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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'''.


[[Colloquia/Spring 2015 | Tentative schedule for Spring 2015]]
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].


== Fall 2014 ==
==Spring 2019==


{| cellpadding="8"
{| cellpadding="8"
!align="left" | date
!align="left" | date  
!align="left" | speaker
!align="left" | speaker
!align="left" | title
!align="left" | title
!align="left" | host(s)
!align="left" | host(s)
|-
|-
|September 12
|Jan 25
| [http://mduchin.math.tufts.edu/index.html Moon Duchin] (Tufts University)
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW
| [[Colloquia#September 12:  Moon Duchin (Tufts University) | Geometry and counting in the Heisenberg group]]
|[[#Beata Randrianantoanina (Miami University Ohio) | Some nonlinear problems in the geometry of Banach spaces and their applications  ]]
| Dymarz and WIMAW
| Tullia Dymarz
|
|-
|Jan 30 '''Wednesday'''
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)
|[[#Lillian Pierce (Duke University) |  Short character sums  ]]
| Boston and Street
|
|-
|-
|September 19
|Jan 31 '''Thursday'''
|[http://www.mast.queensu.ca/~ggsmith/ Gregory G. Smith] (Queen's University)
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)
|[[Colloquia#September 19: Gregory G. Smith (Queen's University) | Nonnegative sections and sums of squares]]
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations  ]]
|Erman
| Street
|
|-
|-
|September 26
|Feb 1
|[http://www.math.uci.edu/~jxin/ Jack Xin] (UC Irvine)
| [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University)
|TBA
|[[# TBA|  TBA ]]
|Jin
| Qin
|
|-
|-
|October 3
|Feb 5 '''Tuesday'''
|[http://math.arizona.edu/~tiep/ Pham Huu Tiep] (University of Arizona)
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)
|[[Colloquia#October 3: Pham Huu Tiep (Arizona) | Adequate subgroups]]
|[[# TBA| TBA  ]]
|Gurevich
| Denisov
|
|-
|-
|October 10
|Feb 8
|[http://www.math.ubc.ca/~adem/ Alejandro Adem] (UBC)
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)
|TBA
|[[#Aaron Naber (Northwestern) |  A structure theory for spaces with lower Ricci curvature bounds  ]]
|Yang
| Street
|
|-
|-
|October 17
|Feb 15
|
|[[# TBA|  TBA  ]]
|  
|  
|
|
|
|-
|-
|October 24
|Feb 22
|[http://www.math.utoronto.ca/almut/ Almut Burchard] (University of Toronto)
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)
|TBA
|[[# TBA|  TBA  ]]
|Stovall
| Erman and Corey
|
|-
|-
|October 31
|March 4
|[http://www.math.uchicago.edu/~ngo/ Bao Chau Ngo] (University of Chicago)
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture
|TBA
|[[# TBA| TBA ]]
|Gurevich
| Kim
|
|-
|-
|November 7
|March 8
|Reserved for possible job interview
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)
|[[# TBA|  TBA  ]]
| Erman
|
|
|-
|March 15
| Maksym Radziwill (Caltech)
|[[# TBA|  TBA  ]]
| Marshall
|
|
|-
|-
|November 14
|March 29
|Reserved for possible job interview
| Jennifer Park (OSU)
|[[# TBA|  TBA  ]]
| Marshall
|
|
|
|-
|-
|November 21
|April 5
|Reserved for possible job interview
| Ju-Lee Kim (MIT)
|[[# TBA|  TBA  ]]
| Gurevich
|
|
|
|-
|-
|November 28
|April 12
|University holiday
| Evitar Procaccia (TAMU)
|[[# TBA|  TBA  ]]
| Gurevich
|
|
|
|-
|-
|December 5
|April 19
|Reserved for possible job interview
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)
|[[# TBA|  TBA  ]]
| Jean-Luc
|
|
|
|-
|-
|December 12
|April 26
| Reserved for possible job interview
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)
|[[# TBA|  TBA  ]]
| WIMAW
|
|
|
|-
|-
|May 3
| Tomasz Przebinda (Oklahoma)
|[[# TBA|  TBA  ]]
| Gurevich
|
|}
|}


== Abstracts ==
== Abstracts ==


===September 12: Moon Duchin (Tufts University)===
===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)===


====Geometry and counting in the Heisenberg group====
Title: Short character sums


The growth function of a finitely-generated group enumerates how many words can be spelled with each possible number of letters-- this should be thought of as a sort of volume growth in any geometric model of the group. A major theorem of Gromov tells us exactly which groups have growth in the polynomial range:  those that are (virtually) nilpotent. But we can still wonder how regular the growth of a nilpotent group is:  is it actually a polynomial?  Or could it exhibit some transcendentality together with pretty slow growth? 
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.


I'll talk about some themes and techniques in the study of group growth and outline a geometry of numbers for nilpotent groups, including a recent result with M. Shapiro settling a long-standing question:  the Heisenberg group -- the simplest non-abelian nilpotent group -- has rational growth in any generating set. 
===Dean Baskin (Texas A&M)===


===September 19: Gregory G. Smith (Queen's University)===
Title: Radiation fields for wave equations


====Nonnegative sections and sums of squares====
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.


A polynomial with real coefficients is nonnegative if it takes on only nonnegative values.  For example, any sum of squares is obviously nonnegative.  For a homogeneous polynomial with respect to the standard grading, Hilbert famously characterized when the converse holds, that is when every nonnegative homogeneous polynomial is a sum of squares.  After reviewing some history of this problem, we will examine this converse in more general settings such as global sections of a line bundles.  This line of inquiry has unexpected connections to classical algebraic geometry and leads to new examples in which every nonnegative homogeneous polynomial is a sum of squares.  This talk is based on joint work with Grigoriy Blekherman and Mauricio Velasco.
===Aaron Naber (Northwestern)===


===October 3: Pham Huu Tiep (Arizona)===
Title: A structure theory for spaces with lower Ricci curvature bounds.


====Adequate subgroups====
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.


The notion of adequate subgroups was introduced by Thorne. It is a weakening of the notion of big subgroups used in generalizations of the Taylor-Wiles method for proving the automorphy of certain Galois representations. Using this idea, Thorne was able to strengthen many automorphy lifting theorems. It was shown recently by Guralnick, Herzig, Taylor, and Thorne that if the degree is small compared to the characteristic then all absolutely irreducible representations are adequate. We will discuss extensions of this result obtained recently in joint work with R. M. Guralnick and F. Herzig. In particular, we show that almost all absolutely irreducible representations in characteristic p of degree less than p are adequate. We will also address a question of Serre about
indecomposable modules in characteristic p of dimension less than 2p-2.


== Past Colloquia ==
== Past Colloquia ==
[[Colloquia/Blank|Blank]]
[[Colloquia/Fall2018|Fall 2018]]
[[Colloquia/Spring2018|Spring 2018]]
[[Colloquia/Fall2017|Fall 2017]]
[[Colloquia/Spring2017|Spring 2017]]
[[Archived Fall 2016 Colloquia|Fall 2016]]
[[Colloquia/Spring2016|Spring 2016]]
[[Colloquia/Fall2015|Fall 2015]]
[[Colloquia/Spring2014|Spring 2015]]
[[Colloquia/Fall2014|Fall 2014]]


[[Colloquia/Spring2014|Spring 2014]]
[[Colloquia/Spring2014|Spring 2014]]

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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