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= Mathematics Colloquium =
= Mathematics Colloquium =


All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.


<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == -->
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].
 
== Fall 2018 ==


== Fall 2016  ==
 
{| cellpadding="8"
!align="left" | date 
!align="left" | speaker
!align="left" | title
!align="left" | host(s)
|-
|September 9
|
|[[#  |    ]]
|
|
|-
|September 16
|[http://www.math.cmu.edu/~ploh/ Po-Shen Loh] (CMU)
|Directed paths: from Ramsey to Pseudorandomness
|Ellenberg
|
|-
|September 23
| [http://www.math.wisc.edu/~craciun/ Gheorghe Craciun] (UW-Madison)
|Toric Differential Inclusions and a Proof of the Global Attractor Conjecture
| Street
|[[#  |    ]]
|-
|September 30
|[http://math.uga.edu/~magyar/ Akos Magyar]  (University of Georgia)
|Geometric Ramsey theory
| Cook
|
|-
|October 7
|
|[[# |    ]]
|
|
|-
|October 14
|  [https://www.math.lsu.edu/~llong/ Ling Long] (LSU)
|Hypergeometric functions over finite fields
| Yang
|
|-
|October 21
|'''No colloquium this week'''
|[[#  |    ]]
|
|
|-
|'''Tuesday, October 25, B139'''
|[http://users.math.yale.edu/users/steinerberger/ Stefan Steinerberger] (Yale)
|Three Miracles in Analysis
|Seeger
|
|-
|October 28
|  [http://order.ph.utexas.edu/people/Reichl.htm Linda Reichl] (UT Austin)
|TBA
|Minh-Binh Tran
|
|-
|'''Monday, October 31'''
|  [https://math.berkeley.edu/~kpmann/ Kathryn Mann] (Berkeley)
|Groups acting on the circle
|Smith
|
|-
|November 4
| [https://www.math.ucdavis.edu/~shkoller/ Steve Shkoller] (UC Davis)
|TBA
| Feldman
|
|-
|Monday, November 7 at 4:30 ([http://www.ams.org/meetings/lectures/maclaurin-lectures AMS Maclaurin lecture])
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (New Zealand Institute for Advanced Study)
|Siegel's problem on small volume lattices
| Marshall
|
|-
|November 11
|  Reserved for possible job talks
|[[# |    ]]
|
|
|-
|November 18
|  Reserved for possible job talks
|[[# |    ]]
|
|
|-
|November 25
|  '''Thanksgiving break'''
|[[# |    ]]
|
|
|-
|December 2
|  Reserved for possible job talks
|[[# |    ]]
|
|
|-
|December 9
|  Reserved for possible job talks
|[[# |    ]]
|
|}


== Spring 2017  ==
 
{| cellpadding="8"
{| cellpadding="8"
!align="left" | date   
!align="left" | date   
Line 127: Line 14:
!align="left" | host(s)
!align="left" | host(s)
|-
|-
|January 20
|Sep 12    '''Room 911'''
|Reserved for possible job talks 
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series
|[[#  |    ]]
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)|  Harry Potter's Cloak via Transformation Optics ]]
|
| Li
|
|
|-
|-
|January 27
|Sep 14    '''Room 911'''
|Reserved for possible job talks
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series
|[[# |   ]]
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth  ]]
|  
| Li
|
|
|-
|-
|February 3
|Sep 21    '''Room 911'''
|
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture
|[[# |    ]]
|[[#Sep 21: Andrew Stuart (Caltech) The Legacy of Rudolph Kalman  ]]
|
|
|-
|February 6 (Wasow lecture)
| Benoit Perthame (University of Paris VI)
|[[# TBATBA ]]  
| Jin
| Jin
|-
|February 10 (WIMAW lecture)
| Alina Chertock (NC State Univ.)
|[[# |  ]]
| WIMAW
|
|
|-
|-
|February 17
|Sep 28
|
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)
|[[#   |     ]]
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]
|  
| Thiffeault
|
|
|-
|-
|February 24
|Oct 5
|
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)
|[[#  |    ]]
|[[#Oct 5: Eyal Subag (Penn State)|  Symmetries of the hydrogen atom and algebraic families ]]
|  
| Gurevich
|
|
|-
|-
|March 3
|Oct 12
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)
| Arie Levit (Yale)
|[[# |   ]]
|[[# TBA| TBA  ]]
|Dymarz
| Gurevich
|
|
|-
|-
|Tuesday, March 7, 4PM (Distinguished Lecture)
|Oct 19
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University)  
Jeremy Teitelbaum (U Connecticut)
|[[#  |    ]]
|[[# TBA|  TBA ]]
|Smith
| Boston
|
|
|-
|-
|Wednesday, March 8, 2:25PM
|Oct 26
| [http://pages.iu.edu/~temam/  Roger Temam] (Indiana University)  
| Douglas Ulmer (Arizona)
|[[#  |    ]]
|[[# TBA|  TBA ]]
|Smith
| Yang
|
|
|-
|-
|March 10
|Nov 2
| '''No Colloquium'''
| Reserved for job talk
|[[# |   ]]
|[[# TBA| TBA  ]]
|
| hosting faculty
|
|
|-
|-
|March 17
|Nov 9
|
| Reserved for job talk
|
|[[# TBA|  TBA  ]]
|
| hosting faculty
|
|
|-
|-
|March 24
|Nov 16
| '''Spring Break'''
| Reserved for job talk
|[[# |   ]]
|[[# TBA| TBA  ]]
|
| hosting faculty
|
|
|-
|-
|Wednesday, March 29 (Wasow)
|Nov 30
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU)
| Reserved for job talk
|[[# TBA|   TBA]]
|[[# TBA| TBA ]]
|Tran
| hosting faculty
|
|
|-
|-
|March 31
|Dec 7
| '''No Colloquium'''
| Reserved for job talk
|[[# |    ]]
|[[# TBATBA  ]]
|
| hosting faculty
|
|-
|April 7
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]
|[[# |   ]]
|Erman
|
|-
|April 14
| Wilfrid Gangbo
|[[# |    ]]
|Feldman & Tran
|
|-
|April 21
|  [http://www.math.stonybrook.edu/~mde/ Mark Andrea de Cataldo]  (Stony Brook)
|TBA
| Maxim
|
|
|-
|April 28
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] 
|[[# TBA|  TBA  ]]
|Li
|}
|}


== Abstracts ==
== Abstracts ==
=== September 16: Po-Shen Loh (CMU) ===
Title: Directed paths: from Ramsey to Pseudorandomness


Abstract: Starting from an innocent Ramsey-theoretic question regarding directed
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===
paths in graphs, we discover a series of rich and surprising connections
Harry Potter's Cloak via Transformation Optics
that lead into the theory around a fundamental result in Combinatorics:
 
Szemeredi's Regularity Lemma, which roughly states that every graph (no
Can we make objects invisible? This has been a subject of human
matter how large) can be well-approximated by a bounded-complexity
fascination for millennia in Greek mythology, movies, science fiction,
pseudorandom object. Using these relationships, we prove that every
etc. including the legend of Perseus versus Medusa and the more recent
coloring of the edges of the transitive N-vertex tournament using three
Star Trek and Harry Potter. In the last fifteen years or so there have been
colors contains a directed path of length at least sqrt(N) e^{log^* N}
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion
which entirely avoids some color.  The unusual function log^* is the
one of them, the so-called "traansformation optics"
inverse function of the tower function (iterated exponentiation).
in a non-technical fashion n the so-called that has received the most attention in the
scientific literature.
 
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===
Journey to the Center of the Earth


=== September 23: Gheorghe Craciun (UW-Madison) ===
We will consider the inverse problem of determining the sound
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture
speed or index of refraction of a medium by measuring the travel times of
waves going through the medium. This problem arises in global seismology
in an attempt to determine the inner structure of the Earth by measuring
travel times of earthquakes. It has also several applications in optics
and medical imaging among others.


Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics.  
The problem can be recast as a geometric problem: Can one determine the
Riemannian metric of a Riemannian manifold with boundary by measuring
the distance function between boundary points? This is the boundary
rigidity problem. We will also consider the problem of determining
the metric from the scattering relation, the so-called lens rigidity
problem. The linearization of these problems involve the integration
of a tensor along geodesics, similar to the X-ray transform.


The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.
We will also describe some recent results, join with Plamen Stefanov
and Andras Vasy, on the partial data case, where you are making
measurements on a subset of the boundary. No previous knowledge of
Riemannian geometry will be assumed.


We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality.
=== Sep 21: Andrew Stuart (Caltech) ===


=== September 30: Akos Magyar (University of Georgia) ===
The Legacy of Rudolph Kalman
Title: Geometric Ramsey theory


Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.


=== October 14: Ling Long (LSU) ===  
=== Sep 28: Gautam Iyer (CMU) ===
Title: Hypergeometric functions over finite fields


Abstract: Hypergeometric functions are special functions with lot of
Stirring and Mixing
symmetries.  In this talk, we will introduce hypergeometric functions over finite
fields, originally due to Greene, Katz and McCarthy, in a way that is
parallel to the classical hypergeometric functions, and discuss their
properties and applications to character sums and the arithmetic of
hypergeometric abelian varieties.
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.


=== Tuesday, October 25, B139: Stefan Steinerberger (Yale) ===
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical
Title: Three Miracles in Analysis
aspects of mixing that arise in the context of fluid dynamics:


Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).
1. How efficiently can stirring "mix"?


===Monday, October 31: Kathryn Mann (Berkeley) ===
2. What is the interaction between diffusion and mixing.
Title: Groups acting on the circle


Abstract:  Given a group G and a manifold M, can one describe all the actions of G on M?  This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group.
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing
results, and talk about a few open problems.


In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others.  We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. 
=== Oct 5: Eyal Subag (Penn State)===


===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===
Symmetries of the hydrogen atom and algebraic families
Title: Siegel's problem on small volume lattices


Abstract: We outline in very general terms the history and the proof of the identification
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetryIn this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modulesI will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system.  No prior knowledge on quantum mechanics or representation theory will be assumed.
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3
Coxeter group extended by the involution preserving the symmetry of this
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.
This solves (in three dimensions) a problem posed by Siegel in 1945Siegel solved this problem in two dimensions by deriving the
signature formula identifying the (2,3,7)-triangle group as having minimal
co-area.
   
There are strong connections with arithmetic hyperbolic geometry in
the proof, and the result has applications in the maximal symmetry groups
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem
and Siegel's result do.


== Past Colloquia ==
== Past Colloquia ==
[[Colloquia/Blank|Blank]]
[[Colloquia/Spring2018|Spring 2018]]
[[Colloquia/Fall2017|Fall 2017]]
[[Colloquia/Spring2017|Spring 2017]]
[[Archived Fall 2016 Colloquia|Fall 2016]]


[[Colloquia/Spring2016|Spring 2016]]
[[Colloquia/Spring2016|Spring 2016]]

Revision as of 10:23, 19 September 2018

Mathematics Colloquium

All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.

The calendar for spring 2019 can be found here.

Fall 2018

date speaker title host(s)
Sep 12 Room 911 Gunther Uhlmann (Univ. of Washington) Distinguished Lecture series Harry Potter's Cloak via Transformation Optics Li
Sep 14 Room 911 Gunther Uhlmann (Univ. of Washington) Distinguished Lecture series Journey to the Center of the Earth Li
Sep 21 Room 911 Andrew Stuart (Caltech) LAA lecture The Legacy of Rudolph Kalman Jin
Sep 28 Gautam Iyer (CMU) Stirring and Mixing Thiffeault
Oct 5 Eyal Subag (Penn State) Symmetries of the hydrogen atom and algebraic families Gurevich
Oct 12 Arie Levit (Yale) TBA Gurevich
Oct 19 Jeremy Teitelbaum (U Connecticut) TBA Boston
Oct 26 Douglas Ulmer (Arizona) TBA Yang
Nov 2 Reserved for job talk TBA hosting faculty
Nov 9 Reserved for job talk TBA hosting faculty
Nov 16 Reserved for job talk TBA hosting faculty
Nov 30 Reserved for job talk TBA hosting faculty
Dec 7 Reserved for job talk TBA hosting faculty

Abstracts

Sep 12: Gunther Uhlmann (Univ. of Washington)

Harry Potter's Cloak via Transformation Optics

Can we make objects invisible? This has been a subject of human fascination for millennia in Greek mythology, movies, science fiction, etc. including the legend of Perseus versus Medusa and the more recent Star Trek and Harry Potter. In the last fifteen years or so there have been several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion one of them, the so-called "traansformation optics" in a non-technical fashion n the so-called that has received the most attention in the scientific literature.

Sep 14: Gunther Uhlmann (Univ. of Washington)

Journey to the Center of the Earth

We will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes. It has also several applications in optics and medical imaging among others.

The problem can be recast as a geometric problem: Can one determine the Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between boundary points? This is the boundary rigidity problem. We will also consider the problem of determining the metric from the scattering relation, the so-called lens rigidity problem. The linearization of these problems involve the integration of a tensor along geodesics, similar to the X-ray transform.

We will also describe some recent results, join with Plamen Stefanov and Andras Vasy, on the partial data case, where you are making measurements on a subset of the boundary. No previous knowledge of Riemannian geometry will be assumed.

Sep 21: Andrew Stuart (Caltech)

The Legacy of Rudolph Kalman

In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.

Sep 28: Gautam Iyer (CMU)

Stirring and Mixing

Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical aspects of mixing that arise in the context of fluid dynamics:

1. How efficiently can stirring "mix"?

2. What is the interaction between diffusion and mixing.

Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing results, and talk about a few open problems.

Oct 5: Eyal Subag (Penn State)

Symmetries of the hydrogen atom and algebraic families

The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.

Past Colloquia

Blank

Spring 2018

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Spring 2015

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012