia.edu/academics/index.htm?facid=apk16 Alexander Karp] (Columbia Teacher's College)<br />
|History of Mathematics Education as a Research Field and as Magistra Vitae<br />
|Kiselev<br />
|-<br />
|Feb 21<br />
|<br />
|<br />
|<br />
|-<br />
|Feb 28<br />
|[http://math.nyu.edu/faculty/shelley/ Michael Shelley] (Courant)<br />
|<br />
|Spagnolie<br />
|-<br />
|March 7<br />
|[http://www.math.northwestern.edu/people/facultyProfiles/steve.zelditch.html Steve Zelditch] (Northwestern)<br />
|<br />
|Seeger<br />
|-<br />
|March 14<br />
|<br />
|[https://www.math.ucdavis.edu/~strohmer Thomas Strohmer] (Davis)<br />
|<br />
|Gurevich<br />
|- <br />
|<strike>March 21</strike><br />
|'''Spring Break'''<br />
|No Colloquium<br />
|<br />
|-<br />
|March 28<br />
|[http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)<br />
|The Two Weight Inequality for the Hilbert Transform<br />
|Street<br />
|-<br />
|April 4<br />
|[http://www.math.brown.edu/~res/ Richard Schwartz] (Brown)<br />
|<br />
|Mari-Beffa<br />
|-<br />
|April 11<br />
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)<br />
|<br />
|Gurevich<br />
|-<br />
|April 18 (Wasow Lecture)<br />
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)<br />
|<br />
|Seeger<br />
|-<br />
|April 25<br />
|[http://www.charlesdoran.net Charles Doran](University of Alberta)<br />
|<br />
|Song<br />
|-<br />
|'''Monday, April 28''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|A mystery concerning algebraic plane curves<br />
|Maxim<br />
|-<br />
|'''Tuesday, April 29''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Matrix factorizations old and new<br />
|Maxim<br />
|-<br />
|'''Wednesday, April 30''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Easy solution of polynomial equations over finite fields<br />
|Maxim<br />
|-<br />
|May 2<br />
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)<br />
|<br />
|Boston<br />
|-<br />
|May 9<br />
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)<br />
|<br />
|WIMAW<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sep 6: Matt Baker (GA Tech) ===<br />
''Riemann-Roch for Graphs and Applications''<br />
<br />
We will begin by formulating the Riemann-Roch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a Riemann-Roch theorem for tropical curves, proved by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof of the Brill-Noether theorem in algebraic geometry (work of by Cools-Draisma-Payne-Robeva), a "volume-theoretic proof" of Kirchhoff's Matrix-Tree Theorem (work of An, Kuperberg, Shokrieh, and the speaker), and a new Chabauty-Coleman style bound for the number of rational points on an algebraic curve over the rationals (work of Katz and Zureick-Brown).<br />
<br />
===Sep 13: Uri Andrews (UW-Madison) ===<br />
''A hop, skip, and a jump through the degrees of relative provability''<br />
<br />
The topic of this talk arises from two directions. On the one hand, Gödel's incompleteness theorem tell us that given any sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic, there is a statement that is true but not provable in T. On the other hand, over the past seventy years, a number of researchers studying witnessing functions for various combinatorial statements have realized the importance of fast-growing functions and the fact that their totality is often not provable over a given sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic (e.g. the Paris-Harrington and the Kirby-Paris theorems).<br />
<br />
I will talk about the structure induced by giving the order (for a fixed T) of relative provability for totality of algorithms. That is, for algorithms describing functions f and g, we say f ≤ g if T along with the totality of g suffices to prove the totality of f. It turns out that this structure is rich, and encodes many facets of the nature of provability over sufficiently strong, consistent, effectively axiomatizable theories for first-order arithmetic. (Work joint with Mingzhong Cai, David Diamondstone, Steffen Lempp, and Joseph S. Miller.)<br />
<br />
===Sep 20: Valerio Toledano Laredo (Northeastern)===<br />
''Flat connections and quantum groups''<br />
<br />
Quantum groups are natural deformations of the Lie algebra of<br />
nxn matrices, and more generally of semisimple Lie algebras.<br />
They first arose in the mid eighties in the study of solvable<br />
models in statistical mechanics.<br />
<br />
I will explain how these algebraic objects can serve as natural<br />
receptacles for the (transcendental) monodromy of flat connections<br />
arising from representation theory.<br />
<br />
These connections exist in rational, trigonometric and elliptic<br />
forms, and lead to quantum groups of increasing interest and<br />
complexity.<br />
<br />
===Wed, Sept 25, 2:30PM Ayelet Lindenstrauss (Indiana University)===<br />
''Taylor Series in Homotopy Theory''<br />
<br />
I will discuss Goodwillie's calculus of functors on topological spaces. To mimic the set-up in real analysis, topological spaces are considered small if their nontrivial homotopy groups start only in higher dimensions. They can be considered close only in relation to a map between them, but a map allows us to construct the difference between two spaces, and two spaces are close if the difference between them is small. Spaces can be summed (in different ways) by taking twisted products of them. It is straightforward to construct the analogs of constant, linear, and higher degree homogenous functors, and they can be assembled into "polynomials" and "infinite sums". There are notions of differentiability and higher derivatives, of Taylor towers, and of analytic functions.<br />
<br />
What might look like a game of analogies is an extremely useful tool because when one looks at functors that map topological spaces not into the category of topological spaces, but into the category of spectra (the stabilized version of the category of spaces, which will be explained), many of them are, in fact, analytic, so they can be constructed from the homogenous functors of different degrees. And we can use appropriate analogs of calculus theorems to understand them better. I will conclude with some recent work of Randy McCarthy and myself, applying Goodwillie's calculus to algebraic K-theory calculations.<br />
<br />
===Sep 25: Jim Demmel (Berkeley) ===<br />
''Communication Avoiding Algorithms for Linear Algebra and Beyond''<br />
<br />
Algorithm have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present algorithms that attain provable lower bounds on communication, and show large speedups compared to their conventional counterparts. These algorithms are for direct and iterative linear algebra, for dense and sparse matrices, as well as direct n-body simulations. Several of these algorithms exhibit perfect strong scaling, in both time and energy: run time (resp. energy) for a fixed problem size drops proportionally to the number of processors p (resp. is independent of p). Finally, we describe extensions to algorithms involving arbitrary loop nests and array accesses, assuming only that array subscripts are affine functions of the loop indices. <br />
<br />
===Sep 26: Jim Demmel (Berkeley) ===<br />
''Implementing Communication Avoiding Algorithms''<br />
<br />
Designing algorithms that avoiding communication, attaining<br />
lower bounds if possible, is critical for algorithms to minimize runtime and<br />
energy on current and future architectures. These new algorithms can have <br />
new numerical stability properties, new ways to encode answers, and new data<br />
structures, not just depend on loop transformations (we need those too!).<br />
We will illustrate with a variety of examples including direct linear algebra<br />
(eg new ways to perform pivoting, new deterministic and randomized<br />
eigenvalue algorithms), iterative linear algebra (eg new ways to reorganize<br />
Krylov subspace methods) and direct n-body algorithms, on architectures<br />
ranging from multicore to distributed memory to heterogeneous.<br />
The theory describing communication avoiding algorithms can give us a large<br />
design space of possible implementations, so we use autotuning to find<br />
the fastest one automatically. Finally, on parallel architectures one can<br />
frequently not expect to get bitwise identical results from multiple runs,<br />
because of dynamic scheduling and floating point nonassociativity; <br />
this can be a problem for reasons from debugging to correctness.<br />
We discuss some techniques to get reproducible results at modest cost.<br />
<br />
===Sep 27: Jim Demmel (Berkeley) ===<br />
''Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays''<br />
<br />
Our goal is to minimize communication, i.e. moving data, since it increasingly<br />
dominates the cost of arithmetic in algorithms. Motivated by this, attainable<br />
communication lower bounds have been established by many authors for a <br />
variety of algorithms including matrix computations.<br />
<br />
The lower bound approach used initially by Irony, Tiskin and Toledo <br />
for O(n^3) matrix multiplication, and later by Ballard et al <br />
for many other linear algebra algorithms, depends on a geometric result by <br />
Loomis and Whitney: this result bounds the volume of a 3D set <br />
(representing multiply-adds done in the inner loop of the algorithm) <br />
using the product of the areas of certain 2D projections of this set <br />
(representing the matrix entries available locally, i.e., without communication).<br />
<br />
Using a recent generalization of Loomis' and Whitney's result, we generalize <br />
this lower bound approach to a much larger class of algorithms, <br />
that may have arbitrary numbers of loops and arrays with arbitrary dimensions, <br />
as long as the index expressions are affine combinations of loop variables.<br />
In other words, the algorithm can do arbitrary operations on any number of <br />
variables like A(i1,i2,i2-2*i1,3-4*i3+7*i_4,…).<br />
Moreover, the result applies to recursive programs, irregular iteration spaces, <br />
sparse matrices, and other data structures as long as the computation can be<br />
logically mapped to loops and indexed data structure accesses. <br />
<br />
We also discuss when optimal algorithms exist that attain the lower bounds; <br />
this leads to new asymptotically faster algorithms for several problems.<br />
<br />
===October 4: Frank Sottile (Texas A&M) ===<br />
''Galois groups of Schubert problems''<br />
<br />
Work of Jordan from 1870 showed how Galois theory<br />
can be applied to enumerative geometry. Hermite earlier<br />
showed the equivalence of Galois groups with geometric <br />
monodromy groups, and in 1979 Harris used this to study <br />
Galois groups of many enumerative problems. Vakil gave <br />
a geometric-combinatorial criterion that implies a Galois <br />
group contains the alternating group. With Brooks and <br />
Martin del Campo, we used Vakil's criterion to show that <br />
all Schubert problems involving lines have at least <br />
alternating Galois group. White and I have given a new <br />
proof of this based on 2-transitivity.<br />
<br />
My talk will describe this background and sketch a <br />
current project to systematically determine Galois groups <br />
of all Schubert problems of moderate size on all small <br />
classical flag manifolds, investigating at least several <br />
million problems. This will use supercomputers employing <br />
several overlapping methods, including combinatorial <br />
criteria, symbolic computation, and numerical homotopy <br />
continuation, and require the development of new <br />
algorithms and software.<br />
<br />
===October 11: Amie Wilkinson (Chicago) ===<br />
<br />
''Robust mechanisms for chaos''<br />
<br />
What are the underlying mechanisms for robustly chaotic behavior in smooth dynamics?<br />
<br />
In addressing this question, I'll focus on the study of diffeomorphisms of a compact manifold, where "chaotic" means "mixing" and and "robustly" means "stable under smooth perturbations." I'll describe recent advances in constructing and using tools called "blenders" to produce stably chaotic behavior with arbitrarily little effort.<br />
<br />
===October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) ===<br />
<br />
''Integrable probability I and II''<br />
<br />
The goal of the talks is to describe the emerging field of integrable<br />
probability, whose goal is to identify and analyze exactly solvable<br />
probabilistic models. The models and results are often easy to describe,<br />
yet difficult to find, and they carry essential information about broad<br />
universality classes of stochastic processes.<br />
<br />
<br />
===October 25: Paul Garrett (Minnesota)=== <br />
<br />
''Boundary-value problems, generalized functions, and zeros of zeta functions''<br />
<br />
Modern analysis (Beppo Levi, Sobolev, Friedrichs, Schwartz) illuminates work of D. Hejhal and Y. Colin de Verdiere from 30 years<br />
ago, clarifying, as in P. Cartier's letter to A. Weil, "how the Riemann Hypothesis was not proven". (Joint with E. Bombieri.)<br />
<br />
===November 1: Allison Lewko (Columbia University) ===<br />
<br />
''On sets of large doubling, Lambda(4) sets, and error-correcting codes''<br />
<br />
We investigate the structure of finite sets A of integers such that A+A is large, presenting a counterexample to natural conjectures in the pursuit of an "anti-Freiman" theory in additive combinatorics. We will begin with a brief history of the problem and its connection to the study of Lambda(4) sets in harmonic analysis, and then we will discuss our counterexample and its construction from error-correcting codes. We will conclude by describing some related open problems.<br />
This is joint work with Mark Lewko.<br />
<br />
===November 8: Tim Riley (Cornell)===<br />
<br />
''Hydra groups''<br />
<br />
A few years ago Will Dison and I constructed a family of<br />
finitely generated groups whose workings include a string-rewriting<br />
phenomenon of extraordinary duration which is reminiscent of Hercules'<br />
battle with the hydra. I will describe this and the investigations it<br />
spurred in hyperbolic geometry, combinatorial group theory, and a<br />
problem of how to calculate efficiently with hugely compressed<br />
representations of integers.<br />
<br />
===November 22: Tianling Jin (University of Chicago)===<br />
<br />
''Solutions of some Monge-Ampere equations with degeneracy or singularities''<br />
<br />
We will first give a new proof of a celebrated theorem of<br />
Jorgens which states that every classical convex solution of det(Hess<br />
u)=1 in R^2 has to be a second order polynomial. Our arguments do not use<br />
complex analysis, and will be applied to establish such Liouville type<br />
theorems for solutions some degenerate Monge-Ampere equations. We will<br />
also discuss some results on existence, regularity, classification, and<br />
asymptotic behavior of solutions of some Monge-Ampere equations with<br />
isolated and line singularities. This is joint work with J. Xiong.<br />
<br />
===Monday, Nov 25: Lin Lin (Lawrence Berkeley National Lab)===<br />
<br />
''Fast algorithms for electronic structure analysis''<br />
<br />
Kohn-Sham density functional theory (KSDFT) is the most widely used<br />
electronic structure theory for molecules and condensed matter systems. For<br />
a system with N electrons, the standard method for solving KSDFT requires<br />
solving N eigenvectors for an O(N) * O(N) Kohn-Sham Hamiltonian matrix.<br />
The computational cost for such procedure is expensive and scales as<br />
O(N^3). We have developed pole expansion plus selected inversion (PEXSI)<br />
method, in which KSDFT is solved by evaluating the selected elements of the<br />
inverse of a series of sparse symmetric matrices, and the overall algorithm<br />
scales at most O(N^2) for all materials including insulators,<br />
semiconductors and metals. The PEXSI method can be used with orthogonal or<br />
nonorthogonal basis set, and the physical quantities including electron<br />
density, energy, atomic force, density of states, and local density of<br />
states are calculated accurately without using the eigenvalues and<br />
eigenvectors. The recently developed massively parallel PEXSI method has<br />
been implemented in SIESTA, one of the most popular electronic structure<br />
software using atomic orbital basis set. The resulting method can allow<br />
accurate treatment of electronic structure in a unprecedented scale. We<br />
demonstrate the application of the method for solving graphene-like<br />
structures with more than 20,000 atoms, and the method can be efficiently<br />
parallelized 10,000 - 100,000 processors on Department of Energy (DOE) high<br />
performance machines.<br />
<br />
===November 26 (Tuesday): Clinton Conley (Cornell)===<br />
<br />
''Descriptive set-theoretic graph theory''<br />
<br />
Familiar graph-theoretic problems (for example, vertex coloring) exhibit a<br />
stark change of character when measurability constraints are placed on the<br />
structures and functions involved. While discussing some ramifications in<br />
descriptive set theory, we also pay special attention to interactions with<br />
probability (concerning random colorings of Cayley graphs) and ergodic<br />
theory (characterizing various dynamical properties of groups). The talk<br />
will include joint work with Alexander Kechris, Andrew Marks, Benjamin<br />
Miller, and Robin Tucker-Drob.<br />
<br />
<br />
===December 2 (Monday): Simon Marshall (Northwestern)===<br />
<br />
''Semiclassical estimates for eigenfunctions on locally symmetric spaces''<br />
<br />
Let M be a compact Riemannian manifold, and f an L^2-normalised Laplace<br />
eigenfunction on M. If p > 2, a theorem of Sogge tells us how large the L^p<br />
norm of f can be in terms of its Laplace eigenvalue. For instance, when p<br />
is infinity this is asking how large the peaks of f can be. I will present<br />
an analogue of Sogge's theorem for eigenfunctions of the full ring of<br />
invariant differential operators on a locally symmetric space, and discuss<br />
some links between this result and number theory.<br />
<br />
===December 4 (Wednesday): Steven Sam (Berkeley)===<br />
<br />
''Free Resolutions and Symmetry''<br />
<br />
This talk is about the use of symmetry in the study of modules and free resolutions in commutative algebra and algebraic geometry, and specifically how it clarifies, organizes, and rigidifies calculations, and how it enables us to find finiteness in situations where it a priori does not seem to exist. I will begin the talk with an example coming from classical invariant theory and determinantal ideals using just some basic notions from linear algebra. Then I will explain some of my own work which builds on this setting in several directions. Finally, I'll discuss a recent program on twisted commutative algebras, developed jointly with Andrew Snowden, which formalizes the synthesis of representation theory and commutative algebra and leads to new finiteness results in seemingly infinite settings.<br />
<br />
===December 6: Paul Hand (MIT)===<br />
<br />
''Simplifications of the Lifting Approach for Quadratic Signal Recovery Problems''<br />
<br />
Many signal recovery problems are quadratic in nature, such as phase<br />
retrieval and sparse principal component analysis. Such problems in<br />
R^n can be convexified by introducing n^2 variables corresponding to<br />
each quadratic combination of unknowns. This approach often gives<br />
rise to an n x n matrix recovery problem that is convex and has<br />
provable recovery guarantees. Because the dimensionality has been<br />
squared, it is an important task to find simplifications that make<br />
computation more tractable. We will discuss two examples where the<br />
lifting approach can be simplified while retaining recovery<br />
guarantees. These examples will be the phase retrieval problem and a<br />
special case of sparse principal component analysis.<br />
<br />
===December 9 (Monday): Jacob Bedrossian (Courant Institute)===<br />
<br />
''Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations''<br />
<br />
We prove asymptotic stability of shear flows close to the<br />
planar, periodic Couette flow in the 2D incompressible Euler equations.<br />
That is, given an initial perturbation of the Couette flow small in a<br />
suitable regularity class, specifically Gevrey space of class smaller than<br />
2, the velocity converges strongly in L2 to a shear flow which is also<br />
close to the Couette flow. The vorticity is asymptotically mixed to small<br />
scales by an almost linear evolution and in general enstrophy is lost in<br />
the weak limit. The strong convergence of the velocity field is sometimes<br />
referred to as inviscid damping, due to the relationship with Landau<br />
damping in the Vlasov equations. Joint work with Nader Masmoudi.<br />
<br />
===Wednesday, Dec 11: Lu Wang (Johns Hopkins)===<br />
<br />
''Rigidity of Self-shrinkers of Mean Curvature Flow''<br />
<br />
The study of mean curvature flow not only is fundamental in geometry, topology and analysis, but also has important applications in applied mathematics, for instance, image processing. One of the most important problems in mean curvature flow is to understand the possible singularities of the flow and self-shrinkers, i.e., self-shrinking solutions of the flow, provide the singularity models.<br />
<br />
In this talk, I will describe the rigidity of asymptotic structures of self-shrinkers. First, I show the uniqueness of properly embedded self-shrinkers asymptotic to any given regular cone. Next, I give a partial affirmative answer to a conjecture of Ilmanen under an infinite order asymptotic assumption, which asserts that the only two-dimensional properly embedded self-shrinker asymptotic to a cylinder along some end is itself the cylinder. The feature of our results is that no completeness of self-shrinkers is required.<br />
<br />
The key ingredients in the proof are a novel reduction of unique continuation for elliptic operators to backwards uniqueness for parabolic operators and the Carleman type techniques. If time permits, I will discuss some applications of our approach to shrinking solitons of Ricci flow.<br />
<br />
===Friday, Dec 13: Chanwoo Kim (Cambridge)===<br />
<br />
''Regularity of the Boltzmann equation in convex domains''<br />
<br />
A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the Boltzmann equation in a strictly convex domain with the specular, bounce-back and diffuse boundary condition. With the aid of a distance function toward the grazing set, we construct weighted classical <math>C^{1}</math> solutions away from the grazing set for all boundary conditions. For the diffuse boundary condition, we construct <math>W^{1,p}</math> solutions for 1< p<2 and weighted <math>W^{1,p}</math> solutions for <math>2\leq p\leq \infty</math> as well. On the other hand, we show second derivatives do not exist up to the boundary in general by constructing counterexamples for all boundary conditions. This is a joint work with Guo, Tonon, Trescases.<br />
<br />
===December 17: Perla Sousi (Cambridge)===<br />
<br />
''The effect of drift on the volume of the Wiener sausage''<br />
<br />
The Wiener sausage at time t is the algebraic sum of a Brownian path on [0,t] and a ball. Does the expected volume of the Wiener sausage increase when we add drift?<br />
How do you compare the expected volume of the usual Wiener sausage to one defined as the algebraic sum of the Brownian path and a square (in 2D) or a cube (in higher dimensions)? We will answer these questions using their relation to the detection problem for Poisson Brownian motions, and rearrangement inequalities on the sphere (with Y. Peres). We will also discuss generalisations of this to Levy processes (with A. Drewitz and R. Sun) as well as an adversarial detection problem and its connections to Kakeya sets (with Babichenko, Peres, Peretz and Winkler).<br />
<br />
<br />
===December 18: Dustin Cartwright (Yale)===<br />
<br />
''Tropical Complexes''<br />
<br />
Tropical geometry is a way of understanding algebraic varieties by the limiting behavior of their degenerations. Through tropicalization, algebraic operations are replaced with combinatorial constructions and piecewise linear functions. I will introduce tropical complexes, which a way of understanding the geometry of algebraic varieties through combinatorics. Tropical complexes are Delta-complexes together with additional integral data, for which one has parallels and concrete comparisons with the behavior of algebraic varieties. <br />
<br />
===January 6: Aaron Lauda (USC)===<br />
<br />
''An introduction to diagrammatic categorification''<br />
<br />
Categorification seeks to reveal a hidden layer in mathematical<br />
structures. Often the resulting structures can be combinatorially<br />
complex objects making them difficult to study. One method of<br />
overcoming this difficulty, that has proven very successful, is to<br />
encode the categorification into a diagrammatic calculus that makes<br />
computations simple and intuitive.<br />
<br />
In this talk I will review some of the original considerations that<br />
led to the categorification philosophy. We will examine how the<br />
diagrammatic perspective has helped to produce new categorifications<br />
having profound applications to algebra, representation theory, and<br />
low-dimensional topology.<br />
<br />
===January 8: Karin Melnick (Maryland)===<br />
<br />
''Normal forms for local flows on parabolic geometries''<br />
<br />
The exponential map in Riemannian geometry conjugates the differential of an isometry at a point with the action of the isometry near the point. It thus provides a linear normal form for all isometries fixing a point. Conformal transformations are not linearizable in general. I will discuss a suite of normal forms theorems in conformal geometry and, more generally, for parabolic geometries, a rich family of geometric structures of which conformal, projective, and CR structures are examples.<br />
<br />
===January 10, 4PM: Yen Do (Yale)===<br />
<br />
''Convergence of Fourier series and multilinear analysis''<br />
<br />
Almost everywhere convergence of the Fourier series of square <br />
integrable functions was first proved by Lennart Carleson in 1966, and <br />
the proof has lead to deep developments in various multilinear settings. <br />
In this talk I would like to introduce a brief history of the subject <br />
and sketch some recent developments, some of these involve my joint <br />
works with collaborators.<br />
<br />
===Mon, January 13: Yi Wang (Stanford)===<br />
<br />
''Isoperimetric Inequality and Q-curvature''<br />
<br />
A well-known question in differential geometry is to prove the<br />
isoperimetric inequality under intrinsic curvature conditions. In<br />
dimension 2, the isoperimetric inequality is controlled by the integral of<br />
the positive part of the Gaussian curvature. In my recent work, I prove<br />
that on simply connected conformally flat manifolds of higher dimensions,<br />
the role of the Gaussian curvature can be replaced by the Branson's<br />
Q-curvature. The isoperimetric inequality is valid if the integral of the<br />
Q-curvature is below a sharp threshold. Moreover, the isoperimetric<br />
constant depends only on the integrals of the Q-curvature. The proof<br />
relies on the theory of $A_p$ weights in harmonic analysis.<br />
<br />
===January 15: Wei Xiang (University of Oxford)===<br />
<br />
''Conservation Laws and Shock Waves''<br />
<br />
The study of continuum physics gave birth to the theory of quasilinear<br />
systems in divergence form, commonly called conservation laws. In this<br />
talk, conservation laws, the Euler equations, and the definition of the<br />
corresponding weak solutions will be introduced first. Then a short history<br />
of the studying of conservation laws and shock waves will be given. Finally<br />
I would like to present two of our current research projects. One is on the<br />
mathematical analysis of shock diffraction by convex cornered wedges, and<br />
the other one is on the validation of weakly nonlinear geometric optics for<br />
entropy solutions of nonlinear hyperbolic systems of conservation laws.<br />
<br />
Fri, Jan 17, 2:25PM, VV901 Adrianna Gillman (Dartmouth) Fast direct solvers for linear partial differential equations<br />
<br />
===Fri, Jan 17: Adrianna Gillman (Dartmouth) ===<br />
''Fast direct solvers for linear partial differential equations''<br />
<br />
The cost of solving a large linear system often determines what can and cannot be modeled computationally in many areas of science and engineering. Unlike Gaussian elimination which scales cubically with the respect to the number of unknowns, fast direct solvers construct an inverse of a linear in system with a cost that scales linearly or nearly linearly. The fast direct solvers presented in this talk are designed for the linear systems arising from the discretization of linear partial differential equations. These methods are more robust, versatile and stable than iterative schemes. Since an inverse is computed, additional right-hand sides can be processed rapidly. The talk will give the audience a brief introduction to the core ideas, an overview of recent advancements, and it will conclude with a sampling of challenging application examples including the scattering of waves.<br />
<br />
===Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) ===<br />
''Intertwinings, wave equations and growth models''<br />
<br />
We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to hyperbolic partial differential equations, symmetric polynomials and the corresponding random growth models. The talk will be devoted to these recent developments which also shed new light on some beautiful old examples of intertwinings. Based on joint works with Vadim Gorin and Soumik Pal. <br />
<br />
<br />
===Jan 24: Yaniv Plan (Michigan) ===<br />
''Low-dimensionality in mathematical signal processing''<br />
<br />
Natural images tend to be compressible, i.e., the amount of information needed to encode an image is small. This conciseness of information -- in other words, low dimensionality of the signal -- is found throughout a plethora of applications ranging from MRI to quantum state tomography. It is natural to ask: can the number of measurements needed to determine a signal be comparable with the information content? We explore this question under modern models of low-dimensionality and measurement acquisition.<br />
<br />
===Feb 14: Alexander Karp (Columbia Teacher's College) ===<br />
''History of Mathematics Education as a Research Field and as Magistra Vitae''<br />
<br />
The presentation will be based on the experience of putting together and editing the Handbook<br />
on the History of Mathematics Education, which will be published by Springer in the near future. <br />
This volume, which was prepared by a large group of researchers from different countries, <br />
contains the first systematic account of the history of the development of mathematics education <br />
in the whole world (and not just in some particular country or region). The editing of such a <br />
book gave rise to thoughts about the methodology of research in this field, and also about what <br />
constitutes an object of such research. These are the thoughts that the presenter intends to share <br />
with his audience. From them, it is natural to pass to an analysis of the current situation and how <br />
it might develop.<br />
<br />
<br />
<br />
===March 28: Michael Lacey (GA Tech) ===<br />
''The Two Weight Inequality for the Hilbert Transform''<br />
<br />
The individual two weight inequality for the Hilbert transform <br />
asks for a real variable characterization of those pairs of weights <br />
(u,v) for which the Hilbert transform H maps L^2(u) to L^2(v). <br />
This question arises naturally in different settings, most famously <br />
in work of Sarason. Answering in the positive a deep <br />
conjecture of Nazarov-Treil-Volberg, the mapping property <br />
of the Hilbert transform is characterized by a triple of conditions, <br />
the first being a two-weight Poisson A2 on the pair of weights, <br />
with a pair of so-called testing inequalities, uniform over all <br />
intervals. This is the first result of this type for a singular <br />
integral operator. (Joint work with Sawyer, C.-Y. Shen and Uriate-Tuero)<br />
<br />
== Past talks ==<br />
<br />
Last year's schedule: [[Colloquia 2012-2013]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=6383Colloquia/Fall182014-01-19T21:05:49Z<p>Shamgar: /* Spring 2014 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Fall 2013 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
|[http://people.math.gatech.edu/~mbaker/ Matt Baker] (Georgia Institute of Technology)<br />
|Riemann-Roch for Graphs and Applications<br />
|Ellenberg<br />
|-<br />
|Sept 13<br />
|[http://math.wisc.edu/~andrews/ Uri Andrews] (University of Wisconsin)<br />
|A hop, skip, and a jump through the degrees of relative provability<br />
|<br />
|-<br />
|Sept 20<br />
|[http://www.math.neu.edu/people/profile/valerio-toledano-laredo Valerio Toledano Laredo] (Northeastern)<br />
|Flat connections and quantum groups<br />
|Gurevich<br />
|-<br />
|'''Wed, Sept 25, 2:30PM in B139'''<br />
|[http://mypage.iu.edu/~alindens/ Ayelet Lindenstrauss] (Indiana University)<br />
|Taylor Series in Homotopy Theory<br />
|Meyer<br />
|-<br />
|'''Wed, Sept 25''' (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication-Avoiding Algorithms for Linear Algebra and Beyond<br />
|Gurevich<br />
|-<br />
|'''Thurs, Sept 26''' (LAA lecture, Joint with Applied Algebra Seminar)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Implementing Communication-Avoiding Algorithms<br />
|Gurevich<br />
|-<br />
|Sept 27 (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays<br />
|Gurevich<br />
|-<br />
|Oct 4<br />
|[http://www.math.tamu.edu/~sottile/ Frank Sottile] (Texas A&M)<br />
|Galois groups of Schubert problems<br />
|Caldararu<br />
|-<br />
|Oct 11<br />
|[http://math.uchicago.edu/~wilkinso/ Amie Wilkinson] (Chicago)<br />
|[[Colloquia#October 11: Amie Wilkinson (Chicago) | Robust mechanisms for chaos]]<br />
|WIMAW (Cladek)<br />
|-<br />
|'''Tues, Oct 15, 4PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability I]]<br />
|Valko<br />
|-<br />
|'''Wed, Oct 16, 2:30PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability II]]<br />
|Valko<br />
|-<br />
|<strike>Oct 18</strike><br />
|No colloquium due to the distinguished lecture<br />
|<br />
|<br />
|-<br />
|Oct 25<br />
|[http://www.math.umn.edu/~garrett/ Paul Garrett] (Minnesota)<br />
|[[Colloquia#October 25: Paul Garrett (Minnesota) | Boundary-value problems, generalized functions, and zeros of zeta functions]]<br />
|Gurevich<br />
|<br />
|<br />
|-<br />
|Nov 1<br />
|[http://www.cs.columbia.edu/~alewko/ Allison Lewko] (Columbia University)<br />
|On sets of large doubling, Lambda(4) sets, and error-correcting codes<br />
|Stovall<br />
|-<br />
|Nov 8<br />
|[http://www.math.cornell.edu/~riley/ Tim Riley] (Cornell)<br />
|[[Colloquia#November 8: Tim Riley (Cornell) | Hydra groups]]<br />
|Dymarz<br />
|-<br />
|Nov 15 and later<br />
|Reserved<br />
|<br />
|Street<br />
|-<br />
|Nov 22<br />
|[http://www.math.uchicago.edu/~tj/ Tianling Jin] (University of Chicago)<br />
|Solutions of some Monge-Ampere equations with degeneracy or singularities.<br />
|Bolotin<br />
|-<br />
|'''Mon, Nov 25, 4PM'''<br />
|[https://web.math.princeton.edu/~linlin/ Lin Lin] (Lawrence Berkeley National Lab)<br />
|Fast algorithms for electronic structure analysis<br />
|Jin<br />
|-<br />
|'''Tue, Nov 26, 4PM, B139'''<br />
|[http://www.math.cornell.edu/m/People/Faculty/conley Clinton Conley] (Cornell)<br />
|[[Colloquia#November 26 (Tuesday): Clinton Conley (Cornell) | Descriptive set-theoretic graph theory]]<br />
|Lempp<br />
|-<br />
|'''Mon, Dec 2, 4PM'''<br />
|[http://www.math.northwestern.edu/~slm/ Simon Marshall] (Northwestern)<br />
|[[Colloquia#December 2 (Monday): Simon Marshall (Northwestern) | Semiclassical estimates for eigenfunctions on locally symmetric spaces]]<br />
|Denissov<br />
|-<br />
|'''Wed, Dec 4, 4PM'''<br />
|[http://math.berkeley.edu/~svs/ Steven Sam] (Berkeley)<br />
|Free Resolutions and Symmetry<br />
|Boston <br />
|-<br />
|'''Fri, Dec 6'''<br />
|[http://math.mit.edu/~hand/ Paul Hand] (MIT)<br />
|[[Colloquia#December 6: Paul Hand (MIT) | Simplifications of the lifting approach for quadratic signal recovery problems]]<br />
|Thiffeault<br />
|-<br />
|'''Fri, Dec. 6 and Sat Dec. 7'''<br />
|<br />
|[http://www.math.umn.edu/~stant001/askey80 Conference in honor of Dick Askey]<br />
|<br />
|-<br />
|'''Mon, Dec. 9, 4pm, VV B239'''<br />
|[http://www.cims.nyu.edu/~jacob/ Jacob Bedrossian] (Courant Institute)<br />
|Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations<br />
|Bolotin<br />
|-<br />
|'''Wed, Dec 11, 4PM'''<br />
|[http://math.jhu.edu/~lwang/ Lu Wang] (Johns Hopkins)<br />
|Rigidity of Self-shrinkers of Mean Curvature Flow<br />
|Viaclovsky <br />
|-<br />
|'''Fri, Dec. 13, 2:25pm, VV 901'''<br />
|[http://chanwookim.wordpress.com/ Chanwoo Kim] (Cambridge)<br />
|Regularity of the Boltzmann equation in convex domains<br />
|Bolotin<br />
|-<br />
|'''Tues, Dec 17, 4PM'''<br />
|[http://www.statslab.cam.ac.uk/~ps422/ Perla Sousi] (Cambridge)<br />
|[[Colloquia#December 17: Perla Sousi (Cambridge) | The effect of drift on the volume of the Wiener sausage]]<br />
|Seppalainen <br />
|-<br />
|'''Wed, Dec 18, 4PM'''<br />
|[http://users.math.yale.edu/~dc597/ Dustin Cartwright] (Yale)<br />
|[[Colloquia#December 18: Dustin Cartwright (Yale) | Tropical Complexes]]<br />
|Gurevich<br />
|}<br />
<br />
== Spring 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|'''Mon, Jan 6, 4PM'''<br />
|[http://www-bcf.usc.edu/~lauda/Aaron_Laudas_Page/Home.html Aaron Lauda] (USC) <br />
|[[Colloquia#January 6: Aaron Lauda (USC) | An introduction to diagrammatic categorification]]<br />
|Caldararu<br />
|-<br />
|'''Wed, Jan 8, 4PM'''<br />
|[http://www2.math.umd.edu/~kmelnick/ Karin Melnick] (Maryland) <br />
|[[Colloquia#January 8: Karin Melnick (Maryland) | Normal forms for local flows on parabolic geometries]]<br />
|Kent<br />
|-<br />
|Jan 10, 4PM<br />
|[http://users.math.yale.edu/~yd82/ Yen Do] (Yale) <br />
|Convergence of Fourier series and multilinear analysis<br />
|Denissov<br />
|-<br />
|'''Mon, Jan 13, 4pm'''<br />
|[http://math.stanford.edu/~wangyi/ Yi Wang] (Stanford)<br />
|Isoperimetric Inequality and Q-curvature<br />
|Viaclovsky<br />
|-<br />
|'''Wen, Jan 15, 4pm'''<br />
|[http://www.maths.ox.ac.uk/people/profiles/wei.xiang Wei Xiang] (University of Oxford)<br />
|[[Colloquia#January 15: Wei Xiang (University of Oxford) |Conservation Laws and Shock Waves]]<br />
|Bolotin<br />
|-<br />
|'''Fri, Jan 17, 2:25PM, VV901'''<br />
|[http://www.math.dartmouth.edu/~gillmana/ Adrianna Gillman] (Dartmouth) <br />
|Fast direct solvers for linear partial differential equations<br />
|Thiffeault<br />
|-<br />
|'''Thu, Jan 23, 2:25, VV901'''<br />
|[http://www.stat.berkeley.edu/~mshkolni/ Mykhaylo Shkolnikov] (Berkeley)<br />
|[[Colloquia#Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) | Intertwinings, wave equations and growth models]]<br />
|Seppalainen<br />
|-<br />
|Jan 24<br />
|[http://www.yanivplan.com/ Yaniv Plan] (Michigan)<br />
|Low-dimensionality in mathematical signal processing<br />
|Thiffeault<br />
|-<br />
|Jan 31<br />
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)<br />
|<br />
|Gurevich<br />
|-<br />
|Feb 7<br />
|David Treumann (Boston College)<br />
|<br />
|Street<br />
|-<br />
|Feb 14<br />
|[http://www.tc.columbia.edu/academics/index.htm?facid=apk16 Alexander Karp] (Columbia Teacher's College)<br />
|History of Mathematics Education as a Research Field and as Magistra Vitae<br />
|Kiselev<br />
|-<br />
|Feb 21<br />
|<br />
|<br />
|<br />
|-<br />
|Feb 28<br />
|[http://math.nyu.edu/faculty/shelley/ Michael Shelley] (Courant)<br />
|<br />
|Spagnolie<br />
|-<br />
|March 7<br />
|[http://www.math.northwestern.edu/people/facultyProfiles/steve.zelditch.html Steve Zelditch] (Northwestern)<br />
|<br />
|Seeger<br />
|-<br />
|March 14<br />
|<br />
|[https://www.math.ucdavis.edu/~strohmer/ Thomas Strohmer] (Davis)<br />
|<br />
|- <br />
|<strike>March 21</strike><br />
|'''Spring Break'''<br />
|No Colloquium<br />
|<br />
|-<br />
|March 28<br />
|[http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)<br />
|The Two Weight Inequality for the Hilbert Transform<br />
|Street<br />
|-<br />
|April 4<br />
|[http://www.math.brown.edu/~res/ Richard Schwartz] (Brown)<br />
|<br />
|Mari-Beffa<br />
|-<br />
|April 11<br />
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)<br />
|<br />
|Gurevich<br />
|-<br />
|April 18 (Wasow Lecture)<br />
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)<br />
|<br />
|Seeger<br />
|-<br />
|April 25<br />
|[http://www.charlesdoran.net Charles Doran](University of Alberta)<br />
|<br />
|Song<br />
|-<br />
|'''Monday, April 28''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|A mystery concerning algebraic plane curves<br />
|Maxim<br />
|-<br />
|'''Tuesday, April 29''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Matrix factorizations old and new<br />
|Maxim<br />
|-<br />
|'''Wednesday, April 30''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Easy solution of polynomial equations over finite fields<br />
|Maxim<br />
|-<br />
|May 2<br />
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)<br />
|<br />
|Boston<br />
|-<br />
|May 9<br />
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)<br />
|<br />
|WIMAW<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sep 6: Matt Baker (GA Tech) ===<br />
''Riemann-Roch for Graphs and Applications''<br />
<br />
We will begin by formulating the Riemann-Roch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a Riemann-Roch theorem for tropical curves, proved by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof of the Brill-Noether theorem in algebraic geometry (work of by Cools-Draisma-Payne-Robeva), a "volume-theoretic proof" of Kirchhoff's Matrix-Tree Theorem (work of An, Kuperberg, Shokrieh, and the speaker), and a new Chabauty-Coleman style bound for the number of rational points on an algebraic curve over the rationals (work of Katz and Zureick-Brown).<br />
<br />
===Sep 13: Uri Andrews (UW-Madison) ===<br />
''A hop, skip, and a jump through the degrees of relative provability''<br />
<br />
The topic of this talk arises from two directions. On the one hand, Gödel's incompleteness theorem tell us that given any sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic, there is a statement that is true but not provable in T. On the other hand, over the past seventy years, a number of researchers studying witnessing functions for various combinatorial statements have realized the importance of fast-growing functions and the fact that their totality is often not provable over a given sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic (e.g. the Paris-Harrington and the Kirby-Paris theorems).<br />
<br />
I will talk about the structure induced by giving the order (for a fixed T) of relative provability for totality of algorithms. That is, for algorithms describing functions f and g, we say f ≤ g if T along with the totality of g suffices to prove the totality of f. It turns out that this structure is rich, and encodes many facets of the nature of provability over sufficiently strong, consistent, effectively axiomatizable theories for first-order arithmetic. (Work joint with Mingzhong Cai, David Diamondstone, Steffen Lempp, and Joseph S. Miller.)<br />
<br />
===Sep 20: Valerio Toledano Laredo (Northeastern)===<br />
''Flat connections and quantum groups''<br />
<br />
Quantum groups are natural deformations of the Lie algebra of<br />
nxn matrices, and more generally of semisimple Lie algebras.<br />
They first arose in the mid eighties in the study of solvable<br />
models in statistical mechanics.<br />
<br />
I will explain how these algebraic objects can serve as natural<br />
receptacles for the (transcendental) monodromy of flat connections<br />
arising from representation theory.<br />
<br />
These connections exist in rational, trigonometric and elliptic<br />
forms, and lead to quantum groups of increasing interest and<br />
complexity.<br />
<br />
===Wed, Sept 25, 2:30PM Ayelet Lindenstrauss (Indiana University)===<br />
''Taylor Series in Homotopy Theory''<br />
<br />
I will discuss Goodwillie's calculus of functors on topological spaces. To mimic the set-up in real analysis, topological spaces are considered small if their nontrivial homotopy groups start only in higher dimensions. They can be considered close only in relation to a map between them, but a map allows us to construct the difference between two spaces, and two spaces are close if the difference between them is small. Spaces can be summed (in different ways) by taking twisted products of them. It is straightforward to construct the analogs of constant, linear, and higher degree homogenous functors, and they can be assembled into "polynomials" and "infinite sums". There are notions of differentiability and higher derivatives, of Taylor towers, and of analytic functions.<br />
<br />
What might look like a game of analogies is an extremely useful tool because when one looks at functors that map topological spaces not into the category of topological spaces, but into the category of spectra (the stabilized version of the category of spaces, which will be explained), many of them are, in fact, analytic, so they can be constructed from the homogenous functors of different degrees. And we can use appropriate analogs of calculus theorems to understand them better. I will conclude with some recent work of Randy McCarthy and myself, applying Goodwillie's calculus to algebraic K-theory calculations.<br />
<br />
===Sep 25: Jim Demmel (Berkeley) ===<br />
''Communication Avoiding Algorithms for Linear Algebra and Beyond''<br />
<br />
Algorithm have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present algorithms that attain provable lower bounds on communication, and show large speedups compared to their conventional counterparts. These algorithms are for direct and iterative linear algebra, for dense and sparse matrices, as well as direct n-body simulations. Several of these algorithms exhibit perfect strong scaling, in both time and energy: run time (resp. energy) for a fixed problem size drops proportionally to the number of processors p (resp. is independent of p). Finally, we describe extensions to algorithms involving arbitrary loop nests and array accesses, assuming only that array subscripts are affine functions of the loop indices. <br />
<br />
===Sep 26: Jim Demmel (Berkeley) ===<br />
''Implementing Communication Avoiding Algorithms''<br />
<br />
Designing algorithms that avoiding communication, attaining<br />
lower bounds if possible, is critical for algorithms to minimize runtime and<br />
energy on current and future architectures. These new algorithms can have <br />
new numerical stability properties, new ways to encode answers, and new data<br />
structures, not just depend on loop transformations (we need those too!).<br />
We will illustrate with a variety of examples including direct linear algebra<br />
(eg new ways to perform pivoting, new deterministic and randomized<br />
eigenvalue algorithms), iterative linear algebra (eg new ways to reorganize<br />
Krylov subspace methods) and direct n-body algorithms, on architectures<br />
ranging from multicore to distributed memory to heterogeneous.<br />
The theory describing communication avoiding algorithms can give us a large<br />
design space of possible implementations, so we use autotuning to find<br />
the fastest one automatically. Finally, on parallel architectures one can<br />
frequently not expect to get bitwise identical results from multiple runs,<br />
because of dynamic scheduling and floating point nonassociativity; <br />
this can be a problem for reasons from debugging to correctness.<br />
We discuss some techniques to get reproducible results at modest cost.<br />
<br />
===Sep 27: Jim Demmel (Berkeley) ===<br />
''Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays''<br />
<br />
Our goal is to minimize communication, i.e. moving data, since it increasingly<br />
dominates the cost of arithmetic in algorithms. Motivated by this, attainable<br />
communication lower bounds have been established by many authors for a <br />
variety of algorithms including matrix computations.<br />
<br />
The lower bound approach used initially by Irony, Tiskin and Toledo <br />
for O(n^3) matrix multiplication, and later by Ballard et al <br />
for many other linear algebra algorithms, depends on a geometric result by <br />
Loomis and Whitney: this result bounds the volume of a 3D set <br />
(representing multiply-adds done in the inner loop of the algorithm) <br />
using the product of the areas of certain 2D projections of this set <br />
(representing the matrix entries available locally, i.e., without communication).<br />
<br />
Using a recent generalization of Loomis' and Whitney's result, we generalize <br />
this lower bound approach to a much larger class of algorithms, <br />
that may have arbitrary numbers of loops and arrays with arbitrary dimensions, <br />
as long as the index expressions are affine combinations of loop variables.<br />
In other words, the algorithm can do arbitrary operations on any number of <br />
variables like A(i1,i2,i2-2*i1,3-4*i3+7*i_4,…).<br />
Moreover, the result applies to recursive programs, irregular iteration spaces, <br />
sparse matrices, and other data structures as long as the computation can be<br />
logically mapped to loops and indexed data structure accesses. <br />
<br />
We also discuss when optimal algorithms exist that attain the lower bounds; <br />
this leads to new asymptotically faster algorithms for several problems.<br />
<br />
===October 4: Frank Sottile (Texas A&M) ===<br />
''Galois groups of Schubert problems''<br />
<br />
Work of Jordan from 1870 showed how Galois theory<br />
can be applied to enumerative geometry. Hermite earlier<br />
showed the equivalence of Galois groups with geometric <br />
monodromy groups, and in 1979 Harris used this to study <br />
Galois groups of many enumerative problems. Vakil gave <br />
a geometric-combinatorial criterion that implies a Galois <br />
group contains the alternating group. With Brooks and <br />
Martin del Campo, we used Vakil's criterion to show that <br />
all Schubert problems involving lines have at least <br />
alternating Galois group. White and I have given a new <br />
proof of this based on 2-transitivity.<br />
<br />
My talk will describe this background and sketch a <br />
current project to systematically determine Galois groups <br />
of all Schubert problems of moderate size on all small <br />
classical flag manifolds, investigating at least several <br />
million problems. This will use supercomputers employing <br />
several overlapping methods, including combinatorial <br />
criteria, symbolic computation, and numerical homotopy <br />
continuation, and require the development of new <br />
algorithms and software.<br />
<br />
===October 11: Amie Wilkinson (Chicago) ===<br />
<br />
''Robust mechanisms for chaos''<br />
<br />
What are the underlying mechanisms for robustly chaotic behavior in smooth dynamics?<br />
<br />
In addressing this question, I'll focus on the study of diffeomorphisms of a compact manifold, where "chaotic" means "mixing" and and "robustly" means "stable under smooth perturbations." I'll describe recent advances in constructing and using tools called "blenders" to produce stably chaotic behavior with arbitrarily little effort.<br />
<br />
===October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) ===<br />
<br />
''Integrable probability I and II''<br />
<br />
The goal of the talks is to describe the emerging field of integrable<br />
probability, whose goal is to identify and analyze exactly solvable<br />
probabilistic models. The models and results are often easy to describe,<br />
yet difficult to find, and they carry essential information about broad<br />
universality classes of stochastic processes.<br />
<br />
<br />
===October 25: Paul Garrett (Minnesota)=== <br />
<br />
''Boundary-value problems, generalized functions, and zeros of zeta functions''<br />
<br />
Modern analysis (Beppo Levi, Sobolev, Friedrichs, Schwartz) illuminates work of D. Hejhal and Y. Colin de Verdiere from 30 years<br />
ago, clarifying, as in P. Cartier's letter to A. Weil, "how the Riemann Hypothesis was not proven". (Joint with E. Bombieri.)<br />
<br />
===November 1: Allison Lewko (Columbia University) ===<br />
<br />
''On sets of large doubling, Lambda(4) sets, and error-correcting codes''<br />
<br />
We investigate the structure of finite sets A of integers such that A+A is large, presenting a counterexample to natural conjectures in the pursuit of an "anti-Freiman" theory in additive combinatorics. We will begin with a brief history of the problem and its connection to the study of Lambda(4) sets in harmonic analysis, and then we will discuss our counterexample and its construction from error-correcting codes. We will conclude by describing some related open problems.<br />
This is joint work with Mark Lewko.<br />
<br />
===November 8: Tim Riley (Cornell)===<br />
<br />
''Hydra groups''<br />
<br />
A few years ago Will Dison and I constructed a family of<br />
finitely generated groups whose workings include a string-rewriting<br />
phenomenon of extraordinary duration which is reminiscent of Hercules'<br />
battle with the hydra. I will describe this and the investigations it<br />
spurred in hyperbolic geometry, combinatorial group theory, and a<br />
problem of how to calculate efficiently with hugely compressed<br />
representations of integers.<br />
<br />
===November 22: Tianling Jin (University of Chicago)===<br />
<br />
''Solutions of some Monge-Ampere equations with degeneracy or singularities''<br />
<br />
We will first give a new proof of a celebrated theorem of<br />
Jorgens which states that every classical convex solution of det(Hess<br />
u)=1 in R^2 has to be a second order polynomial. Our arguments do not use<br />
complex analysis, and will be applied to establish such Liouville type<br />
theorems for solutions some degenerate Monge-Ampere equations. We will<br />
also discuss some results on existence, regularity, classification, and<br />
asymptotic behavior of solutions of some Monge-Ampere equations with<br />
isolated and line singularities. This is joint work with J. Xiong.<br />
<br />
===Monday, Nov 25: Lin Lin (Lawrence Berkeley National Lab)===<br />
<br />
''Fast algorithms for electronic structure analysis''<br />
<br />
Kohn-Sham density functional theory (KSDFT) is the most widely used<br />
electronic structure theory for molecules and condensed matter systems. For<br />
a system with N electrons, the standard method for solving KSDFT requires<br />
solving N eigenvectors for an O(N) * O(N) Kohn-Sham Hamiltonian matrix.<br />
The computational cost for such procedure is expensive and scales as<br />
O(N^3). We have developed pole expansion plus selected inversion (PEXSI)<br />
method, in which KSDFT is solved by evaluating the selected elements of the<br />
inverse of a series of sparse symmetric matrices, and the overall algorithm<br />
scales at most O(N^2) for all materials including insulators,<br />
semiconductors and metals. The PEXSI method can be used with orthogonal or<br />
nonorthogonal basis set, and the physical quantities including electron<br />
density, energy, atomic force, density of states, and local density of<br />
states are calculated accurately without using the eigenvalues and<br />
eigenvectors. The recently developed massively parallel PEXSI method has<br />
been implemented in SIESTA, one of the most popular electronic structure<br />
software using atomic orbital basis set. The resulting method can allow<br />
accurate treatment of electronic structure in a unprecedented scale. We<br />
demonstrate the application of the method for solving graphene-like<br />
structures with more than 20,000 atoms, and the method can be efficiently<br />
parallelized 10,000 - 100,000 processors on Department of Energy (DOE) high<br />
performance machines.<br />
<br />
===November 26 (Tuesday): Clinton Conley (Cornell)===<br />
<br />
''Descriptive set-theoretic graph theory''<br />
<br />
Familiar graph-theoretic problems (for example, vertex coloring) exhibit a<br />
stark change of character when measurability constraints are placed on the<br />
structures and functions involved. While discussing some ramifications in<br />
descriptive set theory, we also pay special attention to interactions with<br />
probability (concerning random colorings of Cayley graphs) and ergodic<br />
theory (characterizing various dynamical properties of groups). The talk<br />
will include joint work with Alexander Kechris, Andrew Marks, Benjamin<br />
Miller, and Robin Tucker-Drob.<br />
<br />
<br />
===December 2 (Monday): Simon Marshall (Northwestern)===<br />
<br />
''Semiclassical estimates for eigenfunctions on locally symmetric spaces''<br />
<br />
Let M be a compact Riemannian manifold, and f an L^2-normalised Laplace<br />
eigenfunction on M. If p > 2, a theorem of Sogge tells us how large the L^p<br />
norm of f can be in terms of its Laplace eigenvalue. For instance, when p<br />
is infinity this is asking how large the peaks of f can be. I will present<br />
an analogue of Sogge's theorem for eigenfunctions of the full ring of<br />
invariant differential operators on a locally symmetric space, and discuss<br />
some links between this result and number theory.<br />
<br />
===December 4 (Wednesday): Steven Sam (Berkeley)===<br />
<br />
''Free Resolutions and Symmetry''<br />
<br />
This talk is about the use of symmetry in the study of modules and free resolutions in commutative algebra and algebraic geometry, and specifically how it clarifies, organizes, and rigidifies calculations, and how it enables us to find finiteness in situations where it a priori does not seem to exist. I will begin the talk with an example coming from classical invariant theory and determinantal ideals using just some basic notions from linear algebra. Then I will explain some of my own work which builds on this setting in several directions. Finally, I'll discuss a recent program on twisted commutative algebras, developed jointly with Andrew Snowden, which formalizes the synthesis of representation theory and commutative algebra and leads to new finiteness results in seemingly infinite settings.<br />
<br />
===December 6: Paul Hand (MIT)===<br />
<br />
''Simplifications of the Lifting Approach for Quadratic Signal Recovery Problems''<br />
<br />
Many signal recovery problems are quadratic in nature, such as phase<br />
retrieval and sparse principal component analysis. Such problems in<br />
R^n can be convexified by introducing n^2 variables corresponding to<br />
each quadratic combination of unknowns. This approach often gives<br />
rise to an n x n matrix recovery problem that is convex and has<br />
provable recovery guarantees. Because the dimensionality has been<br />
squared, it is an important task to find simplifications that make<br />
computation more tractable. We will discuss two examples where the<br />
lifting approach can be simplified while retaining recovery<br />
guarantees. These examples will be the phase retrieval problem and a<br />
special case of sparse principal component analysis.<br />
<br />
===December 9 (Monday): Jacob Bedrossian (Courant Institute)===<br />
<br />
''Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations''<br />
<br />
We prove asymptotic stability of shear flows close to the<br />
planar, periodic Couette flow in the 2D incompressible Euler equations.<br />
That is, given an initial perturbation of the Couette flow small in a<br />
suitable regularity class, specifically Gevrey space of class smaller than<br />
2, the velocity converges strongly in L2 to a shear flow which is also<br />
close to the Couette flow. The vorticity is asymptotically mixed to small<br />
scales by an almost linear evolution and in general enstrophy is lost in<br />
the weak limit. The strong convergence of the velocity field is sometimes<br />
referred to as inviscid damping, due to the relationship with Landau<br />
damping in the Vlasov equations. Joint work with Nader Masmoudi.<br />
<br />
===Wednesday, Dec 11: Lu Wang (Johns Hopkins)===<br />
<br />
''Rigidity of Self-shrinkers of Mean Curvature Flow''<br />
<br />
The study of mean curvature flow not only is fundamental in geometry, topology and analysis, but also has important applications in applied mathematics, for instance, image processing. One of the most important problems in mean curvature flow is to understand the possible singularities of the flow and self-shrinkers, i.e., self-shrinking solutions of the flow, provide the singularity models.<br />
<br />
In this talk, I will describe the rigidity of asymptotic structures of self-shrinkers. First, I show the uniqueness of properly embedded self-shrinkers asymptotic to any given regular cone. Next, I give a partial affirmative answer to a conjecture of Ilmanen under an infinite order asymptotic assumption, which asserts that the only two-dimensional properly embedded self-shrinker asymptotic to a cylinder along some end is itself the cylinder. The feature of our results is that no completeness of self-shrinkers is required.<br />
<br />
The key ingredients in the proof are a novel reduction of unique continuation for elliptic operators to backwards uniqueness for parabolic operators and the Carleman type techniques. If time permits, I will discuss some applications of our approach to shrinking solitons of Ricci flow.<br />
<br />
===Friday, Dec 13: Chanwoo Kim (Cambridge)===<br />
<br />
''Regularity of the Boltzmann equation in convex domains''<br />
<br />
A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the Boltzmann equation in a strictly convex domain with the specular, bounce-back and diffuse boundary condition. With the aid of a distance function toward the grazing set, we construct weighted classical <math>C^{1}</math> solutions away from the grazing set for all boundary conditions. For the diffuse boundary condition, we construct <math>W^{1,p}</math> solutions for 1< p<2 and weighted <math>W^{1,p}</math> solutions for <math>2\leq p\leq \infty</math> as well. On the other hand, we show second derivatives do not exist up to the boundary in general by constructing counterexamples for all boundary conditions. This is a joint work with Guo, Tonon, Trescases.<br />
<br />
===December 17: Perla Sousi (Cambridge)===<br />
<br />
''The effect of drift on the volume of the Wiener sausage''<br />
<br />
The Wiener sausage at time t is the algebraic sum of a Brownian path on [0,t] and a ball. Does the expected volume of the Wiener sausage increase when we add drift?<br />
How do you compare the expected volume of the usual Wiener sausage to one defined as the algebraic sum of the Brownian path and a square (in 2D) or a cube (in higher dimensions)? We will answer these questions using their relation to the detection problem for Poisson Brownian motions, and rearrangement inequalities on the sphere (with Y. Peres). We will also discuss generalisations of this to Levy processes (with A. Drewitz and R. Sun) as well as an adversarial detection problem and its connections to Kakeya sets (with Babichenko, Peres, Peretz and Winkler).<br />
<br />
<br />
===December 18: Dustin Cartwright (Yale)===<br />
<br />
''Tropical Complexes''<br />
<br />
Tropical geometry is a way of understanding algebraic varieties by the limiting behavior of their degenerations. Through tropicalization, algebraic operations are replaced with combinatorial constructions and piecewise linear functions. I will introduce tropical complexes, which a way of understanding the geometry of algebraic varieties through combinatorics. Tropical complexes are Delta-complexes together with additional integral data, for which one has parallels and concrete comparisons with the behavior of algebraic varieties. <br />
<br />
===January 6: Aaron Lauda (USC)===<br />
<br />
''An introduction to diagrammatic categorification''<br />
<br />
Categorification seeks to reveal a hidden layer in mathematical<br />
structures. Often the resulting structures can be combinatorially<br />
complex objects making them difficult to study. One method of<br />
overcoming this difficulty, that has proven very successful, is to<br />
encode the categorification into a diagrammatic calculus that makes<br />
computations simple and intuitive.<br />
<br />
In this talk I will review some of the original considerations that<br />
led to the categorification philosophy. We will examine how the<br />
diagrammatic perspective has helped to produce new categorifications<br />
having profound applications to algebra, representation theory, and<br />
low-dimensional topology.<br />
<br />
===January 8: Karin Melnick (Maryland)===<br />
<br />
''Normal forms for local flows on parabolic geometries''<br />
<br />
The exponential map in Riemannian geometry conjugates the differential of an isometry at a point with the action of the isometry near the point. It thus provides a linear normal form for all isometries fixing a point. Conformal transformations are not linearizable in general. I will discuss a suite of normal forms theorems in conformal geometry and, more generally, for parabolic geometries, a rich family of geometric structures of which conformal, projective, and CR structures are examples.<br />
<br />
===January 10, 4PM: Yen Do (Yale)===<br />
<br />
''Convergence of Fourier series and multilinear analysis''<br />
<br />
Almost everywhere convergence of the Fourier series of square <br />
integrable functions was first proved by Lennart Carleson in 1966, and <br />
the proof has lead to deep developments in various multilinear settings. <br />
In this talk I would like to introduce a brief history of the subject <br />
and sketch some recent developments, some of these involve my joint <br />
works with collaborators.<br />
<br />
===Mon, January 13: Yi Wang (Stanford)===<br />
<br />
''Isoperimetric Inequality and Q-curvature''<br />
<br />
A well-known question in differential geometry is to prove the<br />
isoperimetric inequality under intrinsic curvature conditions. In<br />
dimension 2, the isoperimetric inequality is controlled by the integral of<br />
the positive part of the Gaussian curvature. In my recent work, I prove<br />
that on simply connected conformally flat manifolds of higher dimensions,<br />
the role of the Gaussian curvature can be replaced by the Branson's<br />
Q-curvature. The isoperimetric inequality is valid if the integral of the<br />
Q-curvature is below a sharp threshold. Moreover, the isoperimetric<br />
constant depends only on the integrals of the Q-curvature. The proof<br />
relies on the theory of $A_p$ weights in harmonic analysis.<br />
<br />
===January 15: Wei Xiang (University of Oxford)===<br />
<br />
''Conservation Laws and Shock Waves''<br />
<br />
The study of continuum physics gave birth to the theory of quasilinear<br />
systems in divergence form, commonly called conservation laws. In this<br />
talk, conservation laws, the Euler equations, and the definition of the<br />
corresponding weak solutions will be introduced first. Then a short history<br />
of the studying of conservation laws and shock waves will be given. Finally<br />
I would like to present two of our current research projects. One is on the<br />
mathematical analysis of shock diffraction by convex cornered wedges, and<br />
the other one is on the validation of weakly nonlinear geometric optics for<br />
entropy solutions of nonlinear hyperbolic systems of conservation laws.<br />
<br />
Fri, Jan 17, 2:25PM, VV901 Adrianna Gillman (Dartmouth) Fast direct solvers for linear partial differential equations<br />
<br />
===Fri, Jan 17: Adrianna Gillman (Dartmouth) ===<br />
''Fast direct solvers for linear partial differential equations''<br />
<br />
The cost of solving a large linear system often determines what can and cannot be modeled computationally in many areas of science and engineering. Unlike Gaussian elimination which scales cubically with the respect to the number of unknowns, fast direct solvers construct an inverse of a linear in system with a cost that scales linearly or nearly linearly. The fast direct solvers presented in this talk are designed for the linear systems arising from the discretization of linear partial differential equations. These methods are more robust, versatile and stable than iterative schemes. Since an inverse is computed, additional right-hand sides can be processed rapidly. The talk will give the audience a brief introduction to the core ideas, an overview of recent advancements, and it will conclude with a sampling of challenging application examples including the scattering of waves.<br />
<br />
===Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) ===<br />
''Intertwinings, wave equations and growth models''<br />
<br />
We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to hyperbolic partial differential equations, symmetric polynomials and the corresponding random growth models. The talk will be devoted to these recent developments which also shed new light on some beautiful old examples of intertwinings. Based on joint works with Vadim Gorin and Soumik Pal. <br />
<br />
<br />
===Jan 24: Yaniv Plan (Michigan) ===<br />
''Low-dimensionality in mathematical signal processing''<br />
<br />
Natural images tend to be compressible, i.e., the amount of information needed to encode an image is small. This conciseness of information -- in other words, low dimensionality of the signal -- is found throughout a plethora of applications ranging from MRI to quantum state tomography. It is natural to ask: can the number of measurements needed to determine a signal be comparable with the information content? We explore this question under modern models of low-dimensionality and measurement acquisition.<br />
<br />
===Feb 14: Alexander Karp (Columbia Teacher's College) ===<br />
''History of Mathematics Education as a Research Field and as Magistra Vitae''<br />
<br />
The presentation will be based on the experience of putting together and editing the Handbook<br />
on the History of Mathematics Education, which will be published by Springer in the near future. <br />
This volume, which was prepared by a large group of researchers from different countries, <br />
contains the first systematic account of the history of the development of mathematics education <br />
in the whole world (and not just in some particular country or region). The editing of such a <br />
book gave rise to thoughts about the methodology of research in this field, and also about what <br />
constitutes an object of such research. These are the thoughts that the presenter intends to share <br />
with his audience. From them, it is natural to pass to an analysis of the current situation and how <br />
it might develop.<br />
<br />
<br />
<br />
===March 28: Michael Lacey (GA Tech) ===<br />
''The Two Weight Inequality for the Hilbert Transform''<br />
<br />
The individual two weight inequality for the Hilbert transform <br />
asks for a real variable characterization of those pairs of weights <br />
(u,v) for which the Hilbert transform H maps L^2(u) to L^2(v). <br />
This question arises naturally in different settings, most famously <br />
in work of Sarason. Answering in the positive a deep <br />
conjecture of Nazarov-Treil-Volberg, the mapping property <br />
of the Hilbert transform is characterized by a triple of conditions, <br />
the first being a two-weight Poisson A2 on the pair of weights, <br />
with a pair of so-called testing inequalities, uniform over all <br />
intervals. This is the first result of this type for a singular <br />
integral operator. (Joint work with Sawyer, C.-Y. Shen and Uriate-Tuero)<br />
<br />
== Past talks ==<br />
<br />
Last year's schedule: [[Colloquia 2012-2013]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=6075Colloquia/Fall182013-10-13T15:03:28Z<p>Shamgar: /* Abstracts */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Fall 2013 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
|[http://people.math.gatech.edu/~mbaker/ Matt Baker] (Georgia Institute of Technology)<br />
|Riemann-Roch for Graphs and Applications<br />
|Ellenberg<br />
|-<br />
|Sept 13<br />
|[http://math.wisc.edu/~andrews/ Uri Andrews] (University of Wisconsin)<br />
|A hop, skip, and a jump through the degrees of relative provability<br />
|<br />
|-<br />
|Sept 20<br />
|[http://www.math.neu.edu/people/profile/valerio-toledano-laredo Valerio Toledano Laredo] (Northeastern)<br />
|Flat connections and quantum groups<br />
|Gurevich<br />
|-<br />
|'''Wed, Sept 25, 2:30PM in B139'''<br />
|[http://mypage.iu.edu/~alindens/ Ayelet Lindenstrauss] (Indiana University)<br />
|Taylor Series in Homotopy Theory<br />
|Meyer<br />
|-<br />
|'''Wed, Sept 25''' (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication-Avoiding Algorithms for Linear Algebra and Beyond<br />
|Gurevich<br />
|-<br />
|'''Thurs, Sept 26''' (LAA lecture, Joint with Applied Algebra Seminar)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Implementing Communication-Avoiding Algorithms<br />
|Gurevich<br />
|-<br />
|Sept 27 (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays<br />
|Gurevich<br />
|-<br />
|Oct 4<br />
|[http://www.math.tamu.edu/~sottile/ Frank Sottile] (Texas A&M)<br />
|Galois groups of Schubert problems<br />
|Caldararu<br />
|-<br />
|Oct 11<br />
|[http://math.uchicago.edu/~wilkinso/ Amie Wilkinson] (Chicago)<br />
|[[Colloquia#October 11: Amie Wilkinson (Chicago) | Robust mechanisms for chaos]]<br />
|WIMAW (Cladek)<br />
|-<br />
|'''Tues, Oct 15, 4PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability I]]<br />
|Valko<br />
|-<br />
|'''Wed, Oct 16, 2:30PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability II]]<br />
|Valko<br />
|-<br />
|<strike>Oct 18</strike><br />
|No colloquium due to the distinguished lecture<br />
|<br />
|<br />
|-<br />
|Oct 25<br />
|[http://www.math.umn.edu/~garrett/ Paul Garrett] (Minnesota)<br />
|Boundary-value problems, generalized functions, and zeros of zeta functions<br />
|Gurevich<br />
|<br />
|<br />
|-<br />
|Nov 1<br />
|[http://www.cs.columbia.edu/~alewko/ Allison Lewko] (Columbia University)<br />
|On sets of large doubling, Lambda(4) sets, and error-correcting codes<br />
|Stovall<br />
|-<br />
|Nov 8<br />
|[http://www.math.cornell.edu/~riley/ Tim Riley] (Cornell)<br />
|<br />
|Dymarz<br />
|-<br />
|Nov 15 and later<br />
|Reserved<br />
|<br />
|Street<br />
|-<br />
|'''Fri, Dec. 6 and Sat Dec. 7'''<br />
|No Seminar<br />
|[http://www.math.umn.edu/~stant001/askey80 Conference in honor of Dick Askey]<br />
|<br />
|}<br />
<br />
== Spring 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 24<br />
|[http://homepages.math.uic.edu/~mpopa/ Mihnea Popa] (UIC)<br />
|<br />
|Arinkin<br />
|-<br />
|Jan 31<br />
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)<br />
|<br />
|Gurevich<br />
|-<br />
|Feb 7<br />
|David Treumann (Boston College)<br />
|<br />
|Street<br />
|-<br />
|Feb 14<br />
|[http://www.tc.columbia.edu/academics/index.htm?facid=apk16 Alexander Karp] (Columbia Teacher's College)<br />
|<br />
|Kiselev<br />
|-<br />
|Feb 21<br />
|[http://math.nyu.edu/faculty/shelley/ Michael Shelley] (Courant)<br />
|<br />
|Spagnolie<br />
|-<br />
|Feb 28<br />
|<br />
|<br />
|<br />
|-<br />
|March 7<br />
|<br />
|<br />
|<br />
|-<br />
|March 14<br />
|Temporarily reserved<br />
|<br />
|Spagnolie<br />
|- <br />
|<strike>March 21</strike><br />
|'''Spring Break'''<br />
|No Colloquium<br />
|<br />
|-<br />
|March 28<br />
|[http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)<br />
|The Two Weight Inequality for the Hilbert Transform<br />
|Street<br />
|-<br />
|April 4<br />
|[http://www.math.brown.edu/~res/ Richard Schwartz] (Brown)<br />
|<br />
|Mari-Beffa<br />
|-<br />
|April 11<br />
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)<br />
|<br />
|Gurevich<br />
|-<br />
|April 18 (Wasow Lecture)<br />
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)<br />
|<br />
|Seeger<br />
|-<br />
|April 25<br />
|[http://www.charlesdoran.net Charles Doran](University of Alberta)<br />
|<br />
|Song<br />
|-<br />
|'''Monday, April 28''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|A mystery concerning algebraic plane curves<br />
|Maxim<br />
|-<br />
|'''Tuesday, April 29''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Matrix factorizations old and new<br />
|Maxim<br />
|-<br />
|'''Wednesday, April 30''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Easy solution of polynomial equations over finite fields<br />
|Maxim<br />
|-<br />
|May 2<br />
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)<br />
|<br />
|Boston<br />
|-<br />
|May 9<br />
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)<br />
|<br />
|WIMAW<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sep 6: Matt Baker (GA Tech) ===<br />
''Riemann-Roch for Graphs and Applications''<br />
<br />
We will begin by formulating the Riemann-Roch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a Riemann-Roch theorem for tropical curves, proved by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof of the Brill-Noether theorem in algebraic geometry (work of by Cools-Draisma-Payne-Robeva), a "volume-theoretic proof" of Kirchhoff's Matrix-Tree Theorem (work of An, Kuperberg, Shokrieh, and the speaker), and a new Chabauty-Coleman style bound for the number of rational points on an algebraic curve over the rationals (work of Katz and Zureick-Brown).<br />
<br />
===Sep 13: Uri Andrews (UW-Madison) ===<br />
''A hop, skip, and a jump through the degrees of relative provability''<br />
<br />
The topic of this talk arises from two directions. On the one hand, Gödel's incompleteness theorem tell us that given any sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic, there is a statement that is true but not provable in T. On the other hand, over the past seventy years, a number of researchers studying witnessing functions for various combinatorial statements have realized the importance of fast-growing functions and the fact that their totality is often not provable over a given sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic (e.g. the Paris-Harrington and the Kirby-Paris theorems).<br />
<br />
I will talk about the structure induced by giving the order (for a fixed T) of relative provability for totality of algorithms. That is, for algorithms describing functions f and g, we say f ≤ g if T along with the totality of g suffices to prove the totality of f. It turns out that this structure is rich, and encodes many facets of the nature of provability over sufficiently strong, consistent, effectively axiomatizable theories for first-order arithmetic. (Work joint with Mingzhong Cai, David Diamondstone, Steffen Lempp, and Joseph S. Miller.)<br />
<br />
===Sep 20: Valerio Toledano Laredo (Northeastern)===<br />
''Flat connections and quantum groups''<br />
<br />
Quantum groups are natural deformations of the Lie algebra of<br />
nxn matrices, and more generally of semisimple Lie algebras.<br />
They first arose in the mid eighties in the study of solvable<br />
models in statistical mechanics.<br />
<br />
I will explain how these algebraic objects can serve as natural<br />
receptacles for the (transcendental) monodromy of flat connections<br />
arising from representation theory.<br />
<br />
These connections exist in rational, trigonometric and elliptic<br />
forms, and lead to quantum groups of increasing interest and<br />
complexity.<br />
<br />
===Wed, Sept 25, 2:30PM Ayelet Lindenstrauss (Indiana University)===<br />
''Taylor Series in Homotopy Theory''<br />
<br />
I will discuss Goodwillie's calculus of functors on topological spaces. To mimic the set-up in real analysis, topological spaces are considered small if their nontrivial homotopy groups start only in higher dimensions. They can be considered close only in relation to a map between them, but a map allows us to construct the difference between two spaces, and two spaces are close if the difference between them is small. Spaces can be summed (in different ways) by taking twisted products of them. It is straightforward to construct the analogs of constant, linear, and higher degree homogenous functors, and they can be assembled into "polynomials" and "infinite sums". There are notions of differentiability and higher derivatives, of Taylor towers, and of analytic functions.<br />
<br />
What might look like a game of analogies is an extremely useful tool because when one looks at functors that map topological spaces not into the category of topological spaces, but into the category of spectra (the stabilized version of the category of spaces, which will be explained), many of them are, in fact, analytic, so they can be constructed from the homogenous functors of different degrees. And we can use appropriate analogs of calculus theorems to understand them better. I will conclude with some recent work of Randy McCarthy and myself, applying Goodwillie's calculus to algebraic K-theory calculations.<br />
<br />
===Sep 25: Jim Demmel (Berkeley) ===<br />
''Communication Avoiding Algorithms for Linear Algebra and Beyond''<br />
<br />
Algorithm have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present algorithms that attain provable lower bounds on communication, and show large speedups compared to their conventional counterparts. These algorithms are for direct and iterative linear algebra, for dense and sparse matrices, as well as direct n-body simulations. Several of these algorithms exhibit perfect strong scaling, in both time and energy: run time (resp. energy) for a fixed problem size drops proportionally to the number of processors p (resp. is independent of p). Finally, we describe extensions to algorithms involving arbitrary loop nests and array accesses, assuming only that array subscripts are affine functions of the loop indices. <br />
<br />
===Sep 26: Jim Demmel (Berkeley) ===<br />
''Implementing Communication Avoiding Algorithms''<br />
<br />
Designing algorithms that avoiding communication, attaining<br />
lower bounds if possible, is critical for algorithms to minimize runtime and<br />
energy on current and future architectures. These new algorithms can have <br />
new numerical stability properties, new ways to encode answers, and new data<br />
structures, not just depend on loop transformations (we need those too!).<br />
We will illustrate with a variety of examples including direct linear algebra<br />
(eg new ways to perform pivoting, new deterministic and randomized<br />
eigenvalue algorithms), iterative linear algebra (eg new ways to reorganize<br />
Krylov subspace methods) and direct n-body algorithms, on architectures<br />
ranging from multicore to distributed memory to heterogeneous.<br />
The theory describing communication avoiding algorithms can give us a large<br />
design space of possible implementations, so we use autotuning to find<br />
the fastest one automatically. Finally, on parallel architectures one can<br />
frequently not expect to get bitwise identical results from multiple runs,<br />
because of dynamic scheduling and floating point nonassociativity; <br />
this can be a problem for reasons from debugging to correctness.<br />
We discuss some techniques to get reproducible results at modest cost.<br />
<br />
===Sep 27: Jim Demmel (Berkeley) ===<br />
''Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays''<br />
<br />
Our goal is to minimize communication, i.e. moving data, since it increasingly<br />
dominates the cost of arithmetic in algorithms. Motivated by this, attainable<br />
communication lower bounds have been established by many authors for a <br />
variety of algorithms including matrix computations.<br />
<br />
The lower bound approach used initially by Irony, Tiskin and Toledo <br />
for O(n^3) matrix multiplication, and later by Ballard et al <br />
for many other linear algebra algorithms, depends on a geometric result by <br />
Loomis and Whitney: this result bounds the volume of a 3D set <br />
(representing multiply-adds done in the inner loop of the algorithm) <br />
using the product of the areas of certain 2D projections of this set <br />
(representing the matrix entries available locally, i.e., without communication).<br />
<br />
Using a recent generalization of Loomis' and Whitney's result, we generalize <br />
this lower bound approach to a much larger class of algorithms, <br />
that may have arbitrary numbers of loops and arrays with arbitrary dimensions, <br />
as long as the index expressions are affine combinations of loop variables.<br />
In other words, the algorithm can do arbitrary operations on any number of <br />
variables like A(i1,i2,i2-2*i1,3-4*i3+7*i_4,…).<br />
Moreover, the result applies to recursive programs, irregular iteration spaces, <br />
sparse matrices, and other data structures as long as the computation can be<br />
logically mapped to loops and indexed data structure accesses. <br />
<br />
We also discuss when optimal algorithms exist that attain the lower bounds; <br />
this leads to new asymptotically faster algorithms for several problems.<br />
<br />
===October 4: Frank Sottile (Texas A&M) ===<br />
''Galois groups of Schubert problems''<br />
<br />
Work of Jordan from 1870 showed how Galois theory<br />
can be applied to enumerative geometry. Hermite earlier<br />
showed the equivalence of Galois groups with geometric <br />
monodromy groups, and in 1979 Harris used this to study <br />
Galois groups of many enumerative problems. Vakil gave <br />
a geometric-combinatorial criterion that implies a Galois <br />
group contains the alternating group. With Brooks and <br />
Martin del Campo, we used Vakil's criterion to show that <br />
all Schubert problems involving lines have at least <br />
alternating Galois group. White and I have given a new <br />
proof of this based on 2-transitivity.<br />
<br />
My talk will describe this background and sketch a <br />
current project to systematically determine Galois groups <br />
of all Schubert problems of moderate size on all small <br />
classical flag manifolds, investigating at least several <br />
million problems. This will use supercomputers employing <br />
several overlapping methods, including combinatorial <br />
criteria, symbolic computation, and numerical homotopy <br />
continuation, and require the development of new <br />
algorithms and software.<br />
<br />
===October 11: Amie Wilkinson (Chicago) ===<br />
<br />
''Robust mechanisms for chaos''<br />
<br />
What are the underlying mechanisms for robustly chaotic behavior in smooth dynamics?<br />
<br />
In addressing this question, I'll focus on the study of diffeomorphisms of a compact manifold, where "chaotic" means "mixing" and and "robustly" means "stable under smooth perturbations." I'll describe recent advances in constructing and using tools called "blenders" to produce stably chaotic behavior with arbitrarily little effort.<br />
<br />
===October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) ===<br />
<br />
''Integrable probability I and II''<br />
<br />
The goal of the talks is to describe the emerging field of integrable<br />
probability, whose goal is to identify and analyze exactly solvable<br />
probabilistic models. The models and results are often easy to describe,<br />
yet difficult to find, and they carry essential information about broad<br />
universality classes of stochastic processes.<br />
<br />
<br />
===October: Paul Garrett (Minnesota)=== <br />
<br />
''Boundary-value problems, generalized functions, and zeros of zeta functions''<br />
<br />
Modern analysis (Beppo Levi, Sobolev, Friedrichs, Schwartz) illuminates work of D. Hejhal and Y. Colin de Verdiere from 30 years<br />
ago, clarifying, as in P. Cartier's letter to A. Weil, "how the Riemann Hypothesis was not proven". (Joint with E. Bombieri.)<br />
<br />
<br />
<br />
===November 1: Allison Lewko (Columbia University) ===<br />
<br />
''On sets of large doubling, Lambda(4) sets, and error-correcting codes''<br />
<br />
We investigate the structure of finite sets A of integers such that A+A is large, presenting a counterexample to natural conjectures in the pursuit of an "anti-Freiman" theory in additive combinatorics. We will begin with a brief history of the problem and its connection to the study of Lambda(4) sets in harmonic analysis, and then we will discuss our counterexample and its construction from error-correcting codes. We will conclude by describing some related open problems.<br />
This is joint work with Mark Lewko.<br />
<br />
===March 28: Michael Lacey (GA Tech) ===<br />
''The Two Weight Inequality for the Hilbert Transform''<br />
<br />
The individual two weight inequality for the Hilbert transform <br />
asks for a real variable characterization of those pairs of weights <br />
(u,v) for which the Hilbert transform H maps L^2(u) to L^2(v). <br />
This question arises naturally in different settings, most famously <br />
in work of Sarason. Answering in the positive a deep <br />
conjecture of Nazarov-Treil-Volberg, the mapping property <br />
of the Hilbert transform is characterized by a triple of conditions, <br />
the first being a two-weight Poisson A2 on the pair of weights, <br />
with a pair of so-called testing inequalities, uniform over all <br />
intervals. This is the first result of this type for a singular <br />
integral operator. (Joint work with Sawyer, C.-Y. Shen and Uriate-Tuero)<br />
<br />
== Past talks ==<br />
<br />
Last year's schedule: [[Colloquia 2012-2013]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=6074Colloquia/Fall182013-10-13T14:59:14Z<p>Shamgar: /* Fall 2013 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Fall 2013 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
|[http://people.math.gatech.edu/~mbaker/ Matt Baker] (Georgia Institute of Technology)<br />
|Riemann-Roch for Graphs and Applications<br />
|Ellenberg<br />
|-<br />
|Sept 13<br />
|[http://math.wisc.edu/~andrews/ Uri Andrews] (University of Wisconsin)<br />
|A hop, skip, and a jump through the degrees of relative provability<br />
|<br />
|-<br />
|Sept 20<br />
|[http://www.math.neu.edu/people/profile/valerio-toledano-laredo Valerio Toledano Laredo] (Northeastern)<br />
|Flat connections and quantum groups<br />
|Gurevich<br />
|-<br />
|'''Wed, Sept 25, 2:30PM in B139'''<br />
|[http://mypage.iu.edu/~alindens/ Ayelet Lindenstrauss] (Indiana University)<br />
|Taylor Series in Homotopy Theory<br />
|Meyer<br />
|-<br />
|'''Wed, Sept 25''' (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication-Avoiding Algorithms for Linear Algebra and Beyond<br />
|Gurevich<br />
|-<br />
|'''Thurs, Sept 26''' (LAA lecture, Joint with Applied Algebra Seminar)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Implementing Communication-Avoiding Algorithms<br />
|Gurevich<br />
|-<br />
|Sept 27 (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays<br />
|Gurevich<br />
|-<br />
|Oct 4<br />
|[http://www.math.tamu.edu/~sottile/ Frank Sottile] (Texas A&M)<br />
|Galois groups of Schubert problems<br />
|Caldararu<br />
|-<br />
|Oct 11<br />
|[http://math.uchicago.edu/~wilkinso/ Amie Wilkinson] (Chicago)<br />
|[[Colloquia#October 11: Amie Wilkinson (Chicago) | Robust mechanisms for chaos]]<br />
|WIMAW (Cladek)<br />
|-<br />
|'''Tues, Oct 15, 4PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability I]]<br />
|Valko<br />
|-<br />
|'''Wed, Oct 16, 2:30PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability II]]<br />
|Valko<br />
|-<br />
|<strike>Oct 18</strike><br />
|No colloquium due to the distinguished lecture<br />
|<br />
|<br />
|-<br />
|Oct 25<br />
|[http://www.math.umn.edu/~garrett/ Paul Garrett] (Minnesota)<br />
|Boundary-value problems, generalized functions, and zeros of zeta functions<br />
|Gurevich<br />
|<br />
|<br />
|-<br />
|Nov 1<br />
|[http://www.cs.columbia.edu/~alewko/ Allison Lewko] (Columbia University)<br />
|On sets of large doubling, Lambda(4) sets, and error-correcting codes<br />
|Stovall<br />
|-<br />
|Nov 8<br />
|[http://www.math.cornell.edu/~riley/ Tim Riley] (Cornell)<br />
|<br />
|Dymarz<br />
|-<br />
|Nov 15 and later<br />
|Reserved<br />
|<br />
|Street<br />
|-<br />
|'''Fri, Dec. 6 and Sat Dec. 7'''<br />
|No Seminar<br />
|[http://www.math.umn.edu/~stant001/askey80 Conference in honor of Dick Askey]<br />
|<br />
|}<br />
<br />
== Spring 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 24<br />
|[http://homepages.math.uic.edu/~mpopa/ Mihnea Popa] (UIC)<br />
|<br />
|Arinkin<br />
|-<br />
|Jan 31<br />
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)<br />
|<br />
|Gurevich<br />
|-<br />
|Feb 7<br />
|David Treumann (Boston College)<br />
|<br />
|Street<br />
|-<br />
|Feb 14<br />
|[http://www.tc.columbia.edu/academics/index.htm?facid=apk16 Alexander Karp] (Columbia Teacher's College)<br />
|<br />
|Kiselev<br />
|-<br />
|Feb 21<br />
|[http://math.nyu.edu/faculty/shelley/ Michael Shelley] (Courant)<br />
|<br />
|Spagnolie<br />
|-<br />
|Feb 28<br />
|<br />
|<br />
|<br />
|-<br />
|March 7<br />
|<br />
|<br />
|<br />
|-<br />
|March 14<br />
|Temporarily reserved<br />
|<br />
|Spagnolie<br />
|- <br />
|<strike>March 21</strike><br />
|'''Spring Break'''<br />
|No Colloquium<br />
|<br />
|-<br />
|March 28<br />
|[http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)<br />
|The Two Weight Inequality for the Hilbert Transform<br />
|Street<br />
|-<br />
|April 4<br />
|[http://www.math.brown.edu/~res/ Richard Schwartz] (Brown)<br />
|<br />
|Mari-Beffa<br />
|-<br />
|April 11<br />
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)<br />
|<br />
|Gurevich<br />
|-<br />
|April 18 (Wasow Lecture)<br />
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)<br />
|<br />
|Seeger<br />
|-<br />
|April 25<br />
|[http://www.charlesdoran.net Charles Doran](University of Alberta)<br />
|<br />
|Song<br />
|-<br />
|'''Monday, April 28''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|A mystery concerning algebraic plane curves<br />
|Maxim<br />
|-<br />
|'''Tuesday, April 29''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Matrix factorizations old and new<br />
|Maxim<br />
|-<br />
|'''Wednesday, April 30''' (Distinguished Lecture)<br />
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)<br />
|Easy solution of polynomial equations over finite fields<br />
|Maxim<br />
|-<br />
|May 2<br />
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)<br />
|<br />
|Boston<br />
|-<br />
|May 9<br />
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)<br />
|<br />
|WIMAW<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sep 6: Matt Baker (GA Tech) ===<br />
''Riemann-Roch for Graphs and Applications''<br />
<br />
We will begin by formulating the Riemann-Roch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a Riemann-Roch theorem for tropical curves, proved by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof of the Brill-Noether theorem in algebraic geometry (work of by Cools-Draisma-Payne-Robeva), a "volume-theoretic proof" of Kirchhoff's Matrix-Tree Theorem (work of An, Kuperberg, Shokrieh, and the speaker), and a new Chabauty-Coleman style bound for the number of rational points on an algebraic curve over the rationals (work of Katz and Zureick-Brown).<br />
<br />
===Sep 13: Uri Andrews (UW-Madison) ===<br />
''A hop, skip, and a jump through the degrees of relative provability''<br />
<br />
The topic of this talk arises from two directions. On the one hand, Gödel's incompleteness theorem tell us that given any sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic, there is a statement that is true but not provable in T. On the other hand, over the past seventy years, a number of researchers studying witnessing functions for various combinatorial statements have realized the importance of fast-growing functions and the fact that their totality is often not provable over a given sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic (e.g. the Paris-Harrington and the Kirby-Paris theorems).<br />
<br />
I will talk about the structure induced by giving the order (for a fixed T) of relative provability for totality of algorithms. That is, for algorithms describing functions f and g, we say f ≤ g if T along with the totality of g suffices to prove the totality of f. It turns out that this structure is rich, and encodes many facets of the nature of provability over sufficiently strong, consistent, effectively axiomatizable theories for first-order arithmetic. (Work joint with Mingzhong Cai, David Diamondstone, Steffen Lempp, and Joseph S. Miller.)<br />
<br />
===Sep 20: Valerio Toledano Laredo (Northeastern)===<br />
''Flat connections and quantum groups''<br />
<br />
Quantum groups are natural deformations of the Lie algebra of<br />
nxn matrices, and more generally of semisimple Lie algebras.<br />
They first arose in the mid eighties in the study of solvable<br />
models in statistical mechanics.<br />
<br />
I will explain how these algebraic objects can serve as natural<br />
receptacles for the (transcendental) monodromy of flat connections<br />
arising from representation theory.<br />
<br />
These connections exist in rational, trigonometric and elliptic<br />
forms, and lead to quantum groups of increasing interest and<br />
complexity.<br />
<br />
===Wed, Sept 25, 2:30PM Ayelet Lindenstrauss (Indiana University)===<br />
''Taylor Series in Homotopy Theory''<br />
<br />
I will discuss Goodwillie's calculus of functors on topological spaces. To mimic the set-up in real analysis, topological spaces are considered small if their nontrivial homotopy groups start only in higher dimensions. They can be considered close only in relation to a map between them, but a map allows us to construct the difference between two spaces, and two spaces are close if the difference between them is small. Spaces can be summed (in different ways) by taking twisted products of them. It is straightforward to construct the analogs of constant, linear, and higher degree homogenous functors, and they can be assembled into "polynomials" and "infinite sums". There are notions of differentiability and higher derivatives, of Taylor towers, and of analytic functions.<br />
<br />
What might look like a game of analogies is an extremely useful tool because when one looks at functors that map topological spaces not into the category of topological spaces, but into the category of spectra (the stabilized version of the category of spaces, which will be explained), many of them are, in fact, analytic, so they can be constructed from the homogenous functors of different degrees. And we can use appropriate analogs of calculus theorems to understand them better. I will conclude with some recent work of Randy McCarthy and myself, applying Goodwillie's calculus to algebraic K-theory calculations.<br />
<br />
===Sep 25: Jim Demmel (Berkeley) ===<br />
''Communication Avoiding Algorithms for Linear Algebra and Beyond''<br />
<br />
Algorithm have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present algorithms that attain provable lower bounds on communication, and show large speedups compared to their conventional counterparts. These algorithms are for direct and iterative linear algebra, for dense and sparse matrices, as well as direct n-body simulations. Several of these algorithms exhibit perfect strong scaling, in both time and energy: run time (resp. energy) for a fixed problem size drops proportionally to the number of processors p (resp. is independent of p). Finally, we describe extensions to algorithms involving arbitrary loop nests and array accesses, assuming only that array subscripts are affine functions of the loop indices. <br />
<br />
===Sep 26: Jim Demmel (Berkeley) ===<br />
''Implementing Communication Avoiding Algorithms''<br />
<br />
Designing algorithms that avoiding communication, attaining<br />
lower bounds if possible, is critical for algorithms to minimize runtime and<br />
energy on current and future architectures. These new algorithms can have <br />
new numerical stability properties, new ways to encode answers, and new data<br />
structures, not just depend on loop transformations (we need those too!).<br />
We will illustrate with a variety of examples including direct linear algebra<br />
(eg new ways to perform pivoting, new deterministic and randomized<br />
eigenvalue algorithms), iterative linear algebra (eg new ways to reorganize<br />
Krylov subspace methods) and direct n-body algorithms, on architectures<br />
ranging from multicore to distributed memory to heterogeneous.<br />
The theory describing communication avoiding algorithms can give us a large<br />
design space of possible implementations, so we use autotuning to find<br />
the fastest one automatically. Finally, on parallel architectures one can<br />
frequently not expect to get bitwise identical results from multiple runs,<br />
because of dynamic scheduling and floating point nonassociativity; <br />
this can be a problem for reasons from debugging to correctness.<br />
We discuss some techniques to get reproducible results at modest cost.<br />
<br />
===Sep 27: Jim Demmel (Berkeley) ===<br />
''Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays''<br />
<br />
Our goal is to minimize communication, i.e. moving data, since it increasingly<br />
dominates the cost of arithmetic in algorithms. Motivated by this, attainable<br />
communication lower bounds have been established by many authors for a <br />
variety of algorithms including matrix computations.<br />
<br />
The lower bound approach used initially by Irony, Tiskin and Toledo <br />
for O(n^3) matrix multiplication, and later by Ballard et al <br />
for many other linear algebra algorithms, depends on a geometric result by <br />
Loomis and Whitney: this result bounds the volume of a 3D set <br />
(representing multiply-adds done in the inner loop of the algorithm) <br />
using the product of the areas of certain 2D projections of this set <br />
(representing the matrix entries available locally, i.e., without communication).<br />
<br />
Using a recent generalization of Loomis' and Whitney's result, we generalize <br />
this lower bound approach to a much larger class of algorithms, <br />
that may have arbitrary numbers of loops and arrays with arbitrary dimensions, <br />
as long as the index expressions are affine combinations of loop variables.<br />
In other words, the algorithm can do arbitrary operations on any number of <br />
variables like A(i1,i2,i2-2*i1,3-4*i3+7*i_4,…).<br />
Moreover, the result applies to recursive programs, irregular iteration spaces, <br />
sparse matrices, and other data structures as long as the computation can be<br />
logically mapped to loops and indexed data structure accesses. <br />
<br />
We also discuss when optimal algorithms exist that attain the lower bounds; <br />
this leads to new asymptotically faster algorithms for several problems.<br />
<br />
===October 4: Frank Sottile (Texas A&M) ===<br />
''Galois groups of Schubert problems''<br />
<br />
Work of Jordan from 1870 showed how Galois theory<br />
can be applied to enumerative geometry. Hermite earlier<br />
showed the equivalence of Galois groups with geometric <br />
monodromy groups, and in 1979 Harris used this to study <br />
Galois groups of many enumerative problems. Vakil gave <br />
a geometric-combinatorial criterion that implies a Galois <br />
group contains the alternating group. With Brooks and <br />
Martin del Campo, we used Vakil's criterion to show that <br />
all Schubert problems involving lines have at least <br />
alternating Galois group. White and I have given a new <br />
proof of this based on 2-transitivity.<br />
<br />
My talk will describe this background and sketch a <br />
current project to systematically determine Galois groups <br />
of all Schubert problems of moderate size on all small <br />
classical flag manifolds, investigating at least several <br />
million problems. This will use supercomputers employing <br />
several overlapping methods, including combinatorial <br />
criteria, symbolic computation, and numerical homotopy <br />
continuation, and require the development of new <br />
algorithms and software.<br />
<br />
===October 11: Amie Wilkinson (Chicago) ===<br />
<br />
''Robust mechanisms for chaos''<br />
<br />
What are the underlying mechanisms for robustly chaotic behavior in smooth dynamics?<br />
<br />
In addressing this question, I'll focus on the study of diffeomorphisms of a compact manifold, where "chaotic" means "mixing" and and "robustly" means "stable under smooth perturbations." I'll describe recent advances in constructing and using tools called "blenders" to produce stably chaotic behavior with arbitrarily little effort.<br />
<br />
===October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) ===<br />
<br />
''Integrable probability I and II''<br />
<br />
The goal of the talks is to describe the emerging field of integrable<br />
probability, whose goal is to identify and analyze exactly solvable<br />
probabilistic models. The models and results are often easy to describe,<br />
yet difficult to find, and they carry essential information about broad<br />
universality classes of stochastic processes.<br />
<br />
===November 1: Allison Lewko (Columbia University) ===<br />
<br />
''On sets of large doubling, Lambda(4) sets, and error-correcting codes''<br />
<br />
We investigate the structure of finite sets A of integers such that A+A is large, presenting a counterexample to natural conjectures in the pursuit of an "anti-Freiman" theory in additive combinatorics. We will begin with a brief history of the problem and its connection to the study of Lambda(4) sets in harmonic analysis, and then we will discuss our counterexample and its construction from error-correcting codes. We will conclude by describing some related open problems.<br />
This is joint work with Mark Lewko.<br />
<br />
===March 28: Michael Lacey (GA Tech) ===<br />
''The Two Weight Inequality for the Hilbert Transform''<br />
<br />
The individual two weight inequality for the Hilbert transform <br />
asks for a real variable characterization of those pairs of weights <br />
(u,v) for which the Hilbert transform H maps L^2(u) to L^2(v). <br />
This question arises naturally in different settings, most famously <br />
in work of Sarason. Answering in the positive a deep <br />
conjecture of Nazarov-Treil-Volberg, the mapping property <br />
of the Hilbert transform is characterized by a triple of conditions, <br />
the first being a two-weight Poisson A2 on the pair of weights, <br />
with a pair of so-called testing inequalities, uniform over all <br />
intervals. This is the first result of this type for a singular <br />
integral operator. (Joint work with Sawyer, C.-Y. Shen and Uriate-Tuero)<br />
<br />
== Past talks ==<br />
<br />
Last year's schedule: [[Colloquia 2012-2013]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=5767Colloquia/Fall182013-09-04T00:24:13Z<p>Shamgar: /* Abstracts */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Fall 2013 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
|[http://people.math.gatech.edu/~mbaker/ Matt Baker] (Georgia Institute of Technology)<br />
|Riemann-Roch for Graphs and Applications<br />
|Ellenberg<br />
|-<br />
|Sept 13<br />
|[http://math.wisc.edu/~andrews/ Uri Andrews] (University of Wisconsin)<br />
|<br />
|<br />
|-<br />
|Sept 20<br />
|[http://www.math.neu.edu/people/profile/valerio-toledano-laredo Valerio Toledano Laredo] (Northeastern)<br />
|Flat connections and quantum groups<br />
|Gurevich<br />
|-<br />
|'''Wed, Sept 25, 2:30PM'''<br />
|[http://mypage.iu.edu/~alindens/ Ayelet Lindenstrauss]<br />
|<br />
|Meyer<br />
|-<br />
|'''Wed, Sept 25''' (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication Avoiding Algorithms for Linear Algebra and Beyond<br />
|Gurevich<br />
|-<br />
|'''Thurs, Sept 26''' (LAA lecture, Joint with Applied Algebra Seminar)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Implementing Communication Avoiding Algorithms<br />
|Gurevich<br />
|-<br />
|Sept 27 (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays<br />
|Gurevich<br />
|-<br />
|Oct 4<br />
|[http://www.math.tamu.edu/~sottile/ Frank Sottile] (Texas A&M)<br />
|<br />
|Caldararu<br />
|-<br />
|Oct 11<br />
|[http://math.uchicago.edu/~wilkinso/ Amie Wilkinson] (Chicago)<br />
|<br />
|WIMAW (Cladek)<br />
|-<br />
|'''Tues, Oct 15, 4PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|Integrable probability I<br />
|Valko<br />
|-<br />
|'''Wed, Oct 16, 2:30PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|Integrable probability II<br />
|Valko<br />
|-<br />
|<strike>Oct 18</strike><br />
|No colloquium due to the distinguished lecture<br />
|<br />
|<br />
|-<br />
|Oct 25<br />
|[http://www.math.umn.edu/~garrett/ Paul Garrett] (Minnesota)<br />
|<br />
|Gurevich<br />
|<br />
|<br />
|-<br />
|Nov 1<br />
|[http://www.cs.utexas.edu/~alewko/ Allison Lewko] (Microsoft Research New England)<br />
|<br />
|Stovall<br />
|-<br />
|Nov 8<br />
|[http://www.math.cornell.edu/~riley/ Tim Riley] (Cornell)<br />
|<br />
|Dymarz<br />
|-<br />
|Nov 15 and later<br />
|Reserved<br />
|<br />
|Street<br />
|}<br />
<br />
== Spring 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 24<br />
|<br />
|<br />
|<br />
|-<br />
|Jan 31<br />
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)<br />
|<br />
|Gurevich<br />
|-<br />
|Feb 7<br />
|David Treumann (Boston College)<br />
|<br />
|Street<br />
|-<br />
|Feb 14<br />
|<br />
|<br />
|<br />
|-<br />
|Feb 21<br />
|<br />
|<br />
|<br />
|-<br />
|Feb 28<br />
|<br />
|<br />
|<br />
|-<br />
|March 7<br />
|<br />
|<br />
|<br />
|-<br />
|March 14<br />
|<br />
|<br />
|<br />
|- <br />
|<strike>March 21</strike><br />
|'''Spring Break'''<br />
|No Colloquium<br />
|<br />
|-<br />
|March 28<br />
|[http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)<br />
|The Two Weight Inequality for the Hilbert Transform<br />
|Street<br />
|-<br />
|April 4<br />
|[https://sites.google.com/site/katejuschenko/ Kate Jushchenko] (Northwestern)<br />
|<br />
|Dymarz<br />
|-<br />
|April 11<br />
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)<br />
|<br />
|Gurevich<br />
|-<br />
|April 18 (Wasow Lecture)<br />
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)<br />
|<br />
|A. Seeger<br />
|-<br />
|April 25<br />
|[http://www.charlesdoran.net Charles Doran](University of Alberta)<br />
|<br />
|Song<br />
|-<br />
|May 2<br />
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)<br />
|<br />
|Boston<br />
|-<br />
|May 9<br />
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)<br />
|<br />
|WIMAW<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sep 6: Matt Baker (GA Tech) ===<br />
''Riemann-Roch for Graphs and Applications''<br />
<br />
We will begin by formulating the Riemann-Roch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a Riemann-Roch theorem for tropical curves, proved by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof of the Brill-Noether theorem in algebraic geometry (work of by Cools-Draisma-Payne-Robeva), a "volume-theoretic proof" of Kirchhoff's Matrix-Tree Theorem (work of An, Kuperberg, Shokrieh, and the speaker), and a new Chabauty-Coleman style bound for the number of rational points on an algebraic curve over the rationals (work of Katz and Zureick-Brown).<br />
<br />
===Sep 20: Valerio Toledano (North Eastern)===<br />
''Flat connections and quantum groups''<br />
<br />
Quantum groups are natural deformations of the Lie algebra of<br />
nxn matrices, and more generally of semisimple Lie algebras.<br />
They first arose in the mid eighties in the study of solvable<br />
models in statistical mechanics.<br />
<br />
I will explain how these algebraic objects can serve as natural<br />
receptacles for the (transcendental) monodromy of flat connections<br />
arising from representation theory.<br />
<br />
These connections exist in rational, trigonometric and elliptic<br />
forms, and lead to quantum groups of increasing interest and<br />
complexity.<br />
<br />
<br />
===Sep 25: Jim Demmel (Berkeley) ===<br />
''Communication Avoiding Algorithms for Linear Algebra and Beyond''<br />
<br />
Algorithm have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present algorithms that attain provable lower bounds on communication, and show large speedups compared to their conventional counterparts. These algorithms are for direct and iterative linear algebra, for dense and sparse matrices, as well as direct n-body simulations. Several of these algorithms exhibit perfect strong scaling, in both time and energy: run time (resp. energy) for a fixed problem size drops proportionally to the number of processors p (resp. is independent of p). Finally, we describe extensions to algorithms involving arbitrary loop nests and array accesses, assuming only that array subscripts are affine functions of the loop indices. <br />
<br />
===Sep 26: Jim Demmel (Berkeley) ===<br />
''Implementing Communication Avoiding Algorithms''<br />
<br />
Designing algorithms that avoiding communication, attaining<br />
lower bounds if possible, is critical for algorithms to minimize runtime and<br />
energy on current and future architectures. These new algorithms can have <br />
new numerical stability properties, new ways to encode answers, and new data<br />
structures, not just depend on loop transformations (we need those too!).<br />
We will illustrate with a variety of examples including direct linear algebra<br />
(eg new ways to perform pivoting, new deterministic and randomized<br />
eigenvalue algorithms), iterative linear algebra (eg new ways to reorganize<br />
Krylov subspace methods) and direct n-body algorithms, on architectures<br />
ranging from multicore to distributed memory to heterogeneous.<br />
The theory describing communication avoiding algorithms can give us a large<br />
design space of possible implementations, so we use autotuning to find<br />
the fastest one automatically. Finally, on parallel architectures one can<br />
frequently not expect to get bitwise identical results from multiple runs,<br />
because of dynamic scheduling and floating point nonassociativity; <br />
this can be a problem for reasons from debugging to correctness.<br />
We discuss some techniques to get reproducible results at modest cost.<br />
<br />
===Sep 27: Jim Demmel (Berkeley) ===<br />
''Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays''<br />
<br />
Our goal is to minimize communication, i.e. moving data, since it increasingly<br />
dominates the cost of arithmetic in algorithms. Motivated by this, attainable<br />
communication lower bounds have been established by many authors for a <br />
variety of algorithms including matrix computations.<br />
<br />
The lower bound approach used initially by Irony, Tiskin and Toledo <br />
for O(n^3) matrix multiplication, and later by Ballard et al <br />
for many other linear algebra algorithms, depends on a geometric result by <br />
Loomis and Whitney: this result bounds the volume of a 3D set <br />
(representing multiply-adds done in the inner loop of the algorithm) <br />
using the product of the areas of certain 2D projections of this set <br />
(representing the matrix entries available locally, i.e., without communication).<br />
<br />
Using a recent generalization of Loomis' and Whitney's result, we generalize <br />
this lower bound approach to a much larger class of algorithms, <br />
that may have arbitrary numbers of loops and arrays with arbitrary dimensions, <br />
as long as the index expressions are affine combinations of loop variables.<br />
In other words, the algorithm can do arbitrary operations on any number of <br />
variables like A(i1,i2,i2-2*i1,3-4*i3+7*i_4,…).<br />
Moreover, the result applies to recursive programs, irregular iteration spaces, <br />
sparse matrices, and other data structures as long as the computation can be<br />
logically mapped to loops and indexed data structure accesses. <br />
<br />
We also discuss when optimal algorithms exist that attain the lower bounds; <br />
this leads to new asymptotically faster algorithms for several problems.<br />
<br />
<br />
<br />
===March 28: Michael Lacey (GA Tech) ===<br />
''The Two Weight Inequality for the Hilbert Transform ''<br />
<br />
The individual two weight inequality for the Hilbert transform <br />
asks for a real variable characterization of those pairs of weights <br />
(u,v) for which the Hilbert transform H maps L^2(u) to L^2(v). <br />
This question arises naturally in different settings, most famously <br />
in work of Sarason. Answering in the positive a deep <br />
conjecture of Nazarov-Treil-Volberg, the mapping property <br />
of the Hilbert transform is characterized by a triple of conditions, <br />
the first being a two-weight Poisson A2 on the pair of weights, <br />
with a pair of so-called testing inequalities, uniform over all <br />
intervals. This is the first result of this type for a singular <br />
integral operator. (Joint work with Sawyer, C.-Y. Shen and Uriate-Tuero)<br />
<br />
== Past talks ==<br />
<br />
Last year's schedule: [[Colloquia 2012-2013]]</div>Shamgarhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=5766Colloquia/Fall182013-09-04T00:21:18Z<p>Shamgar: /* Fall 2013 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Fall 2013 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
|[http://people.math.gatech.edu/~mbaker/ Matt Baker] (Georgia Institute of Technology)<br />
|Riemann-Roch for Graphs and Applications<br />
|Ellenberg<br />
|-<br />
|Sept 13<br />
|[http://math.wisc.edu/~andrews/ Uri Andrews] (University of Wisconsin)<br />
|<br />
|<br />
|-<br />
|Sept 20<br />
|[http://www.math.neu.edu/people/profile/valerio-toledano-laredo Valerio Toledano Laredo] (Northeastern)<br />
|Flat connections and quantum groups<br />
|Gurevich<br />
|-<br />
|'''Wed, Sept 25, 2:30PM'''<br />
|[http://mypage.iu.edu/~alindens/ Ayelet Lindenstrauss]<br />
|<br />
|Meyer<br />
|-<br />
|'''Wed, Sept 25''' (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication Avoiding Algorithms for Linear Algebra and Beyond<br />
|Gurevich<br />
|-<br />
|'''Thurs, Sept 26''' (LAA lecture, Joint with Applied Algebra Seminar)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Implementing Communication Avoiding Algorithms<br />
|Gurevich<br />
|-<br />
|Sept 27 (LAA lecture)<br />
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)<br />
|Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays<br />
|Gurevich<br />
|-<br />
|Oct 4<br />
|[http://www.math.tamu.edu/~sottile/ Frank Sottile] (Texas A&M)<br />
|<br />
|Caldararu<br />
|-<br />
|Oct 11<br />
|[http://math.uchicago.edu/~wilkinso/ Amie Wilkinson] (Chicago)<br />
|<br />
|WIMAW (Cladek)<br />
|-<br />
|'''Tues, Oct 15, 4PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|Integrable probability I<br />
|Valko<br />
|-<br />
|'''Wed, Oct 16, 2:30PM''' (Distinguished Lecture)<br />
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)<br />
|Integrable probability II<br />
|Valko<br />
|-<br />
|<strike>Oct 18</strike><br />
|No colloquium due to the distinguished lecture<br />
|<br />
|<br />
|-<br />
|Oct 25<br />
|[http://www.math.umn.edu/~garrett/ Paul Garrett] (Minnesota)<br />
|<br />
|Gurevich<br />
|<br />
|<br />
|-<br />
|Nov 1<br />
|[http://www.cs.utexas.edu/~alewko/ Allison Lewko] (Microsoft Research New England)<br />
|<br />
|Stovall<br />
|-<br />
|Nov 8<br />
|[http://www.math.cornell.edu/~riley/ Tim Riley] (Cornell)<br />
|<br />
|Dymarz<br />
|-<br />
|Nov 15 and later<br />
|Reserved<br />
|<br />
|Street<br />
|}<br />
<br />
== Spring 2014 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 24<br />
|<br />
|<br />
|<br />
|-<br />
|Jan 31<br />
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)<br />
|<br />
|Gurevich<br />
|-<br />
|Feb 7<br />
|David Treumann (Boston College)<br />
|<br />
|Street<br />
|-<br />
|Feb 14<br />
|<br />
|<br />
|<br />
|-<br />
|Feb 21<br />
|<br />
|<br />
|<br />
|-<br />
|Feb 28<br />
|<br />
|<br />
|<br />
|-<br />
|March 7<br />
|<br />
|<br />
|<br />
|-<br />
|March 14<br />
|<br />
|<br />
|<br />
|- <br />
|<strike>March 21</strike><br />
|'''Spring Break'''<br />
|No Colloquium<br />
|<br />
|-<br />
|March 28<br />
|[http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)<br />
|The Two Weight Inequality for the Hilbert Transform<br />
|Street<br />
|-<br />
|April 4<br />
|[https://sites.google.com/site/katejuschenko/ Kate Jushchenko] (Northwestern)<br />
|<br />
|Dymarz<br />
|-<br />
|April 11<br />
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)<br />
|<br />
|Gurevich<br />
|-<br />
|April 18 (Wasow Lecture)<br />
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)<br />
|<br />
|A. Seeger<br />
|-<br />
|April 25<br />
|[http://www.charlesdoran.net Charles Doran](University of Alberta)<br />
|<br />
|Song<br />
|-<br />
|May 2<br />
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)<br />
|<br />
|Boston<br />
|-<br />
|May 9<br />
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)<br />
|<br />
|WIMAW<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Sep 6: Matt Baker (GA Tech) ===<br />
''Riemann-Roch for Graphs and Applications''<br />
<br />
We will begin by formulating the Riemann-Roch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a Riemann-Roch theorem for tropical curves, proved by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof of the Brill-Noether theorem in algebraic geometry (work of by Cools-Draisma-Payne-Robeva), a "volume-theoretic proof" of Kirchhoff's Matrix-Tree Theorem (work of An, Kuperberg, Shokrieh, and the speaker), and a new Chabauty-Coleman style bound for the number of rational points on an algebraic curve over the rationals (work of Katz and Zureick-Brown).<br />
<br />
===Sep 25: Jim Demmel (Berkeley) ===<br />
''Communication Avoiding Algorithms for Linear Algebra and Beyond''<br />
<br />
Algorithm have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present algorithms that attain provable lower bounds on communication, and show large speedups compared to their conventional counterparts. These algorithms are for direct and iterative linear algebra, for dense and sparse matrices, as well as direct n-body simulations. Several of these algorithms exhibit perfect strong scaling, in both time and energy: run time (resp. energy) for a fixed problem size drops proportionally to the number of processors p (resp. is independent of p). Finally, we describe extensions to algorithms involving arbitrary loop nests and array accesses, assuming only that array subscripts are affine functions of the loop indices. <br />
<br />
===Sep 26: Jim Demmel (Berkeley) ===<br />
''Implementing Communication Avoiding Algorithms''<br />
<br />
Designing algorithms that avoiding communication, attaining<br />
lower bounds if possible, is critical for algorithms to minimize runtime and<br />
energy on current and future architectures. These new algorithms can have <br />
new numerical stability properties, new ways to encode answers, and new data<br />
structures, not just depend on loop transformations (we need those too!).<br />
We will illustrate with a variety of examples including direct linear algebra<br />
(eg new ways to perform pivoting, new deterministic and randomized<br />
eigenvalue algorithms), iterative linear algebra (eg new ways to reorganize<br />
Krylov subspace methods) and direct n-body algorithms, on architectures<br />
ranging from multicore to distributed memory to heterogeneous.<br />
The theory describing communication avoiding algorithms can give us a large<br />
design space of possible implementations, so we use autotuning to find<br />
the fastest one automatically. Finally, on parallel architectures one can<br />
frequently not expect to get bitwise identical results from multiple runs,<br />
because of dynamic scheduling and floating point nonassociativity; <br />
this can be a problem for reasons from debugging to correctness.<br />
We discuss some techniques to get reproducible results at modest cost.<br />
<br />
===Sep 27: Jim Demmel (Berkeley) ===<br />
''Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays''<br />
<br />
Our goal is to minimize communication, i.e. moving data, since it increasingly<br />
dominates the cost of arithmetic in algorithms. Motivated by this, attainable<br />
communication lower bounds have been established by many authors for a <br />
variety of algorithms including matrix computations.<br />
<br />
The lower bound approach used initially by Irony, Tiskin and Toledo <br />
for O(n^3) matrix multiplication, and later by Ballard et al <br />
for many other linear algebra algorithms, depends on a geometric result by <br />
Loomis and Whitney: this result bounds the volume of a 3D set <br />
(representing multiply-adds done in the inner loop of the algorithm) <br />
using the product of the areas of certain 2D projections of this set <br />
(representing the matrix entries available locally, i.e., without communication).<br />
<br />
Using a recent generalization of Loomis' and Whitney's result, we generalize <br />
this lower bound approach to a much larger class of algorithms, <br />
that may have arbitrary numbers of loops and arrays with arbitrary dimensions, <br />
as long as the index expressions are affine combinations of loop variables.<br />
In other words, the algorithm can do arbitrary operations on any number of <br />
variables like A(i1,i2,i2-2*i1,3-4*i3+7*i_4,…).<br />
Moreover, the result applies to recursive programs, irregular iteration spaces, <br />
sparse matrices, and other data structures as long as the computation can be<br />
logically mapped to loops and indexed data structure accesses. <br />
<br />
We also discuss when optimal algorithms exist that attain the lower bounds; <br />
this leads to new asymptotically faster algorithms for several problems.<br />
<br />
<br />
<br />
===March 28: Michael Lacey (GA Tech) ===<br />
''The Two Weight Inequality for the Hilbert Transform ''<br />
<br />
The individual two weight inequality for the Hilbert transform <br />
asks for a real variable characterization of those pairs of weights <br />
(u,v) for which the Hilbert transform H maps L^2(u) to L^2(v). <br />
This question arises naturally in different settings, most famously <br />
in work of Sarason. Answering in the positive a deep <br />
conjecture of Nazarov-Treil-Volberg, the mapping property <br />
of the Hilbert transform is characterized by a triple of conditions, <br />
the first being a two-weight Poisson A2 on the pair of weights, <br />
with a pair of so-called testing inequalities, uniform over all <br />
intervals. This is the first result of this type for a singular <br />
integral operator. (Joint work with Sawyer, C.-Y. Shen and Uriate-Tuero)<br />
<br />
== Past talks ==<br />
<br />
Last year's schedule: [[Colloquia 2012-2013]]</div>Shamgar