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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 2014 ==
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)
|-
|-
|'''Mon, Jan 6, 4PM'''
|Jan 25
|[http://www-bcf.usc.edu/~lauda/Aaron_Laudas_Page/Home.html Aaron Lauda] (USC)  
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW
|[[Colloquia#January 6: Aaron Lauda (USC) | An introduction to diagrammatic categorification]]
|[[#Beata Randrianantoanina (Miami University Ohio) | Some nonlinear problems in the geometry of Banach spaces and their applications  ]]
|Caldararu
| Tullia Dymarz
|
|-
|-
|'''Wed, Jan 8, 4PM'''
|Jan 30 '''Wednesday'''
|[http://www2.math.umd.edu/~kmelnick/ Karin Melnick] (Maryland)  
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)
|[[Colloquia#January 8: Karin Melnick (Maryland) | Normal forms for local flows on parabolic geometries]]
|[[#Lillian Pierce (Duke University) | Short character sums  ]]
|Kent
| Boston and Street
|
|-
|-
|Jan 10, 4PM
|Jan 31 '''Thursday'''
|[http://users.math.yale.edu/~yd82/ Yen Do] (Yale)  
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)
|Convergence of Fourier series and multilinear analysis
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations  ]]
|Denissov
| Street
|
|-
|-
|'''Mon, Jan 13, 4pm'''
|Feb 1
|[http://math.stanford.edu/~wangyi/ Yi Wang] (Stanford)
| [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University)
|Isoperimetric Inequality and Q-curvature
|[[# TBA|  TBA  ]]
|Viaclovsky
| Qin
|
|-
|-
|'''Wen, Jan 15, 4pm'''
|Feb 5 '''Tuesday'''
|[http://www.maths.ox.ac.uk/people/profiles/wei.xiang Wei Xiang] (University of Oxford)
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)
|[[Colloquia#January 15: Wei Xiang (University of Oxford) |Conservation Laws and Shock Waves]]
|[[# TBA| TBA  ]]
|Bolotin
| Denisov
|
|-
|-
|'''Fri, Jan 17, 2:25PM, VV901'''
|Feb 8
|[http://www.math.dartmouth.edu/~gillmana/ Adrianna Gillman] (Dartmouth)  
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)
|Fast direct solvers for linear partial differential equations
|[[#Aaron Naber (Northwestern) |  A structure theory for spaces with lower Ricci curvature bounds  ]]
|Thiffeault
| Street
|
|-
|-
|'''Thu, Jan 23, 2:25, VV901'''
|Feb 15
|[http://www.stat.berkeley.edu/~mshkolni/ Mykhaylo Shkolnikov] (Berkeley)
|  
|[[Colloquia#Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) | Intertwinings, wave equations and growth models]]
|[[# TBA| TBA  ]]
|Seppalainen
|  
|
|-
|-
|Jan 24
|Feb 22
|[http://www.yanivplan.com/ Yaniv Plan] (Michigan)
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)
|[http://www.math.wisc.edu/wiki/index.php/Applied/ACMS/absS14#Yaniv_Plan_.28Michigan.29 Low-dimensionality in mathematical signal processing]
|[[# TBA|  TBA  ]]
|Thiffeault
| Erman and Corey
|
|-
|-
|Jan 31
|March 4
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture
|Underwater Networks: A Convergence of  Communications, Control and Sensing
|[[# TBA| TBA ]]
|Gurevich
| Kim
|
|-
|-
|Feb 7
|March 8
|David Treumann (Boston College)
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)
|Functoriality, Smith theory, and the Brauer homomorphism
|[[# TBA| TBA  ]]
|Street
| Erman
|-
|Feb 14
|[http://www.tc.columbia.edu/academics/index.htm?facid=apk16 Alexander Karp] (Columbia Teacher's College)
|History of Mathematics Education as a Research Field and as Magistra Vitae
|Kiselev
|-
|Feb 21
|[http://www.math.uci.edu/~szhitomi/ Svetlana Jitomirskaya] (UC-Irvine)
|Analytic quasiperiodic cocycles
|Kiselev
|-
|Feb 28
|[http://math.nyu.edu/faculty/shelley/ Michael Shelley] (Courant)
|Mathematical models of soft active materials
|Spagnolie
|-
|March 7
|[http://www.math.northwestern.edu/people/facultyProfiles/steve.zelditch.html Steve Zelditch] (Northwestern)
|
|
|Seeger
|-
|-
|March 14
|March 15
|
| Maksym Radziwill (Caltech)
|
|[[# TBA| TBA  ]]
|
| Marshall
|-
|<strike>March 21</strike>
|'''Spring Break'''
|No Colloquium
|
|
|-
|-
|'''March 26, 7pm, WID'''
|March 29
|[https://www.dpmms.cam.ac.uk/people/t.tokieda/ Tadashi Tokieda] (Cambridge)
| Jennifer Park (OSU)
|Toy models
|[[# TBA| TBA  ]]
|Thiffeault (C4 von Neumann Public Lecture)
| Marshall
|-
|March 28
|[http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)
|The Two Weight Inequality for the Hilbert Transform
|Street
|-
|April 4
|[http://www.math.brown.edu/~res/ Richard Schwartz] (Brown)
|
|
|Mari-Beffa
|-
|-
|April 11
|April 5
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)
| Ju-Lee Kim (MIT)
|[[# TBA|  TBA  ]]
| Gurevich
|
|
|Gurevich
|-
|-
|April 18 (Wasow Lecture)
|April 12
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)
|  Evitar Procaccia (TAMU)
|[[# TBA|  TBA  ]]
| Gurevich
|
|
|Seeger
|-
|-
|April 25
|April 19
|[http://www.charlesdoran.net Charles Doran](University of Alberta)
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)
|[[# TBA|  TBA  ]]
| Jean-Luc
|
|
|Song
|-
|-
|'''Monday, April 28''' (Distinguished Lecture)
|April 26
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)
|A mystery concerning algebraic plane curves
|[[# TBA|  TBA  ]]
|Maxim
| WIMAW
|-
|'''Tuesday, April 29''' (Distinguished Lecture)
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)
|Matrix factorizations old and new
|Maxim
|-
|'''Wednesday, April 30''' (Distinguished Lecture)
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)
|Easy solution of polynomial equations over finite fields
|Maxim
|-
|May 2
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)
|
|
|Boston
|-
|-
|May 9
|May 3
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)
| Tomasz Przebinda (Oklahoma)
|[[# TBA|  TBA  ]]
| Gurevich
|
|
|WIMAW
|}
|}


== Abstracts ==
== Abstracts ==


===January 6: Aaron Lauda (USC)===
===Beata Randrianantoanina (Miami University Ohio)===


''An introduction to diagrammatic categorification''
Title: Some nonlinear problems in the geometry of Banach spaces and their applications.


Categorification seeks to reveal a hidden layer in mathematical
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.
structures. Often the resulting structures can be combinatorially
complex objects making them difficult to study. One method of
overcoming this difficulty, that has proven very successful, is to
encode the categorification into a diagrammatic calculus that makes
computations simple and intuitive.


In this talk I will review some of the original considerations that
===Lillian Pierce (Duke University)===
led to the categorification philosophy.  We will examine how the
diagrammatic perspective has helped to produce new categorifications
having  profound applications to algebra, representation theory, and
low-dimensional topology.


===January 8: Karin Melnick (Maryland)===
Title: Short character sums


''Normal forms for local flows on parabolic geometries''
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.


The exponential map in Riemannian geometry conjugates the differential of an isometry at a point with the action of the isometry near the point. It thus provides a linear normal form for all isometries fixing a point. Conformal transformations are not linearizable in general. I will discuss a suite of normal forms theorems in conformal geometry and, more generally, for parabolic geometries, a rich family of geometric structures of which conformal, projective, and CR structures are examples.
===Dean Baskin (Texas A&M)===


===January 10, 4PM: Yen Do (Yale)===
Title: Radiation fields for wave equations


''Convergence of Fourier series and multilinear analysis''
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.


Almost everywhere convergence of the Fourier series of square
===Aaron Naber (Northwestern)===
integrable functions was first proved by Lennart Carleson in 1966, and
the proof has lead to deep developments in various multilinear settings.
In this talk I would like to introduce a brief history of the subject
and sketch some recent developments, some of these involve my joint
works with collaborators.


===Mon, January 13: Yi Wang (Stanford)===
Title: A structure theory for spaces with lower Ricci curvature bounds.


''Isoperimetric Inequality and Q-curvature''
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.


A well-known question in differential geometry is to prove the
isoperimetric inequality under intrinsic curvature conditions. In
dimension 2, the isoperimetric inequality is controlled by the integral of
the positive part of the Gaussian curvature. In my recent work, I prove
that on simply connected conformally flat manifolds of higher dimensions,
the role of the Gaussian curvature can be replaced by the Branson's
Q-curvature. The isoperimetric inequality is valid if the integral of the
Q-curvature is below a sharp threshold. Moreover, the isoperimetric
constant depends only on the integrals of the Q-curvature. The proof
relies on the theory of $A_p$ weights in harmonic analysis.


===January 15: Wei Xiang (University of Oxford)===
== Past Colloquia ==
 
''Conservation Laws and Shock Waves''
 
The study of continuum physics gave birth to the theory of quasilinear
systems in divergence form, commonly called conservation laws. In this
talk, conservation laws, the Euler equations, and the definition of the
corresponding weak solutions will be introduced first. Then a short history
of the studying of conservation laws and shock waves will be given. Finally
I would like to present two of our current research projects. One is on the
mathematical analysis of shock diffraction by convex cornered wedges, and
the other one is on the validation of weakly nonlinear geometric optics for
entropy solutions of nonlinear hyperbolic systems of conservation laws.
 
Fri, Jan 17, 2:25PM, VV901 Adrianna Gillman (Dartmouth) Fast direct solvers for linear partial differential equations
 
===Fri, Jan 17: Adrianna Gillman (Dartmouth) ===
''Fast direct solvers for linear partial differential equations''


The cost of solving a large linear system often determines what can and cannot be modeled computationally in many areas of science and engineering. Unlike Gaussian elimination which scales cubically with the respect to the number of unknowns, fast direct solvers construct an inverse of a linear in system with a cost that scales linearly or nearly linearly. The fast direct solvers presented in this talk are designed for the linear systems arising from the discretization of linear partial differential equations. These methods are more robust, versatile and stable than iterative schemes. Since an inverse is computed, additional right-hand sides can be processed rapidly. The talk will give the audience a brief introduction to the core ideas, an overview of recent advancements, and it will conclude with a sampling of challenging application examples including the scattering of waves.
[[Colloquia/Blank|Blank]]


===Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) ===
[[Colloquia/Fall2018|Fall 2018]]
''Intertwinings, wave equations and growth models''


We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to hyperbolic partial differential equations, symmetric polynomials and the corresponding random growth models. The talk will be devoted to these recent developments which also shed new light on some beautiful old examples of intertwinings. Based on joint works with Vadim Gorin and Soumik Pal.
[[Colloquia/Spring2018|Spring 2018]]


[[Colloquia/Fall2017|Fall 2017]]


===Jan 24: Yaniv Plan (Michigan) ===
[[Colloquia/Spring2017|Spring 2017]]
''Low-dimensionality in mathematical signal processing''


Natural images tend to be compressible, i.e., the amount of information needed to encode an image is small. This conciseness of information -- in other words, low dimensionality of the signal -- is found throughout a plethora of applications ranging from MRI to quantum state tomography. It is natural to ask: can the number of measurements needed to determine a signal be comparable with the information content? We explore this question under modern models of low-dimensionality and measurement acquisition.
[[Archived Fall 2016 Colloquia|Fall 2016]]


===Thur, Jan 30: Urbashi Mitra (USC) ===
[[Colloquia/Spring2016|Spring 2016]]
''Underwater Networks: A Convergence of  Communications, Control and Sensing''


The oceans cover 71% of the earth’s surface and represent one of the least explored frontiers, yet the oceans are integral to climate regulation, nutrient production, oil retrieval and transportation. Future scientific and technological efforts to achieve better understanding of oceans and water-related applications will rely heavily on our ability to communicate reliably between instruments, vehicles (manned and unmanned), human operators, platforms and sensors of all types.  Underwater acoustic communication techniques have not reached the same maturity as those for terrestrial radio communications and present some unique opportunities for new developments in information and communication theories.  Key features of underwater acoustic communication channels are examined: slow speed of propagation, significant delay spreads, sparse multi-path, time-variation and range-dependent available bandwidth.  Another unique feature of underwater networks is that the cost of communication, sensing and control are often comparable resulting in new tradeoffs between these activities.    We examine some new results (with implications wider than underwater systems) in  channel identifiability,  communicating over channels with state and cooperative game theory motivated by the underwater network application.
[[Colloquia/Fall2015|Fall 2015]]


===Feb 7: David Treumann (Boston College) ===
[[Colloquia/Spring2014|Spring 2015]]
''Functoriality, Smith theory, and the Brauer homomorphism''


Smith theory is a technique for relating the mod p homologies of X and of the fixed points of X by an automorphism of order p.  I will discuss how, in the setting of locally symmetric spaces, it provides an easy method (no trace formula) for lifting mod p automorphic forms from G^{sigma} to G, where G is an arithmetic group and sigma is an automorphism of G of order p.  This lift is compatible with Hecke actions via an analog of the Brauer homomorphism from modular representation theory, and is often compatible with a homomorphism of L-groups on the Galois side.  The talk is based on joint work with Akshay Venkatesh.  I hope understanding the talk will require less number theory background than understanding the abstract.
[[Colloquia/Fall2014|Fall 2014]]


===Feb 14: Alexander Karp (Columbia Teacher's College) ===
[[Colloquia/Spring2014|Spring 2014]]
''History of Mathematics Education as a Research Field and as Magistra Vitae''
 
The presentation will be based on the experience of putting together and editing the Handbook
on the History of Mathematics Education, which will be published by Springer in the near future.
This volume, which was prepared by a large group of researchers from different countries,
contains the first systematic account of the history of the development of mathematics education
in the whole world (and not just in some particular country or region). The editing of such a
book gave rise to thoughts about the methodology of research in this field, and also about what
constitutes an object of such research. These are the thoughts that the presenter intends to share
with his audience. From them, it is natural to pass to an analysis of the current situation and how
it might develop.
 
===Feb 21: Svetlana Jitomirskaya (UC-Irvine)===
''Analytic quasiperiodic cocycles''
 
Analytic quasiperiodic matrix cocycles is a simple dynamical
system, where analytic and dynamical properties are related in an
unexpected and remarkable way. We will focus on this relation, leading to
a new approach to the proof of joint continuity of Lyapunov exponents in
frequency and cocycle, at irrational frequency, first proved for SL(2,C)
cocycles in Bourgain-Jitom., 2002. The approach is powerful enough to
handle singular and multidimensional cocycles, thus establishing the above
continuity in full generality. This has important consequences including
a dense open version of Bochi-Viana theorem in this setting, with a
completely different underlying mechanism of the proof. A large part of
the talk  is a report on a joint work with A. Avila and C. Sadel.
 
 
===March 28: Michael Lacey (GA Tech) ===
''The Two Weight Inequality for the Hilbert Transform''
 
The individual two weight inequality for the Hilbert transform
asks for a real variable characterization of those pairs of weights
(u,v) for which the Hilbert transform H maps L^2(u) to L^2(v).
This question arises naturally in different settings, most famously
in work of Sarason. Answering in the positive a deep
conjecture of Nazarov-Treil-Volberg, the mapping property
of the Hilbert transform is characterized by a triple of conditions,
the first being a two-weight Poisson A2 on the pair of weights,
with a pair of so-called testing inequalities, uniform over all
intervals.  This is the first result of this type for a singular
integral operator.  (Joint work with Sawyer, C.-Y. Shen and Uriate-Tuero)
 
== Past Colloquia ==


[[Colloquia/Fall2013|Fall 2013]]
[[Colloquia/Fall2013|Fall 2013]]

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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