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__NOTOC__
= 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]].
 
==Spring 2019==


== Fall 2016  ==
 
{| cellpadding="8"
{| cellpadding="8"
!align="left" | date   
!align="left" | date   
Line 15: Line 13:
!align="left" | host(s)
!align="left" | host(s)
|-
|-
|September 9
|Jan 25
|  
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW
|[[#  |    ]]
|[[#Beata Randrianantoanina (Miami University Ohio) |  Some nonlinear problems in the geometry of Banach spaces and their applications ]]
|
| Tullia Dymarz
|
|
|-
|-
|September 16
|Jan 30 '''Wednesday'''
|[http://www.math.cmu.edu/~ploh/ Po-Shen Loh] (CMU)
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)
|Directed paths: from Ramsey to Pseudorandomness
|[[#Lillian Pierce (Duke University) |  Short character sums  ]]
|Ellenberg
| Boston and Street
|
|
|-
|-
|September 23
|Jan 31 '''Thursday'''
| [http://www.math.wisc.edu/~craciun/ Gheorghe Craciun] (UW-Madison)
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)
|Toric Differential Inclusions and a Proof of the Global Attractor Conjecture
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations  ]]
| Street
| Street
| 
|[[#  |    ]]
| 
|-
|September 30
|[http://math.uga.edu/~magyar/ Akos Magyar]  (University of Georgia)
|Geometric Ramsey theory
| Cook
|
|
|-
|-
|October 7
|Feb 1
|  
| [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University)
|[[# |   ]]
|[[# TBA| TBA  ]]
|
| Qin
|
|
|-
|-
|October 14
|Feb 5 '''Tuesday'''
| [https://www.math.lsu.edu/~llong/ Ling Long] (LSU)
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)
|Hypergeometric functions over finite fields
|[[# TBA|  TBA  ]]
| Yang
| Denisov
|
|
|-
|-
|October 21
|Feb 8
|'''No colloquium this week'''
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)
|[[#  |    ]]
|[[#Aaron Naber (Northwestern) |  A structure theory for spaces with lower Ricci curvature bounds ]]
|
| Street
|
|
|-
|-
|'''Tuesday, October 25, B139'''
|Feb 15
|[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"
!align="left" | date 
!align="left" | speaker
!align="left" | title
!align="left" | host(s)
|-
|January 20
|Reserved for possible job talks 
|[[#  |    ]]
| 
|
|-
|January 27
|Reserved for possible job talks
|[[# |    ]]
|  
|  
|
|[[# TBA|  TBA  ]]
|-
|February 3
| 
|[[#  |    ]]
|
|-
|February 6 (Wasow lecture)
| Benoit Perthame (University of Paris VI)
|[[# TBA|  TBA ]]
| Jin
|  
|-
|February 10
| '''No Colloquium'''
|[[# |  ]]  
|  
|  
|
|
|-
|-
|February 17
|Feb 22
|
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)
|[[#   |     ]]
|[[# TBA| TBA  ]]
|  
| Erman and Corey
|
|
|-
|-
|February 24
|March 4
|
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture
|[[# |   ]]
|[[# TBA| TBA ]]
|  
| Kim
|
|
|-
|-
|March 3
|March 8
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)
|[[# |   ]]
|[[# TBA| TBA  ]]
|Dymarz
| Erman
|
|
|-
|-
|Tuesday, March 7, 4PM (Distinguished Lecture)
|March 15
| [http://pages.iu.edu/~temam/  Roger Temam] (Indiana University)  
| Maksym Radziwill (Caltech)
|[[#  |    ]]
|[[# TBA|  TBA ]]
|Smith
| Marshall
|
|
|-
|-
|Wednesday, March 8, 2:25PM
|March 29
| [http://pages.iu.edu/~temam/  Roger Temam] (Indiana University)  
| Jennifer Park (OSU)
|[[#  |    ]]
|[[# TBA|  TBA ]]
|Smith
| Marshall
|
|
|-
|-
|March 10
|April 5
| '''No Colloquium'''
| Ju-Lee Kim (MIT)
|[[# |   ]]
|[[# TBA| TBA  ]]
|
| Gurevich
|
|
|-
|-
|March 17
|April 12
|   
|  Evitar Procaccia (TAMU)
|
|[[# TBA|  TBA  ]]
|
| Gurevich
|
|
|-
|-
|March 24
|April 19
| '''Spring Break'''
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)
|[[# |   ]]
|[[# TBA| TBA  ]]
|
| Jean-Luc
|
|
|-
|-
|Wednesday, March 29 (Wasow)
|April 26
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU)  
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)
|[[# TBA|   TBA]]
|[[# TBA| TBA ]]
|Tran
| WIMAW
|
|
|-
|-
|March 31
|May 3
| '''No Colloquium'''
| Tomasz Przebinda (Oklahoma)
|[[# |   ]]
|[[# TBA|  TBA  ]]
|
| Gurevich
|
|-
|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
===Beata Randrianantoanina (Miami University Ohio)===
paths in graphs, we discover a series of rich and surprising connections
 
that lead into the theory around a fundamental result in Combinatorics:
Title: Some nonlinear problems in the geometry of Banach spaces and their applications.
Szemeredi's Regularity Lemma, which roughly states that every graph (no
matter how large) can be well-approximated by a bounded-complexity
pseudorandom object.  Using these relationships, we prove that every
coloring of the edges of the transitive N-vertex tournament using three
colors contains a directed path of length at least sqrt(N) e^{log^* N}
which entirely avoids some color.  The unusual function log^* is the
inverse function of the tower function (iterated exponentiation).


=== September 23: Gheorghe Craciun (UW-Madison) ===
Abstract: Nonlinear problems in the geometry of Banach spaces have been studied since the inception of the field. In this talk I will outline some of the history, some of modern applications, and some open directions of research. The talk will be accessible to graduate students of any field of mathematics.
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture


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.
===Lillian Pierce (Duke University)===


The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.
Title: Short character sums


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.  
Abstract: A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.


=== September 30: Akos Magyar (University of Georgia) ===  
===Dean Baskin (Texas A&M)===
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.
Title: Radiation fields for wave equations


=== October 14: Ling Long (LSU) ===
Abstract: Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.
Title: Hypergeometric functions over finite fields


Abstract: Hypergeometric functions are special functions with lot of
===Aaron Naber (Northwestern)===
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) ===
Title: A structure theory for spaces with lower Ricci curvature bounds.
Title: Three Miracles in Analysis


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).
Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be?  This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples.  The work discussed is joint with Cheeger, Jiang and with Li.


===Monday, October 31: Kathryn Mann (Berkeley) ===
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. 
== Past Colloquia ==


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. 
[[Colloquia/Blank|Blank]]


===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===
[[Colloquia/Fall2018|Fall 2018]]
Title: Siegel's problem on small volume lattices


Abstract: We outline in very general terms the history and the proof of the identification
[[Colloquia/Spring2018|Spring 2018]]
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 1945.  Siegel 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 ==
[[Colloquia/Fall2017|Fall 2017]]
 
[[Colloquia/Spring2017|Spring 2017]]
 
[[Archived Fall 2016 Colloquia|Fall 2016]]


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

Latest revision as of 14:43, 24 January 2019

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.

Spring 2019

date speaker title host(s)
Jan 25 Beata Randrianantoanina (Miami University Ohio) WIMAW Some nonlinear problems in the geometry of Banach spaces and their applications Tullia Dymarz
Jan 30 Wednesday Lillian Pierce (Duke University) Short character sums Boston and Street
Jan 31 Thursday Dean Baskin (Texas A&M) Radiation fields for wave equations Street
Feb 1 Jianfeng Lu (Duke University) TBA Qin
Feb 5 Tuesday Alexei Poltoratski (Texas A&M University) TBA Denisov
Feb 8 Aaron Naber (Northwestern) A structure theory for spaces with lower Ricci curvature bounds Street
Feb 15 TBA
Feb 22 Angelica Cueto (Ohio State) TBA Erman and Corey
March 4 Vladimir Sverak (Minnesota) Wasow lecture TBA Kim
March 8 Jason McCullough (Iowa State) TBA Erman
March 15 Maksym Radziwill (Caltech) TBA Marshall
March 29 Jennifer Park (OSU) TBA Marshall
April 5 Ju-Lee Kim (MIT) TBA Gurevich
April 12 Evitar Procaccia (TAMU) TBA Gurevich
April 19 Jo Nelson (Rice University) TBA Jean-Luc
April 26 Kavita Ramanan (Brown University) TBA WIMAW
May 3 Tomasz Przebinda (Oklahoma) TBA Gurevich

Abstracts

Beata Randrianantoanina (Miami University Ohio)

Title: Some nonlinear problems in the geometry of Banach spaces and their applications.

Abstract: Nonlinear problems in the geometry of Banach spaces have been studied since the inception of the field. In this talk I will outline some of the history, some of modern applications, and some open directions of research. The talk will be accessible to graduate students of any field of mathematics.

Lillian Pierce (Duke University)

Title: Short character sums

Abstract: A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.

Dean Baskin (Texas A&M)

Title: Radiation fields for wave equations

Abstract: Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.

Aaron Naber (Northwestern)

Title: A structure theory for spaces with lower Ricci curvature bounds.

Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li.


Past Colloquia

Blank

Fall 2018

Spring 2018

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Spring 2015

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012

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