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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'''.


== Spring 2016  ==
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].
 
 
==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)
|-
|-
| '''January 22'''
|Jan 25
|<!--[https://web.math.princeton.edu/~caraiani/ Ana Caraiani] (Princeton)-->
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW
| <!-- [[Colloquia#September 11:  Speaker (University) | title]] -->
|[[#Beata Randrianantoanina (Miami University Ohio) | Some nonlinear problems in the geometry of Banach spaces and their applications  ]]
| <!--Host-->
| Tullia Dymarz
|
|-
|-
| '''January 28 (Th 4pm VV901)'''  
|Jan 30 '''Wednesday'''
| [https://web.math.princeton.edu/~ssivek/ Steven Sivek] (Princeton)
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)
|     [[Colloquia#September 11:  Speaker (University) | The augmentation category of a Legendrian knot]]
|[[#Lillian Pierce (Duke University) | Short character sums  ]]
| Ellenberg
| Boston and Street
|
|-
|-
| '''January 29'''  
|Jan 31 '''Thursday'''
|[https://web.math.princeton.edu/~caraiani/ Ana Caraiani] (Princeton)
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)
| [[Colloquia#September 11:  Ana Caraiani (Princeton) | Locally symmetric spaces, torsion classes, and the geometry of period domains]]
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations  ]]
| Ellenberg
| Street
|
|-
|-
| '''February 5'''
|Feb 1
|[http://math.uchicago.edu/~souganidis/ Takis Souganidis] (University of Chicago)
| [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University)
| [[Colloquia#September 11: Takis Souganidis (University of Chicago) | Scalar Conservation Laws with Rough Dependence]]
|[[# TBA|  TBA ]]
| Lin
| Qin
|
|-
|-
| '''February 12'''  
|Feb 5 '''Tuesday'''
|[http://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)  
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)
| <!-- [[Colloquia#September 11: Speaker (University) | title]] -->
|[[# TBA|  TBA ]]
| Jean-Luc
| Denisov
|
|-
|-
| '''February 19'''
|Feb 8
| [https://people.math.osu.edu/lafont.1/ Jean-François Lafont] (Ohio State)  
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)
| <!-- [[Colloquia#September 11:  Speaker (University) | title]] -->
|[[#Aaron Naber (Northwestern) |   A structure theory for spaces with lower Ricci curvature bounds  ]]
| Dymarz
| Street
|
|-
|-
| '''February 26'''
|Feb 15
|Hiroyoshi Mitake (Hiroshima university)   
|  
| <!-- [[Colloquia#September 11: Speaker (University) | title]] -->
|[[# TBA|  TBA ]]
| Tran
|  
|
|-
|-
| '''March 4'''
|Feb 22
| [http://www.columbia.edu/~gb2030/ Guillaume Bal] (Columbia University)
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)
| <!-- [[Colloquia#September 11: Speaker (University) | title]] -->
|[[# TBA|  TBA ]]
| Li, Jin
| Erman and Corey
|
|-
|-
| '''March 11'''
|March 4
| [http://math.umn.edu/~luskin Mitchell Luskin] (University of Minnesota)
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture
| [[Colloquia#March 11:  Mitchell Luskin (UMN) | Mathematical Modeling of Incommensurate 2D Materials]]
|[[# TBA| TBA ]]
| Li
| Kim
|
|-
|-
| '''March 18'''
|March 8
| [http://www.math.lsa.umich.edu/~spatzier/ Ralf Spatzier] (University of Michigan)  
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)
| [[Colloquia#March 18: Ralf Spatzier (University of Michigan) | TBA]]
|[[# TBA| TBA ]]
| Dymarz
| Erman
|
|-
|-
| '''March 25'''
|March 15
| Spring Break<!-- [webpage Speaker Name] (University) -->   
| Maksym Radziwill (Caltech)
| <!-- [[Colloquia#September 11: Speaker (University) | title]] -->
|[[# TBA|  TBA ]]
| <!-- host -->
| Marshall
|
|-
|-
| '''April 1'''
|March 29
| [http://www.math.uci.edu/~cterng/ Chuu-Lian Terng] (UC Irvine) -->   
| Jennifer Park (OSU)
| [[Colloquia#April 1: Chuu-Lian Terng (UC Irvine) | TBA]] -->
|[[# TBA| TBA ]]
| Mari-Beffa
| Marshall
|
|-
|-
| '''April 8'''
|April 5
| [https://web.math.princeton.edu/~aionescu/ Alexandru Ionescu] (Princeton)  
| Ju-Lee Kim (MIT)
| [[Colloquia#April 8: Alexandru Ionescu (Princeton) | TBA]]  
|[[# TBA| TBA ]]
| Wainger/Seeger
| Gurevich
|
|-
|-
| '''April 15'''
|April 12
| [https://www.kcl.ac.uk/nms/depts/mathematics/people/atoz/wigmani.aspx Igor Wigman] (King's College - London)  
| Evitar Procaccia (TAMU)
| [[Colloquia#September 11: Speaker (University) |Nodal Domains of Eigenfunctions]]
|[[# TBA|  TBA ]]
| Gurevich/Marshall
| Gurevich
|
|-
|-
| '''April 22'''
|April 19
| [http://www.cims.nyu.edu/~bourgade/ Paul Bourgade] (NYU)
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)
| [[Colloquia#April 22: Paul Bourgade (NYU) | TBA]]
|[[# TBA| TBA ]]
| Seppalainen/Valko
| Jean-Luc
|
|-
|-
| '''April 29'''
|April 26
| [http://www.physics.upenn.edu/~kamien/kamiengroup/ Randall Kamien] (U Penn)  
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)
| [[Colloquia#April 29: Randall Kamien (U Penn) | TBA]]  
|[[# TBA| TBA ]]
| Spagnolie
| WIMAW
|
|-
|-
| '''May 6'''
|May 3
| [https://www.math.upenn.edu/~shaneson/ Julius Shaneson] (University of Pennsylvania)    
| Tomasz Przebinda (Oklahoma)
| [[Colloquia#September 11: Julius Shaneson (University of Pennsylvania) | TBA]]  
|[[# TBA| TBA ]]
| Maxim/Kjuchukova
| Gurevich
|
|}
|}


== Abstracts ==
== 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.


=== January 28: Steven Sivek (Princeton) ===  
===Lillian Pierce (Duke University)===
Title: The augmentation category of a Legendrian knot


Abstract: A well-known principle in symplectic geometry says that information about the smooth structure on a manifold should be captured by the symplectic geometry of its cotangent bundle.  One prominent example of this is Nadler and Zaslow's microlocalization correspondence, an equivalence between a category of constructible sheaves on a manifold and a symplectic invariant of its cotangent bundle called the Fukaya category.
Title: Short character sums


The goal of this talk is to describe a model for a relative version of this story in the simplest case, corresponding to Legendrian knots in the standard contact 3-space. This construction, called the augmentation category, is a powerful invariant which is defined in terms of holomorphic curves but can also be described combinatorially. I will describe some interesting properties of this category and relate it to a category of sheaves on the plane.  This is joint work with Lenny Ng, Dan Rutherford, Vivek Shende, and Eric Maslow.
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.


=== January 29: Ana Caraiani (Princeton) ===  
===Dean Baskin (Texas A&M)===
Title:  Locally symmetric spaces, torsion classes, and the geometry of period domains


Abstract: The Langlands program is an intricate network of conjectures, which are meant to connect different areas of mathematics, such as number theory, harmonic analysis and representation theory. One striking consequence of the Langlands program is the Ramanujan conjecture, which is a statement purely within harmonic analysis, about the growth rate of Fourier coefficients of modular forms. It turns out to be intimately connected to the Weil conjectures, a statement about the cohomology of projective, smooth varieties defined over finite fields.
Title: Radiation fields for wave equations


I will explain this connection and then move towards a mod p analogue of these ideas. More precisely, I will explain a strategy for understanding torsion occurring in the cohomology of locally symmetric spaces and how to detect which degrees torsion will contribute to. The main theorem is joint work with Peter Scholze and relies on a p-adic version of Hodge theory and on recent developments in p-adic geometry.
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)===


===March 11: Mitchell Luskin (UMN) ===
Title: A structure theory for spaces with lower Ricci curvature bounds.
Title: Mathematical Modeling of Incommensurate 2D Materials


Abstract: Incommensurate materials are found in crystals, liquid crystals, and quasi-crystals. Stacking a few layers of 2D materials such as graphene and molybdenum disulfide, for example, opens the possibility to tune the elastic, electronic, and optical properties of these materials. One of the main issues encountered in the mathematical modeling of layered 2D materials is that lattice mismatch and rotations between the layers destroys the periodic character of the system. This leads to complex commensurate-incommensurate transitions and pattern formation.
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.


Even basic concepts like the Cauchy-Born strain energy density, the electronic density of states, and the Kubo-Greenwood formulas for transport properties have not been given a rigorous analysis in the incommensurate setting. New approximate approaches will be discussed and the validity and efficiency of these approximations will be examined from mathematical and numerical analysis perspectives.
====  ====


== 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/Fall2015|Fall 2015]]

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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