https://www.math.wisc.edu/wiki/index.php?title=Special:NewPages&feed=atom&hideredirs=1&limit=50&offset=&namespace=0&username=&tagfilter=&size-mode=max&size=0UW-Math Wiki - New pages [en]2021-02-27T12:48:59ZFrom UW-Math WikiMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php/Applied/ACMS/Fall2021Applied/ACMS/Fall20212021-02-22T14:23:04Z<p>Spagnolie: /* Fall 2021 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Applied and Computational Mathematics Seminar =<br />
<br />
*'''When:''' Fridays at 2:25pm (except as otherwise indicated)<br />
*'''Where:''' 901 Van Vleck Hall<br />
*'''Organizers:''' [http://www.math.wisc.edu/~qinli/ Qin Li], [http://www.math.wisc.edu/~spagnolie/ Saverio Spagnolie] and [http://www.math.wisc.edu/~jeanluc Jean-Luc Thiffeault]<br />
*'''To join the ACMS mailing list:''' Send mail to [mailto:acms+join@g-groups.wisc.edu acms+join@g-groups.wisc.edu].<br />
<br />
<br><br />
<br />
== Fall 2021 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| Oct 1<br />
|[https://lsa.umich.edu/cscs/people/core-faculty/doering.html Charles Doering] (Michigan)<br />
|''[[Applied/ACMS/absF21#Charles Doering (Michigan)|TBA]]''<br />
|Jean-Luc<br />
|-<br />
| Nov 5<br />
|[https://people.maths.ox.ac.uk/vella/ Dominic Vella] (Oxford)<br />
|''[[Applied/ACMS/absF21#Dominic Vella (Oxford)|TBA]]''<br />
|Saverio<br />
|}<br />
<br />
== Future semesters ==<br />
<br />
*[[Applied/ACMS/Spring2022|Spring 2022]]<br />
<br />
<br />
----<br />
<br />
== Archived semesters ==<br />
<br />
*[[Applied/ACMS/Fall2020|Fall 2020]]<br />
*[[Applied/ACMS/Spring2020|Spring 2020]]<br />
*[[Applied/ACMS/Fall2019|Fall 2019]]<br />
*[[Applied/ACMS/Spring2019|Spring 2019]]<br />
*[[Applied/ACMS/Fall2018|Fall 2018]]<br />
*[[Applied/ACMS/Spring2018|Spring 2018]]<br />
*[[Applied/ACMS/Fall2017|Fall 2017]]<br />
*[[Applied/ACMS/Spring2017|Spring 2017]]<br />
*[[Applied/ACMS/Fall2016|Fall 2016]]<br />
*[[Applied/ACMS/Spring2016|Spring 2016]]<br />
*[[Applied/ACMS/Fall2015|Fall 2015]]<br />
*[[Applied/ACMS/Spring2015|Spring 2015]]<br />
*[[Applied/ACMS/Fall2014|Fall 2014]]<br />
*[[Applied/ACMS/Spring2014|Spring 2014]]<br />
*[[Applied/ACMS/Fall2013|Fall 2013]]<br />
*[[Applied/ACMS/Spring2013|Spring 2013]]<br />
*[[Applied/ACMS/Fall2012|Fall 2012]]<br />
*[[Applied/ACMS/Spring2012|Spring 2012]]<br />
*[[Applied/ACMS/Fall2011|Fall 2011]]<br />
*[[Applied/ACMS/Spring2011|Spring 2011]]<br />
*[[Applied/ACMS/Fall2010|Fall 2010]]<br />
<!--<br />
*[http://www.math.wisc.edu/~jeanluc/ACMS/archive/Spring10.html Spring 2010]<br />
*[http://www.math.wisc.edu/~jeanluc/ACMS/archive/Fall09.html Fall 2009]<br />
*[http://www.math.wisc.edu/~jeanluc/ACMS/archive/Spring09.html Spring 2009]<br />
*[http://www.math.wisc.edu/~jeanluc/ACMS/archive/Fall08.html Fall 2008]<br />
*[http://www.math.wisc.edu/~jeanluc/ACMS/archive/Spring08.html Spring 2008]<br />
*[http://www.math.wisc.edu/~jeanluc/ACMS/archive/Fall07.html Fall 2007]<br />
*[http://www.math.wisc.edu/~jeanluc/ACMS/archive/Spring07.html Spring 2007]<br />
*[http://www.math.wisc.edu/~jeanluc/ACMS/archive/Fall06.html Fall 2006]<br />
--><br />
<br />
<br><br />
<br />
----<br />
Return to the [[Applied|Applied Mathematics Group Page]]</div>Jeanluchttps://www.math.wisc.edu/wiki/index.php/TechTA_pageTechTA page2021-01-27T17:27:44Z<p>Nagreen: </p>
<hr />
<div>We have TAs who will function as Technical TAs.<br />
<br />
'''Hours'''<br />
<br />
During the Spring Semester 2021, they are<br />
<br />
*Erika Pirnes<br />
*Di Chen<br />
*Tianhong Huang<br />
<br />
Each TechTA will either have office hours, or will have more flexible times where they are responsible for answering the TechTA email (techta@math.wisc.edu).<br />
<br />
As of Spring 2021, those times are<br />
<br />
*Monday 10am-12pm: Tianhong Huang <br />
*Monday 1-230pm: Erika Pirnes<br />
*Tuesday 6:00pm-8:00pm: Di Chen<br />
*Wednesday 10am-12pm: Tianhong Huang<br />
*Thursday 6:00pm-8:00pm: Di Chen<br />
<br />
Erika will have some flex hours to monitor the email during off times.<br />
<br />
Sara Nagreen will also monitor the email when otherwise it is not monitored.<br />
<br />
'''Job Duties'''<br />
<br />
What sort of questions can a TechTA expect?<br />
<br />
* How does Zoom work?<br />
* Why doesn't my Zoom work the way I expect?<br />
* I am trying to do something in Canvas and it isn't working/I don't know how.</div>Nagreenhttps://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle/newsletter12521Madison Math Circle/newsletter125212021-01-24T04:47:03Z<p>Andrews: Created page with "<div class="middlecol" style="display:inline-block;text-align: left;"> <div style="display: flex;justify-content: space-between;align-items: center;padding-left:50px;padding-..."</p>
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<br />
Jan 25, 2021<br />
<br />
<div class="contentEditable"><br />
<br />
[Open in your browser](%5BSHOWEMAIL%5D)<br />
[Tell a friend](%5BFORWARD%5D)<br />
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<div style="display:flex;flex-wrap:wrap;justify-content: center;width:100%;"><br />
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[![Featured images](images/logo2.png){.banner}](https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle%20)<br />
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<div style="flex:1 1 200px;"><br />
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<div style="background-color:#E4A552;padding-left:50px;padding-right:50px;padding-top:25px;padding-bottom:25px;"><br />
<br />
Madison Math Circle {#madison-math-circle style="font-size:16px;color:#ffffff;font-weight:normal;margin:0;"}<br />
===================<br />
<br />
Providing Madison children with a friendly environment that fosters learning beautiful mathematical theories beyond the regular school curriculum and developing critical thinking and problem solving skills.<br />
<br />
</div><br />
<br />
<div style="background:white;padding:10px;display:flex;align-items: center;justify-content: center;margin-top:10px;"><br />
<br />
![](images/pick.png)<br />
<div style="margin-left:100px;"><br />
<br />
Pick's theorem<br />
==============<br />
<br />
### February 1, 2021 at 5-6pm<br />
<br />
by Connor Simpson<br />
-----------------<br />
<br />
[Join us on Zoom](https://www.google.com/url?q=https://uwmadison.zoom.us/j/97810093411?pwd%3DM2ZDT2cwWkZ4SDMrVkpWRUlQL2FLQT09&sa=D&source=hangouts&ust=1611549251005000&usg=AFQjCNG-X0VT4BK--oC4oP1EyAil_GbSEQ)<br />
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------<br />
<br />
Pick's theorem relates the area of a polygon whose vertices lie on points of an evenly spaced grid to the number of grid points inside it. We'll do a sequence of examples to discover this theorem, outline a proof, and consider 3-dimensional analogues.<br />
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</div><br />
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</div><br />
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<div style="display:flex;background:333333;margin-top:15px;flex-wrap:wrap;margin:5px -5px 0px;"><br />
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<div style="background:white;flex:1 1 400px;padding:20px;min-width:300px;margin:5px;"><br />
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<br />
Math Circle is Back!<br />
====================<br />
<br />
(virtually for now)<br />
-------------------<br />
<br />
</div><br />
<br />
<br />
After a semester off, we are excited to wake from our slumber! Until we can go back to normal in-person meetings, the Madison Math Circle will operate in a reduced format during the semester.<br />
<br />
<br />
We will have a monthly Zoom talk on the first Monday of every month (February through May). It's a lot less than before, but do not fret! On weeks without a talk, we will send out a lovely math-filled newsletter — just like this one! Each newsletter will have a riddle or two for you to grapple with and a fun math video to watch.<br />
<br />
<br />
Looking forward to a great semester of learning!<br />
<br />
– Professor Andrews<br />
<br />
</div><br />
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<div style="flex:1 1 400px;margin:5px;text-align:center;display:flex;flex-direction:column;background:#333333;"><br />
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<div style="background:white;padding:10px;height:100%;display:flex;flex-direction: column;justify-content: space-around;align-items:center;"><br />
<br />
Video of the Week<br />
=================<br />
<br />
<div class="video-responsive"><br />
<br />
</div><br />
<br />
Remark: The last part of the video contains some material requiring some knowledge of trigonometry. The first 20 minutes needs no background.<br />
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</div><br />
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</div><br />
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</div><br />
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<div style="display:flex;flex-wrap:wrap;background:cornsilk;justify-content: center;margin-top:5px;"><br />
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<br />
![product image](images/hancock.jpg){.banner}<br />
<br />
</div><br />
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<div style="flex: 1 1 500px;padding:20px;"><br />
<br />
Weekly Stumper<br />
--------------<br />
<br />
Hancock tower in Chicago has 100 floors. Your task is to find the highest floor of Hancock tower from which you can drop an ostrich egg without it cracking. For each of the following cases, describe a procedure that always finds the right answer, and in the worst case scenario has the lowest number of drops. So, a procedure which might give the right answer in 1 drop, but might also take 100 drops is less good than a procedure which always takes 90 drops.<br />
<br />
1. You have exactly one ostrich egg<br />
2. You own an ostrich farm (so, you have an unlimited supply of eggs)<br />
3. You have exactly two ostrich eggs<br />
<br />
Example for a “bad” procedure for case 1 that may not result in the exact correct answer: drop your single egg from floor 100. If it doesn’t break, then floor 100 is the highest floor from which you can drop an egg without cracking it, but if the egg breaks, then you are out of eggs and did not find the answer.<br />
<br />
<div style="text-align: center;margin-top:30px;"><br />
<br />
[Send in your solution](https://forms.gle/3G9Bh6AcKNDQWqQr8){.link2}<br />
<br />
</div><br />
<br />
</div><br />
<br />
</div><br />
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</div><br />
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<div style="display:flex;justify-content: space-between;align-items:flex-end;padding:40px;"><br />
<br />
<div><br />
<br />
<span style="font-weight:bold;">[Madison Math Circle](https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle)</span><br />
[Forward to a friend](%5BFORWARD%5D)<br />
<br />
</div><br />
<br />
<div><br />
<br />
[![facebook icon](images/facebook2.png){width="52" height="52"}](https://www.facebook.com/madisonmathcircle)<br />
<br />
</div><br />
<br />
</div></div>Andrewshttps://www.math.wisc.edu/wiki/index.php/Applied/Physical_Applied_Math/Fall2020Applied/Physical Applied Math/Fall20202021-01-21T15:47:59Z<p>Spagnolie: Created page with "== Fall 2020 == {| cellpadding="8" !align="left" | date !align="left" | speaker !align="left" | title |- |Sept. 3 |Organizational meeting | |- |Sept. 10 |''no group meeting..."</p>
<hr />
<div>== Fall 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sept. 3<br />
|Organizational meeting<br />
|<br />
|-<br />
|Sept. 10<br />
|''no group meeting''<br />
|''faculty meeting @ 3:30pm''<br />
|-<br />
|Sept. 17<br />
|Saverio<br />
|<br />
|-<br />
|Sept. 24<br />
|Wil<br />
|Geometric flows and moving surfaces<br />
|-<br />
|Oct 1<br />
|Bryan<br />
|Homogenization of the advection-diffusion equation in the presence of a source<br />
|-<br />
|Oct 8<br />
|<br />
|''faculty meeting''<br />
|-<br />
|Oct 15<br />
|Chris<br />
|Evolutionary stable strategies and the connection between game theory and the Ising model<br />
|-<br />
|Oct 22<br />
|Yu<br />
|Narrow exit problem with sink flow<br />
|-<br />
|Oct 29<br />
|Hongfei<br />
|Complex model of swimmer interactions<br />
|-<br />
|Nov 5<br />
|Jean-Luc<br />
|Equilibria of Fokker-Planck equations<br />
|-<br />
|Nov 12<br />
|Hongyi Huang<br />
|Bubbles!<br />
|-<br />
|Nov 19<br />
|<br />
|Watch party for ''Gallery of Fluid Motion'' videos<br />
|-<br />
|Nov 26<br />
|<br />
|''Thanksgiving''<br />
|-<br />
|Dec 3<br />
|<br />
|''faculty meeting''<br />
|-<br />
|Dec 10<br />
|Saverio<br />
|Hydrodynamic interaction of swimmer with boundary<br />
|-<br />
|}</div>Spagnoliehttps://www.math.wisc.edu/wiki/index.php/Algebra_in_Statistics_and_Computation_SeminarAlgebra in Statistics and Computation Seminar2021-01-21T09:22:31Z<p>Jose: /* March 11: Carlos Amendola Ceron */</p>
<hr />
<div>'''When''': 1:30-2:25, Thursdays (1:30-1:45pm Social Chit-Chat, 1:45-2:25 Talk Time)<br />
<br />
'''Where''': Virtual: https://uwmadison.zoom.us/j/95934501565<br />
<br />
'''Contact''': [https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez], [https://sites.google.com/wisc.edu/zinanwang/ Zinan Wang] (Lead)<br />
<br />
'''Remark''': This informal seminar is held on the second Thursday of the month<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date<br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | <br />
|- <br />
|February 11<br />
|[https://www.math.ubc.ca/~erobeva/ Elina Robeva (UBC)]<br />
|Hidden Variables in Linear Causal Models<br />
|-<br />
|March 11<br />
|[http://www.luke-amendola.appspot.com/ Carlos Amendola Ceron (ULM)]<br />
|Likelihood Geometry of Correlation Models<br />
|<br />
|-<br />
|April 8<br />
|[https://people.maths.ox.ac.uk/seigal/ Anna Seigal (Oxford)]<br />
|TBD<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===March 11: Carlos Amendola Ceron===<br />
Title: Likelihood Geometry of Correlation Models.<br />
<br />
Abstract: Correlation matrices are standardized covariance matrices. They form an affine space of symmetric matrices defined by setting the diagonal entries to one. In this talk we will consider the fascinating geometry of maximum likelihood estimation for this model and linear submodels that encode additional symmetries. We also consider the problem of minimizing two closely related functions of the covariance matrix, the Stein's loss and the symmetrized Stein's loss, which lead naturally to the algebraic statistical concepts of dual ML degree and SSL degree. I will also present exciting open problems in this direction.<br />
<br />
This is joint work with [http://www.econ.upf.edu/~piotr/ Piotr Zwiernik].<br />
<br />
===February 11: Elina Robeva===<br />
Title: Hidden Variables in Linear Causal Models.<br />
<br />
References: https://arxiv.org/abs/1807.07561 https://arxiv.org/abs/2001.10426, and https://arxiv.org/abs/2010.05306 <br />
<br />
Abstract: Identifying causal relationships between random variables from observational data is an important hard problem in many areas of data science. The presence of hidden variables, though quite realistic, pauses a variety of further problems. Linear structural equation models, which express each variable as a linear combination of all of its parent variables, have long been used for learning causal structure from observational data. Surprisingly, when the variables in a linear structural equation model are non-Gaussian the full causal structure can be learned without interventions, while in the Gaussian case one can only learn the underlying graph up to a Markov equivalence class. In this talk, we first discuss how one can use high-order cumulant information to learn the structure of a linear non-Gaussian structural equation model with hidden variables. While prior work posits that each hidden variable is the common cause of two observed variables, we allow each hidden variable to be the common cause of multiple observed variables. Next, we discuss hidden variable Gaussian causal models and the difficulties that arise with learning those. We show it is hard to even describe the Markov equivalence classes in this case, and we give a semi algebraic description of a large class of these models.<br />
<br />
<br />
----<br />
<br />
== Other events to note ==<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | event/title<br />
!align="left" | location/speaker<br />
!align="left" | info<br />
|-<br />
|Fourth Thursday's of the month<br />
|[https://www.math.wisc.edu/wiki/index.php/Applied_Algebra_Seminar Applied Algebra Seminar, UW Madison]<br />
|Virtual<br />
|-<br />
|Second Tuesday of the month, 10am<br />
|[http://wiki.siam.org/siag-ag/index.php/Webinar SIAM SAGA] <br />
|Virtual: [https://www.youtube.com/playlist?list=PLf_ipOSbWC84HloBwtq3vVJKYE4rwfeSs Recordings]<br />
|[https://siam.zoom.us/webinar/register/WN_nMdM3GXHTTuZyjn5fGf4jA Registration] needed once.<br />
|-<br />
|Biweekly Mondays <br />
|[https://sites.google.com/view/algstatsonline/home Algebraic Statistics Online Seminar (ASOS)]<br />
|Virtual: [https://sites.google.com/view/algstatsonline/past-talks-and-recordings Recordings]<br />
|Mailing list [https://lists.lrz.de/mailman/listinfo/algstatsonline sign-up] for Zoom-links<br />
|-<br />
|Fall 2020 <br />
|[https://www.math.wisc.edu/~jose/ASC ASC Seminar]<br />
|Virtual<br />
|-<br />
|More events <br />
|[https://www.math.wisc.edu/wiki/index.php/Applied_Algebra_Seminar_Spring_2021#Related_events_to_note are listed here]<br />
|-<br />
|}</div>Zwang894https://www.math.wisc.edu/wiki/index.php/Applied_Algebra_Seminar_Spring_2021Applied Algebra Seminar Spring 20212021-01-20T03:06:53Z<p>Jrlindberg: /* Abstracts */</p>
<hr />
<div>'''When''': 1:30pm, Thursdays<br />
<br />
'''Where''': Virtual: [https://uwmadison.zoom.us/j/93664753217 https://uwmadison.zoom.us/j/93664753217]<br />
<br />
'''List''': to join email mathaas+join@g-groups.wisc.edu and subscribe to the google group<br />
<br />
'''Contact''': Shamgar Gurevich, Jose Israel Rodriguez, [https://sites.google.com/view/julialindberg/home/ Julia Lindberg] (Lead)<br />
<br />
'''Remark''': This seminar is held on the fourth Thursday of the month<br />
<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|February 25<br />
| [https://sites.google.com/site/grrigg/ Greg Blekherman (Georgia Tech)]<br />
| [[#Greg Blekherman|Locally Positive Semidefinite Matrices]]<br />
| Virtual<br />
|-<br />
|March 25<br />
| [https://ecse.monash.edu/staff/james/ James Saunderson (Monash University)]<br />
| TBD<br />
| Virtual<br />
|-<br />
|April 22<br />
|TBD<br />
| <br />
|-<br />
<br />
|-<br />
|}<br />
<br />
== Spring 2020 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|February 20<br />
|[https://wid.wisc.edu/people/carla-michini/// Carla Michini (UW Madison)]<br />
|[[#Carla Michini|Short simplex paths in lattice polytopes]]<br />
|Local<br />
|-<br />
|March 5<br />
| [https://www.math.wisc.edu/~rzachariah/// Alisha Zachariah (UW Madison)]<br />
| [[#Alisha Zachariah|Efficient Estimation of a Sparse Delay-Doopler Channel]]<br />
| Local<br />
|-<br />
|March 19 <br />
|Spring Break<br />
| <br />
|-<br />
|March 26<br />
|(Seminar on Hiatus because of Covid-19)<br />
<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Greg Blekherman===<br />
'''Locally Positive Semidefinite Matrices<br />
'''<br />
<br />
The cone of positive semidefinite matrices plays a prominent role in optimization, and many hard computational problems have well-performing semidefinite relaxations. In practice, enforcing the constraint that a large matrix is positive semidefinite can be expensive. We introduce the cone of k-locally posiitive semidefinite matrices, which consists of matrices all of whose k by k principal submatrices are positive semidefinite. We consider the distance between the cones of positive and locally positive semidefinite matrices, and possible eigenvalues of locally positive semidefinite matrices. Hyperbolic polynomials play a role in some of the proofs. Joint work with Santanu Dey, Marco Molinaro, Kevin Shu and Shengding Sun.<br />
<br />
----<br />
<br />
===Carla Michini===<br />
'''Short simplex paths in lattice polytopes<br />
'''<br />
<br />
We consider the problem of optimizing a linear function over a lattice polytope P contained in [0,k]^n and defined via m linear inequalities. We design a simplex algorithm that, given an initial vertex, reaches an optimal vertex by tracing a path along the edges of P of length at most O(n^6 k log k). The length of this path is independent on m and is the best possible up to a polynomial function, since it is only polynomially far from the worst case diameter. The number of arithmetic operations needed to compute the next vertex in the path is polynomial in n, m and log k. If k is polynomially bounded by n and m, the algorithm runs in strongly polynomial time. This is a joint work with Alberto Del Pia.<br />
<br />
----<br />
<br />
===Alisha Zachariah===<br />
'''Efficiently Estimating a Sparse Delay-Doppler Channel<br />
''' <br />
<br />
Multiple wireless sensing tasks, e.g., radar detection for driver safety, involve estimating the ”channel” or relationship between signal transmitted and received. In this talk, I will focus on a certain type of channel known as the delay-doppler channel. This channel model starts to be applicable in high frequency carrier settings, which are increasingly common with recent developments in mmWave technology. Moreover, in this setting, both the channel model and existing technologies are amenable to working with signals of large bandwidth, and using such signals is a standard approach to achieving high resolution channel estimation. However, when high resolution is desirable, this approach creates a tension with the desire for efficiency because, in particular, it immediately implies that the signals in play live in a space of very high dimension N (e.g., ~10^6 in some applications), as per the Shannon-Nyquist sampling theorem.<br />
<br />
To address this, I will propose a randomized algorithm for channel estimation in the k-sparse setting (e.g., k objects in radar detection), with sampling and space complexity both on the order of k(log N)^2, and arithmetic complexity on the order of k(log N)^3+k^2, for N sufficiently large. <br />
<br />
While this algorithm seems to be extremely efficient -- to the best of our knowledge, the first of this nature in terms of complexity -- it is just a simple combination of three ingredients, two of which are well-known and widely used, namely digital chirp signals and discrete Gaussian filter functions, and the third being recent developments in Sparse Fast Fourier Transform algorithms.<br />
<br />
----<br />
<br />
== Related events to note ==<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | event/title<br />
!align="left" | location/speaker<br />
!align="left" | info<br />
|-<br />
|Postponed<br />
|[https://www.math.wisc.edu/wiki/index.php/Applied_Algebra_Days_Tensors/// Applied Algebra Days 4 - Tensors ]<br />
| Several talks on tensors <br />
|-<br />
|1:30pm, 2nd Thursday of the month<br />
|[https://www.math.wisc.edu/wiki/index.php/Algebra_in_Statistics_and_Computation_Seminar Informal Seminar: Algebra in Statistics and Computation]<br />
|Virtual<br />
|-<br />
|3:30pm<br />
|[https://www.math.wisc.edu/wiki/index.php/SIAM_Student_Chapter_Seminar SIAM Student Chapter]<br />
|Virtual<br />
|-<br />
|10am, 2nd Tuesday of the month<br />
|[http://wiki.siam.org/siag-ag/index.php/Webinar SIAM SAGA] <br />
|Virtual: [https://www.youtube.com/playlist?list=PLf_ipOSbWC84HloBwtq3vVJKYE4rwfeSs Recordings]<br />
|[https://siam.zoom.us/webinar/register/WN_nMdM3GXHTTuZyjn5fGf4jA Registration] needed once.<br />
|-<br />
|10am, Most Tuesdays<br />
|[https://www.mis.mpg.de/nlalg/seminars/naso.html Nonlinear algebra seminar online] <br />
|Virtual: [https://www.mis.mpg.de/nlalg/seminars/2020.html#id31516 Recordings]<br />
|[https://www.mis.mpg.de/nlalg/seminars/naso.html Registration] required once<br />
|-<br />
|Biweekly Mondays <br />
|[https://sites.google.com/view/algstatsonline/home Algebraic Statistics Online Seminar (ASOS)]<br />
|Virtual: [https://sites.google.com/view/algstatsonline/past-talks-and-recordings Recordings]<br />
|Mailing list [https://lists.lrz.de/mailman/listinfo/algstatsonline sign-up] for Zoom-links<br />
|-<br />
|January 26th-29th, 2021 <br />
|[https://sites.google.com/view/agmlsanya/ Sanya Workshop on Algebraic Geometry and Machine Learning]<br />
|Virtual: [https://sites.google.com/view/agmlsanya/talks Recordings]<br />
|-<br />
|July 29-30, 2021 <br />
|[http://www.iaa.tu-bs.de/AppliedAlgebra/RACG/RACG.html Real algebraic geometry and convex geometry Conference]<br />
|TBD: TU Braunschweig, Germany or Online<br />
|-<br />
|}<br />
----</div>Josehttps://www.math.wisc.edu/wiki/index.php/Applied/ACMS/absS21Applied/ACMS/absS212021-01-19T19:17:32Z<p>Chennan: /* ACMS Abstracts: Spring 2021 */</p>
<hr />
<div>= ACMS Abstracts: Spring 2021 =<br />
<br />
=== Christina Kurzthaler (Princeton) ===<br />
<br />
Complex Transport Phenomena<br />
<br />
Abstract: Self-propelled agents are intrinsically out of equilibrium and exhibit a variety of unusual transport features. In this talk, I will discuss the spatiotemporal dynamics of catalytic Janus colloids characterized in terms of the intermediate scattering function. Our findings show quantitative agreement of our analytic theory for the active Brownian particle model with experimental observations from the smallest length scales, where translational diffusion and self-propulsion dominate, up to the larges ones, which probe the rotational diffusion of the active agents. In the second part of this talk, I will address the hydrodynamic interactions between sedimenting particles and surfaces with corrugated topographies, omnipresent in biological and microfluidic environments. I will present an analytic theory for the roughness-induced mobility and discuss the sedimentation behavior of a sphere next to periodic and randomly structured surfaces.<br />
<br />
=== Antoine Remond-Tiedrez (UW) === <br />
<br />
Instability of an Anisotropic Micropolar Fluid<br />
<br />
Abstract: Many aerosols and suspensions, or more broadly fluids containing a non-trivial structure at a microscopic scale, can be described by the theory of micropolar fluids. The resulting equations couple the Navier-Stokes equations which describe the macroscopic motion of the fluid to evolution equations for the angular momentum and the moment of inertia associated with the microcopic structure. In this talk we will discuss the case of viscous incompressible three-dimensional micropolar fluids. We will discuss how, when subject to a fixed torque acting at the microscopic scale, the nonlinear stability of the unique equilibrium of this system depends on the shape of the microstructure.<br />
<br />
=== Hugo Touchette (Stellenbosch University) ===<br />
<br />
Large deviation theory: From physics to mathematics and back<br />
<br />
Abstract: I will give a basic overview of the theory of large deviations, developed by Varadhan (Abel Prize 2007) in the 1970s, and of its applications in statistical physics. In the first part of the talk, I will discuss the basics of this theory and its historical sources, which can be traced back in mathematics to Cramer (1938) and Sanov (1960) and, on the physics side, to Einstein (1910) and Boltzmann (1877). In the second part, I will show how the theory can be applied to study equilibrium and nonequilibrium systems and to express many key concepts of statistical physics in a clear mathematical way.<br />
<br />
=== Tijana Pfander (Ludwig-Maximilians-University of Munich) ===<br />
<br />
Towards next generation data assimilation algorithms for convective scale applications<br />
<br />
Abstract: The initial state for a geophysical numerical model is produced by combining observational data with a short-range model simulation using a data assimilation algorithm. Particularly challenging is the application of these algorithms in weather forecasting at the convective scale. For convective scale applications, high resolution nonlinear numerical models are used. In addition, intermittent convection is present in the simulations and observations, often leading to errors in locations and intensity of convective storms. In addition, the state vector has a large size, one third of which contains variables whose non-negativity needs to be preserved, and the estimation of the state vector has to be done frequently in order to catch fast changing convection. Finally, often, not only one, but rather an ensemble of predictions is needed in order to correctly specify, for example, the uncertainty of rain at a particular location, even further increasing the computational considerations.<br />
In current practice, many data assimilation methods do not preserve the non-negativity of variables and rely on Gaussian assumptions. We present an algorithm that could be used for weather forecasting at the convective scale, that is based on the ensemble Kalman filter (EnKF) and quadratic programming. This algorithm outperforms the EnKF as well as the EnKF with the lognormal change of variables for all ensemble sizes. For a model that was designed to mimic the important characteristics of convective motion, preserving non-negativity of rain and conserving mass reduce the error in all fields; they prevent the data assimilation algorithm from producing artificial mass or artificial rain. Finally, important reduction in the computational costs has been recently achieved, making it possible to apply this algorithm in high dimensional weather forecasting problems in the future.<br />
<br />
=== Quanling Deng (UW) ===<br />
<br />
Spectral approximation of elliptic operators by softFEM, isogeometric analysis, and the hybrid high-order method<br />
<br />
Abstract: In this talk, I will first introduce the variational formulation for the numerical spectral approximation of the second-order elliptic operators, followed by the introduction of the particular methods: softFEM, isogeometric analysis (IGA), and the hybrid high-order (HHO) method. The main idea of softFEM is to reduce the stiffness of the variational problem by subtracting to the standard stiffness bilinear form a least-squares penalty on the gradient jumps across the mesh interfaces. I will discuss briefly the motivation and why one wants to soften the stiffness of the resulting systems arising from the classical FEM. I will present a sharp upper bound on the softness parameter weighting the stabilization bilinear form so as to maintain coercivity for the softFEM bilinear form and then prove that softFEM delivers the optimal convergence rates as the standard Galerkin FEM approximation for the eigenvalues and the eigenvectors. The main idea of IGA is to apply highly-smooth basis functions within the Galerkin FEM framework. For this method, I will present dispersion analysis and develop analytical eigenpairs for the resulting generalized matrix eigenvalue problems. Lastly, the HHO method is formulated using cell and face unknowns which are polynomials of some degree. The key idea for the discrete eigenvalue problem is to introduce a discrete operator where the face unknowns have been eliminated. Using the abstract theory of spectral approximation of compact operators in Hilbert spaces, we prove that the eigenvalues converge as $h^{2t}$ and the eigenfunctions as $h^{t}$ in the $H^1$-seminorm, where $h$ is the mesh-size, $t\in [s,k+1]$ depends on the smoothness of the eigenfunctions, and $s>\frac12$ results from the elliptic regularity theory. The convergence rates for smooth eigenfunctions are thus $h^{2k+2}$ for the eigenvalues and $h^{k+1}$ for the eigenfunctions. The first two methods are continuous Galerkin (CG) methods while the third one is a discontinuous Galerkin (DG) method. I will make comparisons by showing some numerical examples.</div>Jeanluchttps://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2021/AbstractsNTSGrad Spring 2021/Abstracts2021-01-18T05:49:46Z<p>Yfu68: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Spring 2021 semester. To go back to the main GNTS page, click [[NTSGrad_Spring_2021|here.]]<br />
<br />
<br />
== Jan 26 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Eiki Norizuki'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''$p$-adic groups and their representations''<br />
|-<br />
| bgcolor="#BCD2EE" | This will be a prep talk for Thursday's NTS talk.<br />
We will talk about subgroups and decompositions of $p$-adic groups as well as the Bruhat-Tits tree of $\text{SL}_2$.<br />
We try to understand the right class of representations for $p$-adic groups which turn out to be smooth admissible representations.<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 2 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Supersingular locus of Unitary Shimura variety''<br />
|-<br />
| bgcolor="#BCD2EE" |I will give a summary of supersingular locus of Unitary Shimura variety. This description is really the first and an important step to understand the structure of Unitary Shimura variety. Turns out that the description of such locus will boil down to certain linear algebra. The final result will be the supersingular locus have a stratification, and the incidence relation will be closely related with the Bruhat-Tits building of unitary group. Also, each strata is closely related with affine Deligne Lustig variety. The Dieudonne module theory will be summarized. Take it for granted, all the remaining material can follow easily!<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 9 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ivan Aidun'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Simple Sieving''<br />
|-<br />
| bgcolor="#BCD2EE" |The idea of sieving out primes is among the oldest in mathematics. However, it has proven incredibly fruitful, and now sieve techniques lie behind some of the most striking results in modern number theory, such as the results of Zhang, Maynard, and the Polymath project on bounded gaps between primes. In this talk, I will develop some of the basic sieve constructions, from Eratosthenes and Legendre to Brun, and hint at some of the developments that lie beyond. This talk will be accessible to a general mathematical audience.<br />
|} <br />
</center><br />
<br />
<br><br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 16 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Asvin G'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''F_un with F_1''<br />
|-<br />
| bgcolor="#BCD2EE" | You have probably heard of a field with one element in various places and might have been, very understandably, confused. How can there be a field with one element and even if there is, how could it possible be interesting? I will try and explain the philosophy behind why this is a reasonable thing to wish for and various mathematical facts that *should* be interpreted through this lens. <br />
<br />
The talk will just be a bunch of examples of the various manifestations of the field with one element throughout mathematics! <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Feb 23 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yu Fu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''CM liftings of Abelian Varieties''<br />
|-<br />
| bgcolor="#BCD2EE" | This will be a introductory talk to introduce the CM liftings of Abelian Varieties. <br />
Honda-Tate theory tells us every abelian variety over a finite field can be lifted to an abelian variety with smCM in characteristic 0. There are various lifting problems if you drop/change some of the conditions, i.e. Is it an isogeny or residue class field extension necessary? Can we lift any abelian variety over a finite field to a normal domain up to isogeny? Etc.etc.<br />
Let's explore with some fun examples!<br />
|} <br />
</center><br />
<br />
<br></div>Hkim832https://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2021NTSGrad Fall 20212021-01-18T05:45:57Z<p>Hkim832: /* Spring 2021 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' https://uwmadison.zoom.us/j/95552727189?pwd=ck1abCtPelJ2dVpDcDdoaVIzK25UQT09. Please contact one of the organizers for the password.<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
We are recording these talks and putting them as unlisted videos on Youtube. The links for these videos can be found in the following link: https://docs.google.com/document/d/1SHaiAI4ODPxIN8pm96naFjqUHyDsr0S6JS0SKWqaK1I/edit.<br />
Note that this link is available to members of the seminar only.<br />
<br />
= Spring 2021 Semester: Schedule =<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="#D0D0D0" width="300" align="center"|Jan 26th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Eiki Norizuki<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring_2021/Abstracts#Jan_26|$p$-adic groups and their representations]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 2nd<br />
| bgcolor="#F0A0A0" width="300" align="center"|Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring_2021/Abstracts#Feb_2|Supersingular locus of Unitary Shimura variety]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 9th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ivan Aidun<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring_2021/Abstracts#Feb_9|Simple Sieving]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 16th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring_2021/Abstracts#Feb_16|F_un with F_1]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 23rd<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring_2021/Abstracts#Feb_23|CM liftings of Abelian Varieties]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 2nd<br />
| bgcolor="#F0A0A0" width="300" align="center"|Will Hardt<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring_2021/Abstracts#Mar_2]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 9th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring_2021/Abstracts#Mar_9]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 16th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring_2021/Abstracts#Mar_16]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 23th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Dionel Jaime<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring_2021/Abstracts#Mar_23]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 30th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ruofan Jiang<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring_2021/Abstracts#Mar_30]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|April 6th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Jiaqi Hou<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring_2021/Abstracts#Apr_6]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|April 13th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yunus Tuncbilek<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring_2021/Abstracts#Apr_13]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|April 20th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring_2021/Abstracts#Apr_20]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|April 27th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring_2021/Abstracts#Apr_27]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|May 4th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring_2021/Abstracts#May_4]]<br />
|-<br />
<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Yu Fu (yfu68@wisc.edu)<br />
<br />
Hyun Jong Kim[https://sites.google.com/wisc.edu/hyunjongkim] (hyunjong.kim@math.wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Boggess<br />
<br />
Soumya Sankar<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Fall 2020 is [[NTSGrad_Fall_2020|here]].<br><br />
The seminar webpage for Spring 2020 is [[NTSGrad_Spring_2020|here]].<br><br />
The seminar webpage for Fall 2019 is [[NTSGrad_Fall_2019|here]].<br><br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Hkim832https://www.math.wisc.edu/wiki/index.php/Algebra_and_Algebraic_Geometry_Seminar_Spring_2021Algebra and Algebraic Geometry Seminar Spring 20212021-01-17T00:10:59Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://www.math.wisc.edu/wiki/index.php/Toric_Varieties_Fan_ClubToric Varieties Fan Club2021-01-16T23:50:46Z<p>Asobieska: </p>
<hr />
<div>This is the page for the Spring 2021 Toric Varieties Fan Club (Reading Group), which is open to all UW Math grad students, but will require a certain amount of participation and work to receive course credit (details below).<br />
<br />
== Resources ==<br />
<br />
We plan to read Cox, Little, and Schenck's ''Toric Varieties'', which can be downloaded here: [https://b-ok.cc/book/1054810/568761].<br />
<br />
== Meeting Schedule ==<br />
<br />
14 weeks total, starting on January 25, adjusting throughout the semester as necessary.<br />
<br />
Meetings will be on Mondays and Wednesdays at 1-2:30pm, where the first hour is devoted to reviewing the assigned reading (about 10 pages), led by a designated speaker, and the half-hour is used to collaborate on exercises. Meetings will be held virtually using this link: [https://uwmadison.zoom.us/j/94806372074].<br />
<br />
<br />
'''Optimistic Reading Schedule:'''<br />
<br />
'''Week 1'''<br />
<br />
Monday, January 25: Ch. 1.0 Affine Varieties Background (Speaker: Ola Sobieska)<br />
<br />
Wednesday, January 27: Ch. 1.1 Introduction to Affine Toric Varieties (Speaker: Ola Sobieska)<br />
<br />
<br />
'''Week 2'''<br />
<br />
Monday, February 1: Ch. 1.2 Cones and Affine Toric Varieties (Speaker: Ivan Aidun)<br />
<br />
Wednesday, February 3: Ch. 1.3 Properties of Affine Toric Varieties (Speaker: Ola Sobieska)<br />
<br />
<br />
'''Week 3'''<br />
<br />
Monday, February 8: Ch. 2.1 Lattice Points and Projective Toric Varieties (Speaker: Zinan Wang)<br />
<br />
Wednesday, February 10: Ch. 2.2 Lattice Points and Polytopes (Speaker: Maya Banks)<br />
<br />
<br />
'''Week 4'''<br />
<br />
Monday, February 15: Ch. 2.3 Polytopes and Projective Toric Varieties (Speaker: Will Hardt)<br />
<br />
Wednesday, February 17: Ch. 2.4 Properties of Projective Toric Varieties (Speaker: Ivan Aidun)<br />
<br />
<br />
'''Week 5'''<br />
<br />
Monday, February 22: Catch-up/Review Day<br />
<br />
Wednesday, February 24: Ch. 3.1 Fans and Normal Toric Varieties (Speaker: Caitlyn Booms)<br />
<br />
<br />
'''Week 6'''<br />
<br />
Monday, March 1: Ch. 3.2 The Orbit-Cone Correspondence (Speaker: Zinan Wang)<br />
<br />
Wednesday, March 3: Ch. 3.3 Toric Morphisms (Speaker: Ola Sobieska)<br />
<br />
<br />
'''Week 7'''<br />
<br />
Monday, March 8: Ch. 3.4 Complete and Proper (Speaker: TBD)<br />
<br />
Wednesday, March 10: Catch-up/Review Day<br />
<br />
<br />
'''Week 8'''<br />
<br />
Monday, March 15: Ch. 4.0 Valuations, Divisors, and Sheaves Background (Speaker: Will Hardt)<br />
<br />
Wednesday, March 17: Ch. 4.1 Weil Divisors on Toric Varieties (Speaker: Maya Banks)<br />
<br />
<br />
'''Week 9'''<br />
<br />
Monday, March 22: Ch. 4.2 Cartier Divisors on Toric Varieties (Speaker: TBD)<br />
<br />
Wednesday, March 24: Ch. 4.3 The Sheaf of a Torus-Invariant Divisor (Speaker: TBD)<br />
<br />
<br />
'''Week 10'''<br />
<br />
Monday, March 29: Ch. 5.0 Quotients in Algebraic Geometry Background (Speaker: TBD)<br />
<br />
Wednesday, March 31: Ch. 5.1 Quotient Constructions of Toric Varieties (Speaker: Caitlyn Booms)<br />
<br />
<br />
'''Week 11'''<br />
<br />
Monday, April 5: Ch. 5.2 The Total Coordinate Ring (Speaker: TBD)<br />
<br />
Wednesday, April 7: Ch. 5.3 Sheaves on Toric Varieties (Speaker: TBD)<br />
<br />
<br />
'''Week 12'''<br />
<br />
Monday, April 12: Ch. 5.4 Homogenization and Polytopes (Speaker: TBD)<br />
<br />
Wednesday, April 14: Ch. 6.0 Sheaves and Line Bundles Background (Speaker: Caitlyn Booms)<br />
<br />
<br />
'''Week 13'''<br />
<br />
Monday, April 19: Ch. 6.1 Ample and Basepoint Free Divisors on Complete Toric Varieties (Speaker: TBD)<br />
<br />
Wednesday, April 21: Ch. 6.2 Polytopes and Projective Toric Varieties (Speaker: TBD)<br />
<br />
<br />
'''Week 14'''<br />
<br />
Monday, April 26: Ch. 6.3 The Nef and Mori Cones (Speaker: TBD)<br />
<br />
Wednesday, April 28: Ch. 6.4 The Simplicial Case (Speaker: TBD)<br />
<br />
== General Meeting Structure ==<br />
<br />
This reading group will be structured as follows. Every meeting will have an assigned speaker, who will usually be one of the reading group participants, but could at times be a professor or other guest speaker. It will be expected that everyone attending will read the assigned sections prior to the meeting. The speaker is expected to additionally work out some examples prior and will be responsible for lecturing on the reading material and guiding the group discussion during the meeting. The schedule will be adjusted throughout the semester. Daniel Erman will be our faculty advisor, and in order to receive credit (up to 3 credits), participants will be expected to attend all meetings, be the speaker twice, and do several exercises. We may also use Macaulay2 during the exercise portions to get comfortable both computing examples by hand and by using a computer.<br />
<br />
'''If you are interested in joining this reading group or have any questions, please contact Caitlyn Booms at cbooms@wisc.edu or Aleksandra (Ola) Sobieska at asobieska@wisc.edu by January 24, 2021.'''</div>Cboomshttps://www.math.wisc.edu/wiki/index.php/Applied/ACMS/Fall2020Applied/ACMS/Fall20202021-01-14T21:24:18Z<p>Jeanluc: Created page with "== Fall 2020 == {| cellpadding="8" !align="left" | date !align="left" | speaker !align="left" | title !align="left" | host(s) |- | Sep 11 |[https://cee.stanford.edu/people..."</p>
<hr />
<div>== Fall 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| Sep 11<br />
|[https://cee.stanford.edu/people/nicholas-ouellette Nick Ouellette (Stanford)]<br />
|''[[Applied/ACMS/absF20#Nick Ouellette (Stanford)|Tensor Geometry in the Turbulent Cascade]]''<br />
|Jean-Luc<br />
|-<br />
| Sep 18<br />
|[https://www.researchgate.net/profile/Harry_Lee24 Harry Lee (UW-Madison and UMich)]<br />
|''[[Applied/ACMS/absF20#Harry Lee (UW-Madison, UMich)|Recent extension of V.I. Arnold's and J.L. Synge's mathematical theory of shear flows]]''<br />
|Wally<br />
|-<br />
| Sep 25<br />
|[https://www.mtholyoke.edu/people/spencer-smith Spencer Smith (Mount Holyoke)]<br />
|''[[Applied/ACMS/absF20#Spencer Smith (Mount Holyoke)|Braids on a lattice and maximally efficient mixing in active matter systems]]''<br />
|Jean-Luc<br />
|-<br />
| Oct 2<br />
|[https://zhizhenz.ece.illinois.edu/ Zhizhen Jane Zhao] (UIUC)<br />
|''[[Applied/ACMS/absF20#Zhizhen Jane Zhao (UIUC)|Exploiting Group and Geometric Structures for Massive Data Analysis]]''<br />
| Li & Chen<br />
|<br />
|<br />
|-<br />
| Oct 9<br />
|[https://igppweb.ucsd.edu/~mmorzfeld/ Matthias Morzfeld] (Scripps & UCSD)<br />
|''[[Applied/ACMS/absF20#Matthias Morzfeld (Scripps & UCSD)|What is Bayesian inference, why is it useful in Earth science and why is it challenging to do numerically?]]''<br />
| Chen<br />
|<br />
|<br />
|-<br />
| Oct 16<br />
|[https://jingweihu-math.github.io/webpage/ Jingwei Hu] (Purdue)<br />
|''[[Applied/ACMS/absF20#Jingwei Hu (Purdue)|A new stability and convergence proof of the Fourier-Galerkin spectral method for the spatially homogeneous Boltzmann equation]]''<br />
| Li<br />
|<br />
|-<br />
| Oct 23<br />
|[https://www.aos.wisc.edu/~dvimont/Home.html Dan Vimont] (UW-Madison, AOS)<br />
|''[[Applied/ACMS/absF20#Dan Vimont (UW-Madison, AOS)|Advances in Linear Inverse Modeling for Understanding Tropical Pacific Climate Variability]]''<br />
| Stechmann<br />
|<br />
|-<br />
| Oct 30<br />
|[http://www.dam.brown.edu/people/spsmith/ Sam Punshon-Smith] (Brown)<br />
|''[[Applied/ACMS/absF20#Sam Punshon-Smith (Brown)|Scalar mixing and the Batchelor spectrum in stochastic fluid mechanics]]''<br />
| Li<br />
|<br />
|-<br />
| Nov 6<br />
|[https://www.math.uci.edu/people/yimin-zhong Yimin Zhong] (UCI, Duke)<br />
|''[[Applied/ACMS/absF20#Yimin Zhong (UCI and Duke)|Quantitative PhotoAcoustic Tomography (PAT) with simplified PN approximation]]''<br />
|Li<br />
|<br />
|-<br />
| Nov 13<br />
|'''1:30pm''' [https://www.cmu.edu/biolphys/deserno/ Markus Deserno] (Carnegie Mellon)<br />
|''[[Applied/ACMS/absF20#Markus Deserno (Carnegie Mellon)|Spontaneous curvature, differential stress, and bending modulus of asymmetric lipid membranes]]''<br />
(Virtual, link to recording [https://www.math.wisc.edu/~appliedmathlab/Seminars/ACMS_111320_Deserno.mp4 here])<br />
|Spagnolie<br />
|-<br />
| Nov 20<br />
|[https://www.usna.edu/Users/math/lunasin/index.php/ Evelyn Lunasin] (USNA)<br />
|''[[Applied/ACMS/absF20#Evelyn Lunasin (USNA)|Finite Number of Determining Parameters for the 1D Kuramoto-Sivashinsky equation with Applications to Feedback Control and Data Assimilations]]''<br />
|Jean-Luc & Chen<br />
|-<br />
| Nov 27<br />
|''Thangksgiving recess''<br />
|<br />
|<br />
|-<br />
| Dec 4<br />
||[https://www.math.arizona.edu/people/chertkov Michael Chertkov] (U. Arizona)<br />
|''[[Applied/ACMS/absF20#Michael Chertkov (U Arizona)|Harvesting Data and Model Revolution in Natural and Engineering Sciences]]''<br />
|Zepeda-Nunez<br />
|<br />
|<br />
|-<br />
|}</div>Jeanluchttps://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021NTS ABSTRACTSpring20212021-01-12T01:23:23Z<p>Ellenber: /* Mar 11 */</p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS Main Page]<br />
<br />
<br />
== Jan 28 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Monica Nevins'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Interpreting the local character expansion of p-adic SL(2)<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Harish-Chandra—Howe local character expansion expresses the character of an admissible representation of a p-adic group G as a linear combination with complex coefficients of the (finitely many!) Fourier transforms of nilpotent orbital integrals \(\widehat{\mu}_{\mathcal{O}}\) --- near the identity. Approaching from another direction: we can restrict the representation to any compact open subgroup K of G, obtaining its branching rules, which also describe the representation near the identity, in a different sense. <br />
We show that for G=SL(2,k), k a nonarchimedean local field, where the branching rules to maximal compact open subgroups K are known, each of these terms \(\widehat{\mu}_{\mathcal{O}}\) can be interpreted as the character \(\tau_{\mathcal{O}}\) of a representation of K, up to an error term arising from the zero orbit. Moreover, the irreducible components of \(\tau_{\mathcal{O}}\) are explicitly constructed from the K -orbits in \(\mathcal{O}\). This work in progress offers a conjectural alternative interpretation of branching rules of admissible representations. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 4 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ke Chen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On CM points away from the Torelli locus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Coleman conjectured in 1980's that when g is an integer sufficiently large, the open Torelli locus T_g in the Siegel modular variety A_g should contain at most finitely many CM points, namely Jacobians of ''general'' curves of high genus should not admit complex multiplication. We show that certain CM points do not lie in T_g if they parametrize abelian varieties isogeneous to products of simple CM abelian varieties of low dimension. The proof relies on known results on Faltings height and Sato-Tate equidistributions. This is a joint work with Kang Zuo and Xin Lv.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Feb 11 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Dmitry Gourevitch'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Relations between Fourier coefficients of automorphic forms, with applications to vanishing and to Eulerianity<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In recent works with H. P. A. Gustafsson, A. Kleinschmidt, D. Persson, and<br />
S. Sahi, we found a way to express any automorphic form through its Fourier coefficients, using adelic integrals, period integrals and discrete summation – generalizing the Piatetski-Shapiro – Shalika decomposition for GL(n).<br />
I will explain the general idea behind our formulas, and illustrate it on examples.<br />
I will also show applications to vanishing and Eulerianity of Fourier coefficients.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Feb 18 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Eyal Kaplan'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The generalized doubling method, multiplicity one and the application to global functoriality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
One of the fundamental difficulties in the Langlands program is to handle the non-generic case.<br />
The doubling method, developed by Piatetski-Shapiro and Rallis in the 80s, pioneered the study of L-functions<br />
for cuspidal non-generic automorphic representations of classical groups. Recently, this method has been generalized<br />
in several aspects with interesting applications. In this talk I will survey the different components of the <br />
generalized doubling method, describe the fundamental multiplicity one result obtained recently in a joint <br />
work with Aizenbud and Gourevitch, and outline the application to global functoriality.<br />
Parts of the talk are also based on a collaboration with Cai, Friedberg and Ginzburg.<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Feb 25 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Roger Van Peski'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Random matrices, random groups, singular values, and symmetric functions<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Since the 1989 work of Friedman-Washington, the cokernels of random p-adic matrices drawn from various distributions have provided models for random finite abelian p-groups arising in number theory and combinatorics, the most famous being the class groups of quadratic imaginary number fields. Since any finite abelian p-group is isomorphic to a direct sum of cyclic groups $\bigoplus_i \mathbb{Z}/p^{\lambda_i}\mathbb{Z}$, it is equivalent to study the random integer partition $\lambda = (\lambda_1, \lambda_2,\ldots)$, which is analogous to the singular values of a complex random matrix. We show that the behavior of such partitions under taking products and corners of random p-adic matrices is governed by the Hall-Littlewood polynomials, recovering and explaining some previous results relating p-adic matrix cokernels to these polynomials. We use these exact results to study the joint asymptotic behavior of the cokernels of products of many random p-adic matrices $A_\tau \cdots A_1$, with $\tau$ acting as a discrete time parameter. We show that the parts $\lambda_i$ of the corresponding partition have a simple description via an interacting particle system, and their fluctuations converge under rescaling to independent Brownian motions. At both the exact and asymptotic level we explain connections between our results and existing results on singular values of complex random matrices: both are in fact degenerations of the same operations on random partitions coming from Macdonald polynomials.<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Mar 4 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Amos Nevo'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Intrinsic Diophantine approximation on homogeneous algebraic varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Classical Diophantine approximation quantifies the denseness of the set of rational vectors in their ambient Euclidean space. A far-reaching extension of the classical theory calls for quantifying the denseness of rational points in general homogeneous algebraic varieties. This was raised as an open problem by Serge Lang already half a century ago, but progress towards it was achieved only in a limited number of special cases. A systematic approach to this problem for homogeneous varieties associated with semi-simple groups has been developed in recent years, in joint work with A. Ghosh and A. Gorodnik. The methods employ dynamical arguments and effective ergodic theory, and employ spectral estimates in the automorphic representation of semi-simple groups. In the case of homogeneous spaces with semi-simple stability group, this approach leads to the derivation of pointwise uniform and almost sure Diophantine exponents, as well as analogs of Khinchin's and W. Schmidt's theorems, with some of the results being best possible. We will explain some of the main results and some of the ingredients in their proof, focusing on some easily accessible examples.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Mar 11 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Carlo Pagano'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On the negative Pell conjecture<br />
|-<br />
| bgcolor="#BCD2EE" | The negative Pell equation has been studied since many centuries. Euler already provided an interesting criterion in terms of continued fractions. In 1995 Peter Stevenhagen proposed a conjecture for the frequency of the solvability of this equation, when one varies the real quadratic field. I will discuss an upcoming joint work with Peter Koymans where we establish Stevenhagen's conjecture. <br />
|} <br />
</center><br />
<br />
<br></div>Shihttps://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2020NTS Fall Semester 20202021-01-12T01:13:29Z<p>Shi: /* Spring 2020 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
Back to the number theory seminar main webpage: [https://www.math.wisc.edu/wiki/index.php/NTS Main page]<br />
<br />
<br />
= Fall 2020 Semester =<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" | Sep 3 (9：00 am)<br />
| bgcolor="#F0B0B0" align="center" | Yifeng Liu<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Sep_3 Beilinson-Bloch conjecture and arithmetic inner product formula]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 10<br />
| bgcolor="#F0B0B0" align="center" | Yufei Zhao<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Sep_10 The joints problem for varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 17<br />
| bgcolor="#F0B0B0" align="center" | Ziquan Yang<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Sep_17 A Crystalline Torelli Theorem for Supersingular K3^&#91;n&#93;-type Varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 24<br />
| bgcolor="#F0B0B0" align="center" | Yousheng Shi<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Sep_24 Kudla Rapoport conjecture over the ramified primes]<br />
|- <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 1<br />
| bgcolor="#F0B0B0" align="center" | Liyang Yang<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Oct_1 Average Central L-values on U(2,1)$\times$ U(1,1), Nonvanishing and Subconvexity]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 7 (Wed. at 7pm)<br />
| bgcolor="#F0B0B0" align="center" | Shamgar Gurevich (UW - Madison)<br />
| bgcolor="#BCE2FE"|Harmonic Analysis on GLn over Finite Fields <br />
(Register at https://uni-sydney.zoom.us/meeting/register/tJAocOGhqjwiE91DEddxUhCudfQX5mzp-cPQ)<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 15<br />
| bgcolor="#F0B0B0" align="center" | [http://people.math.harvard.edu/~yujiex/ Yujie Xu] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Oct_15 On normalization in the integral models of Shimura varieties of Hodge type]<br />
(Register at https://harvard.zoom.us/meeting/register/tJYlduqrrDgqGNRmtfw245PNXp_XGCzMlkYm)<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 22<br />
| bgcolor="#F0B0B0" align="center" | Artane Siad <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Oct_22 Average 2-torsion in the class group of monogenic fields]<br />
<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 29<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/view/guillermo-mantilla-soler Guillermo Mantilla-Soler]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Oct_29 A complete invariant for real S_n number fields]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 5(11 AM)<br />
| bgcolor="#F0B0B0" align="center" | Anup Dixit<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Nov_5 On generalized Brauer-Siegel conjecture and Euler-Kronecker constants]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 12<br />
| bgcolor="#F0B0B0" align="center" | Si Ying Lee<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Nov_12 Eichler-Shimura relations for Hodge type Shimura varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 19<br />
| bgcolor="#F0B0B0" align="center" | Chao Li <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Nov_19 On the Kudla-Rapoport conjecture]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 26<br />
| bgcolor="#F0B0B0" align="center" | Thanksgiving (no seminar)<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 3<br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Dec_3 Singular modular forms on quaternionic E_8]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 10 (9:00 AM)<br />
| bgcolor="#F0B0B0" align="center" | Daxin Xu<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Dec_10 Bessel F-isocrystals for reductive groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 17<br />
| bgcolor="#F0B0B0" align="center" | Qirui Li<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Dec_17 Biquadratic Guo-Jacquet Fundamental Lemma and its arithmetic generalizations]<br />
|- <br />
|}<br />
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*to be confirmed</div>Shihttps://www.math.wisc.edu/wiki/index.php/Colloquia/Fall2020Colloquia/Fall20202020-12-15T02:55:15Z<p>Vadicgor: Created page with "__NOTOC__ <b>UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b> <!--- in Van Vleck B239, '''unless otherwise indicated'''. ---> =Fall 2020= == Septem..."</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2020=<br />
<br />
== September 25, 2020, [https://www.math.tamu.edu/~jml/ Joseph Landsberg] (Texas A&M) ==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
'''From theoretic computer science to algebraic geometry: how the complexity of matrix multiplication led me to the Hilbert scheme of points.'''<br />
<br />
In 1968 Strassen discovered the way we multiply nxn matrices<br />
(row/column)<br />
is not the most efficient algorithm possible. Subsequent work has led to<br />
the astounding conjecture that as the size n of the matrices grows, it<br />
becomes<br />
almost as easy to multiply matrices as it is to add them. I will give a<br />
history<br />
of this problem and explain why it is natural to study it using<br />
algebraic geometry<br />
and representation theory. I will conclude by discussing recent exciting<br />
developments<br />
that explain the second phrase in the title.<br />
<br />
== October 9, 2020, [https://impa.br/en_US/page-pessoas/carolina-araujo/ Carolina Araujo] (IMPA) ==<br />
<br />
(Hosted by Ellenberg)<br />
<br />
'''Symmetries in Algebraic Geometry and Cremona transformations'''<br />
<br />
In this talk I will discuss symmetries of complex algebraic varieties. When studying a projective variety $X$, one usually wants to understand its symmetries. Conversely, the structure of the group of automorphisms of $X$ encodes relevant geometric properties of $X$. After describing some examples of automorphism groups of projective varieties, I will discuss why the notion of automorphism is too rigid in the scope of birational geometry. We are then led to consider another class of symmetries of $X$, its birational self-maps. Birational self-maps of the projective space $\mathbb{P}^n$ are called Cremona transformations. Describing the structure of the group of Cremona transformations of the plane is a classical problem that goes back to the 19th century. In higher dimensions, not so much is known, and a natural problem is to construct interesting subgroups of the Cremona group. I will end by discussing a recent work with Alessio Corti and Alex Massarenti, where we investigate subgroups of the Cremona group consisting of symmetries preserving some special meromorphic volume forms.<br />
<br />
== October 23, 2020, [http://www.math.toronto.edu/quastel/ Jeremy Quastel] (University of Toronto) ==<br />
<br />
(Hosted by Gorin)<br />
<br />
'''Towards KPZ Universality'''<br />
<br />
The 1-d KPZ universality class contains random interface growth models<br />
as well as random polymer free energies and driven diffusive systems. <br />
The KPZ fixed point has now been determined, through the exact solution of a special model<br />
in the class, TASEP, and is expected to describe the asymptotic fluctuations for all models in the class.<br />
It is an integrable Markov process, with transition probabilities described by a system of integrable PDE’s. <br />
Very recently, new techniques have become available to prove <br />
the convergence of the KPZ equation itself, as well as some non-integrable extensions<br />
of TASEP, to the KPZ fixed point. This talk will be a gentle introduction to these developments<br />
with no prior knowledge assumed. The results are, variously, joint works with <br />
Daniel Remenik, Konstantin Matetski, and Sourav Sarkar.<br />
<br />
== November 6, 2020, [http://math.jhu.edu/~sakellar/ Yiannis Sakellaridis] (Johns Hopkins University)==<br />
<br />
(Hosted by Gurevitch)<br />
<br />
'''Harmonic analysis, intersection cohomology, and L-functions.'''<br />
<br />
The goal of this lecture will be to describe a link between geometric-topological objects (certain intersection complexes on singular loop spaces), and objects of arithmetic interest (L-functions). The link between the two is by a Fourier/spectral transform. I will begin by giving an overview of Iwasawa–Tate theory, which expresses the Riemann zeta function as the Mellin transform of a certain theta series, and will conclude by describing joint work with Jonathan Wang (MIT), which expresses other L-functions as spectral transforms of functions obtained from intersection complexes on singular arc spaces. No prior familiarity with notions such as L-functions or intersection cohomology will be assumed.<br />
<br />
== November 20, 2020, [https://web.ma.utexas.edu/users/ntran/ Ngoc Mai Tran] (University of Texas) ==<br />
<br />
(Hosted by Rodriguez)<br />
<br />
'''Does your problem have a tropical solution?'''<br />
<br />
Tropical mathematics is mathematics done in the min-plus (or max-plus) algebra.<br />
The power of tropical mathematics comes from two key ideas: (a) tropical objects are limits of classical ones, and (b) the geometry of tropical objects is polyhedral. In this talk I'll demonstrate how these two ideas are used to solve a variety of problems in different domains the last 10 years, from deep neural networks, semigroups theory, auction theory and extreme value statistics.<br />
<br />
== December 4, 2020, [http://math.sfsu.edu/federico/ Federico Ardila] (San Francisco) ==<br />
<br />
(Hosted by Ellenberg)<br />
<br />
'''Measuring polytopes through their algebraic structure.'''<br />
<br />
Generalized permutahedra are a beautiful family of polytopes with a rich combinatorial structure, and strong connections to optimization and algebraic geometry. We prove they are the universal family of polyhedra with a certain Hopf-algebraic structure. This Hopf-algebraic structure is compatible with McMullen’s foundational work on the polytope algebra.<br />
<br />
Our construction provides a unifying framework to organize and study many combinatorial families; for example:<br />
<br />
1. It uniformly answers open questions and recovers known results about graphs, posets, matroids, hypergraphs, simplicial complexes, and others.<br />
<br />
2. It shows that permutahedra and associahedra “know" how to compute the multiplicative and compositional inverses of power series.<br />
<br />
3. It explains the mysterious fact that many combinatorial invariants of matroids, posets, and graphs can also be thought of as measures on polytopes, satisfying the inclusion-exclusion relations.<br />
<br />
This is joint work with Marcelo Aguiar (2017) and Mario Sanchez (2020).</div>Vadicgorhttps://www.math.wisc.edu/wiki/index.php/Past_Probability_Seminars_Fall_2020Past Probability Seminars Fall 20202020-12-15T01:40:01Z<p>Vadicgor: Created page with "__NOTOC__ = Fall 2020 = <b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted. <b>We usually end for questions at 3:20 PM.</b> <b> IMPORTANT: </b> In..."</p>
<hr />
<div>__NOTOC__<br />
<br />
= Fall 2020 =<br />
<br />
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted. <br />
<b>We usually end for questions at 3:20 PM.</b><br />
<br />
<b> IMPORTANT: </b> In Fall 2020 the seminar is being run online. [https://uwmadison.zoom.us/j/91828707031?pwd=YUJXMUJkMDlPR0VRdkRCQVJtVndIdz09 ZOOM LINK]<br />
<br />
If you would like to sign up for the email list to receive seminar announcements then please join [https://groups.google.com/a/g-groups.wisc.edu/forum/#!forum/probsem our group].<br />
<br />
== September 17, 2020, [https://www.math.tamu.edu/~bhanin/ Boris Hanin] (Princeton and Texas A&M) ==<br />
<br />
'''Pre-Talk: (1:00pm)'''<br />
<br />
'''Neural Networks for Probabilists''' <br />
<br />
Deep neural networks are a centerpiece in modern machine learning. They are also fascinating probabilistic models, about which much remains unclear. In this pre-talk I will define neural networks, explain how they are used in practice, and give a survey of the big theoretical questions they have raised. If time permits, I will also explain how neural networks are related to a variety of classical areas in probability and mathematical physics, including random matrix theory, optimal transport, and combinatorics of hyperplane arrangements.<br />
<br />
'''Talk: (2:30pm)'''<br />
<br />
'''Effective Theory of Deep Neural Networks''' <br />
<br />
Deep neural networks are often considered to be complicated "black boxes," for which a full systematic analysis is not only out of reach but also impossible. In this talk, which is based on ongoing joint work with Sho Yaida and Daniel Adam Roberts, I will make the opposite claim. Namely, that deep neural networks with random weights and biases are exactly solvable models. Our approach applies to networks at finite width n and large depth L, the regime in which they are used in practice. A key point will be the emergence of a notion of "criticality," which involves a finetuning of model parameters (weight and bias variances). At criticality, neural networks are particularly well-behaved but still exhibit a tension between large values for n and L, with large values of n tending to make neural networks more like Gaussian processes and large values of L amplifying higher cumulants. Our analysis at initialization has many consequences also for networks during after training, which I will discuss if time permits.<br />
<br />
== September 24, 2020, [https://people.ucd.ie/neil.oconnell Neil O'Connell] (Dublin) ==<br />
<br />
'''Some new perspectives on moments of random matrices'''<br />
<br />
The study of `moments' of random matrices (expectations of traces of powers of the matrix) is a rich and interesting subject, with fascinating connections to enumerative geometry, as discovered by Harer and Zagier in the 1980’s. I will give some background on this and then describe some recent work which offers some new perspectives (and new results). This talk is based on joint work with Fabio Deelan Cunden, Francesco Mezzadri and Nick Simm.<br />
<br />
== October 1, 2020, [https://marcusmichelen.org/ Marcus Michelen] (UIC) ==<br />
<br />
'''Roots of random polynomials near the unit circle'''<br />
<br />
It is a well-known (but perhaps surprising) fact that a polynomial with independent random coefficients has most of its roots very close to the unit circle. Using a probabilistic perspective, we understand the behavior of roots of random polynomials exceptionally close to the unit circle and prove several limit theorems; these results resolve several conjectures of Shepp and Vanderbei. We will also discuss how our techniques provide a heuristic, probabilistic explanation for why random polynomials tend to have most roots near the unit circle. Based on joint work with Julian Sahasrabudhe.<br />
<br />
== October 8, 2020, [http://sites.harvard.edu/~sus977/index.html Subhabrata Sen] (Harvard) ==<br />
<br />
'''Large deviations for dense random graphs: beyond mean-field'''<br />
<br />
In a seminal paper, Chatterjee and Varadhan derived an Erdős-Rényi random graph, viewed as a random graphon. This directly provides LDPs for continuous functionals such as subgraph counts, spectral norms, etc. In contrast, very little is understood about this problem if the underlying random graph is inhomogeneous or constrained.<br />
<br />
In this talk, we will explore large deviations for dense random graphs, beyond the “mean-field” setting. In particular, we will study large deviations for uniform random graphs with given degrees, and a family of dense block model<br />
random graphs. We will establish the LDP in each case, and identify the rate function. In the block model setting, we will use this LDP to study the upper tail problem for homomorphism densities of regular sub-graphs. Our results establish that this problem exhibits a symmetry/symmetry-breaking transition, similar to one observed for Erdős-Rényi random graphs.<br />
<br />
Based on joint works with Christian Borgs, Jennifer Chayes, Souvik Dhara, Julia Gaudio and Samantha Petti.<br />
<br />
== October 15, 2020, [https://math.cornell.edu/philippe-sosoe Philippe Sosoe] (Cornell) ==<br />
<br />
Title: '''Concentration in integrable polymer models'''<br />
<br />
I will discuss a general method, applicable to all known integrable stationary polymer models, to obtain nearly optimal bounds on the<br />
central moments of the partition function and the occupation lengths for each level of the polymer system. The method was developed<br />
for the O'Connell-Yor polymer, but was subsequently extended to discrete integrable polymers. As an application, we obtain<br />
localization of the OY polymer paths along a straight line on the scale O(n^{2/3+o(1)}). <br />
<br />
Joint work with Christian Noack.<br />
<br />
==October 22, 2020, [http://www.math.toronto.edu/balint/ Balint Virag] (Toronto) ==<br />
<br />
Title: '''The heat and the landscape'''<br />
<br />
Abstract: The directed landscape is the conjectured universal scaling limit of the<br />
most common random planar metrics. Examples are planar first passage<br />
percolation, directed last passage percolation, distances in percolation<br />
clusters, random polymer models, and exclusion processes. The limit laws of distances of objects are given by the KPZ fixed point.<br />
<br />
We show that the KPZ fixed point is characterized by the Baik Ben-Arous<br />
Peche statistics well-known from random matrix theory.<br />
<br />
This provides a general and elementary method for showing convergence to<br />
the KPZ fixed point. We apply this method to two models related to<br />
random heat flow: the O'Connell-Yor polymer and the KPZ equation.<br />
<br />
Note: there will be a follow-up talk with details about the proofs at 11am, Friday, October 23.<br />
<br />
==October 29, 2020, [https://www.math.wisc.edu/node/80 Yun Li] (UW-Madison) ==<br />
<br />
Title: '''Operator level hard-to-soft transition for β-ensembles'''<br />
<br />
Abstract: It was shown that the soft and hard edge scaling limits of β-ensembles can be characterized as the spectra of certain random Sturm-Liouville operators. By tuning the parameter of the hard edge process one can obtain the soft edge process as a scaling limit. In this talk, I will present the corresponding limit on the level of the operators. This talk is based on joint work with Laure Dumaz and Benedek Valkó.<br />
<br />
== November 5, 2020, [http://sayan.web.unc.edu/ Sayan Banerjee] (UNC at Chapel Hill) ==<br />
<br />
Title: '''Persistence and root detection algorithms in growing networks'''<br />
<br />
Abstract: Motivated by questions in Network Archaeology, we investigate statistics of dynamic networks<br />
that are ''persistent'', that is, they fixate almost surely after some random time as the network grows. We<br />
consider ''generalized attachment models'' of network growth where at each time $n$, an incoming vertex<br />
attaches itself to the network through $m_n$ edges attached one-by-one to existing vertices with probability<br />
proportional to an ''arbitrary function'' $f$ of their degree. We identify the class of attachment functions $f$ for<br />
which the ''maximal degree vertex'' persists and obtain asymptotics for its index when it does not. We also<br />
show that for tree networks, the ''centroid'' of the tree persists and use it to device polynomial time root<br />
finding algorithms and quantify their efficacy. Our methods rely on an interplay between dynamic<br />
random networks and their continuous time embeddings.<br />
<br />
This is joint work with Shankar Bhamidi.<br />
<br />
== November 12, 2020, [https://cims.nyu.edu/~ajd594/ Alexander Dunlap] (NYU Courant Institute) ==<br />
<br />
Title: '''A forward-backward SDE from the 2D nonlinear stochastic heat equation'''<br />
<br />
Abstract: I will discuss a two-dimensional stochastic heat equation in the weak noise regime with a nonlinear noise strength. I will explain how pointwise statistics of solutions to this equation, as the correlation length of the noise is taken to 0 but the noise is attenuated by a logarithmic factor, can be related to a forward-backward stochastic differential equation (FBSDE) depending on the nonlinearity. In the linear case, the FBSDE can be explicitly solved and we recover results of Caravenna, Sun, and Zygouras. Joint work with Yu Gu (CMU).<br />
<br />
== November 19, 2020, [https://statistics.wharton.upenn.edu/profile/dingjian/ Jian Ding] (University of Pennsylvania) ==<br />
<br />
Title: '''Correlation length of two-dimensional random field Ising model via greedy lattice animal'''<br />
<br />
Abstract: In this talk, I will discuss two-dimensional random field Ising model where the disorder is given by i.i.d. mean zero Gaussian variables with small variance. In particular, I will present a recent joint work with Mateo Wirth on (one notion of) the correlation length, which is the critical size of the box at which the influences to spin magnetization from the boundary conditions and from the random field are comparable. Our work draws a connection to the greedy lattice animal normalized by the boundary size.<br />
<br />
== December 3, 2020, [https://www.math.wisc.edu/people/faculty-directory Tatyana Shcherbina] (UW-Madison) ==<br />
<br />
Title: '''SUSY transfer matrix approach for the real symmetric 1d random band matrices '''<br />
<br />
Abstract: Random band matrices (RBM) are natural intermediate models to study <br />
eigenvalue statistics and quantum propagation in disordered systems, <br />
since they interpolate between mean-field type Wigner matrices and <br />
random Schrodinger operators. In particular, RBM can be used to model the <br />
Anderson metal-insulator phase transition. The conjecture states that the eigenvectors <br />
of $N\times N$ RBM are completely delocalized and the local spectral statistics governed <br />
by the Wigner-Dyson statistics for large bandwidth $W$ (i.e. the local behavior is <br />
the same as for Wigner matrices), and by Poisson statistics for a small $W$ <br />
(with exponentially localized eigenvectors). The transition is conjectured to <br />
be sharp and for RBM in one spatial dimension occurs around the critical <br />
value $W=\sqrt{N}$. Recently, we proved the universality of the correlation <br />
functions for the whole delocalized region $W\gg \sqrt{N}$ for a certain type <br />
of Hermitian Gaussian RBM. This result was obtained by <br />
application of the supersymmetric method (SUSY) combined with the transfer matrix approach. <br />
In this talk I am going to discuss how this technique can be adapted to the <br />
real symmetric case.<br />
<br />
== December 10, 2020, [https://www.ewbates.com/ Erik Bates] (UW-Madison) ==<br />
<br />
Title: '''Empirical measures, geodesic lengths, and a variational formula in first-passage percolation'''<br />
<br />
Abstract: We consider the standard first-passage percolation model on $\mathbb{Z}^d$, in which each edge is assigned an i.i.d. nonnegative weight, and the passage time between any two points is the smallest total weight of a nearest-neighbor path between them. Our primary interest is in the empirical measures of edge-weights observed along geodesics from $0$ to $n\mathbf{e}_1$. For various dense families of edge-weight distributions, we prove that these measures converge weakly to a deterministic limit as $n$ tends to infinity. The key tool is a new variational formula for the time constant. In this talk, I will derive this formula and discuss its implications for the convergence of both empirical measures and lengths of geodesics.<br />
<br />
<br />
[[Past Seminars]]</div>Vadicgor