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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]].
 
==Spring 2019==


== Spring 2016  ==
 
{| 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#February 12: Gautam Iyer (CMU)| Homogenization and Anomalous Diffusion]]
|[[# 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#February 19:  Jean-François Lafont (Ohio State) | Rigidity and flexibility of almost-isometries]]
|[[#Aaron Naber (Northwestern) |   A structure theory for spaces with lower Ricci curvature bounds  ]]
| Dymarz
| Street
|
|-
|-
| '''February 26'''
|Feb 15
|Hiroyoshi Mitake (Hiroshima university)   
|  
| [[Colloquia#February 26: Hiroyoshi Mitake (Hiroshima university) | On asymptotic speed of the crystal growth]]
|[[# 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: Guillaume Bal (Columbia University) | Inverse and Control Transport Problems]]
|[[# 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)
|  CANCELED
|[[# 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
|  
| Jennifer Park (OSU)
|   CANCELED
|[[# TBA|  TBA  ]]
| Marshall
|
|
|-
|-
| '''April 8'''
|April 5
| [https://web.math.princeton.edu/~aionescu/ Alexandru Ionescu] (Princeton)  
| Ju-Lee Kim (MIT)
| [[Colloquia#April 8: Alexandru Ionescu (Princeton) | On long-term existence of solutions of water wave models]]  
|[[# 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) | Random matrices beyond mean-field]]
|[[# 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) | Liquid crystals and their (algebraic) topology]]  
|[[# TBA|  TBA ]]
| Spagnolie
| WIMAW
|
|-
|-
| '''May 4'''
|May 3
| [https://www.math.ias.edu/people/faculty/sarnak Peter Sarnak] (Princeton and IAS)  
| Tomasz Przebinda (Oklahoma)
| [[Colloquia#May 4: Peter Sarnak (Princeton and IAS) | Strong approximation for Markoff surfaces]] (Note special day; still 4 pm in B239)
|[[# TBA|  TBA ]]
| Marshall
| Gurevich
|-
|
| '''May 6'''
|  
|}
|}


== Abstracts ==
== Abstracts ==


===Beata Randrianantoanina (Miami University Ohio)===


=== January 28: Steven Sivek (Princeton) ===
Title: Some nonlinear problems in the geometry of Banach spaces and their applications.
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.
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.


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


=== January 29: Ana Caraiani (Princeton) ===
Title: Short character sums
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.
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 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.
===Dean Baskin (Texas A&M)===


Title: Radiation fields for wave equations


=== February 5: Takis Souganidis (University of Chicago) ===
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:  Scalar Conservation Laws with Rough Dependence


I will present a recently developed theory for scalar conservation laws with nonlinear multiplicative rough signal dependence. I will describe the difficulties, introduce the notion of pathwise entropy/kinetic solution and its well-posedness. I will also talk about the long time behavior of the solutions as well as some regularization by noise type results.
===Aaron Naber (Northwestern)===


=== February 12:  Gautam Iyer (CMU) ===
Title:  A structure theory for spaces with lower Ricci curvature bounds.


Homogenization and Anomalous Diffusion
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.


Homogenization is a well known technique used to approximate the macroscopic behaviour of a material with microscopic impurities.
While this originally arose in the study of composite materials, it has applications to various other fields, and I will focus on a few results
motivated by fluid dynamics. One well known result in this direction is by GI Taylor estimating the dispersion rate of a solute in a pipe. The
length scales involved in typical pipelines, however, are too short for this result to apply. I will conclude with a few recent "intermediate time" results describing the effective behaviour in scaling regimes outside those of standard homogenization results.


=== February 19: Jean-François Lafont (Ohio State) ===
== Past Colloquia ==


Rigidity and flexibility of almost-isometries
[[Colloquia/Blank|Blank]]


An almost isometry (AI) is a quasi-isometry (QI) with multiplicative
[[Colloquia/Fall2018|Fall 2018]]
constant =1. Given two metrics on a closed manifold, Milnor-Swarc implies
that the lifted metrics on the universal cover are QI to each other. When are
they AI to each other? In the rigidity direction, we give various examples
where the only time such lifts are AI is when they are isometric (joint with
Kar and Schmidt). In the flexible direction, we show that for higher genus
surfaces, any two metrics have lifts which, after possibly scaling one of the
lifted metrics, are AI to each other (joint with Schmidt and van Limbeek). In
the latter examples, one can further show that the AI is usually not equivariant
with respect to the group actions.


=== February 26: Hiroyoshi Mitake (Hiroshima University) ===
[[Colloquia/Spring2018|Spring 2018]]
In the talk, I will propose a model equation to study the crystal growth as a prototype, which is described by a level-set mean curvature flow equation with driving and source terms. We establish the well-posedness of solutions, and study the asymptotic speed. Interestingly, a new type of nonlinear phenomena in terms of asymptotic speed of solutions appears because of the double nonlinear effects coming from the surface evolution and the source term, which is sensitive to the shapes of source terms. This is a joint work with Y. Giga (U. Tokyo), and H. V. Tran (U. Wisconsin-Madison).


=== March 11: Mitchell Luskin (UMN) ===
[[Colloquia/Fall2017|Fall 2017]]
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.
[[Colloquia/Spring2017|Spring 2017]]


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.
[[Archived Fall 2016 Colloquia|Fall 2016]]


===March 18: Ralf Spatzier (UMichigan)===
[[Colloquia/Spring2016|Spring 2016]]
 
CANCELED: Rigidity in Geometry and Dynamics
 
I will survey some rigidity phenomena in dynamics and also geometry, with emphasis on the notion of higher rank.
This first emerged in Margulis’ celebrated work on superrrigidity but has also been important in more recent work on symmetry in dynamical systems.
How special is it for maps commute with each other?  Smale asked this problem fifty years ago, and answers are finally emerging.  Much depends on the differentiability
of the maps: it gets harder the more differentiable the map is. Sometimes we can even classify such maps.  I’ll discuss this and
related phenomena.
 
 
 
=== April 8: Alexandru Ionescu (Princeton) ===
 
Title:  On long-term existence of solutions of water wave models
 
I will talk about some recent work on long-term/global regularity of solutions of water wave models in 2 and 3 dimensions. The
models we consider describe the evolution of an inviscid perfect fluid in
a free boundary domain, under the influence of gravity and/or surface
tension. This is joint work with Fabio Pusateri and, in part, with Yu Deng and
Benoit Pausader.
 
 
===April 22: Paul Bourgade (NYU)===
 
Title: Random matrices beyond mean-field
 
 
Random matrix statistics were proposed by Eugene Wigner as a new class of universal statistical laws for highly correlated systems. 
We will first review established instances of this conjecture for mean-field matrix models. We will then propose an approach towards the spectral analysis of non mean-field models, which are closer to Wigner's original vision.
A key role is played by a new patching of quantum unique ergodicity estimates.
 
 
=== April 29: Randall Kamien (U Penn) ===
 
Title: Liquid Crystals and their (Algebraic) Topology
 
Liquid Crystals, the materials in your iPhone, are complex materials with varying degrees of internal order.  I will discuss and demonstrate how algebraic topology can be used to identify and characterize long-lived configurations.  I will also describe how conic sections naturally arise in these structures as intersections of simple polynomials.
 
=== May 4: Peter Sarnak (Princeton and IAS) ===
 
Title: Strong approximation for Markoff surfaces
 
We discuss the transitivity properties of the group of morphisms generated by Vieta involutions on the solutions in congruences to the Markoff equation as well as to other Markoff type affine cubic surfaces. These are dictated in part by the finite orbits of these actions on the algebraic points. The latter can be determined effectively and in special cases is connected to the problem of determining all algebraic Painleve VI's. Applications to forms of strong approximation for integer points and to sieving on such affine surfaces, as well as to Markoff numbers will be given.
 
Joint work with J.Bourgain and A.Gamburd.
===
 
== Past Colloquia ==


[[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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