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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'''.


== Fall 2013 ==
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)
|-
|-
|Sept 6
|Jan 25
|[http://people.math.gatech.edu/~mbaker/ Matt Baker] (Georgia Institute of Technology)
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW
|Riemann-Roch for Graphs and Applications
|[[#Beata Randrianantoanina (Miami University Ohio) | Some nonlinear problems in the geometry of Banach spaces and their applications  ]]
|Ellenberg
| Tullia Dymarz
|-
|Sept 13
|[http://math.wisc.edu/~andrews/ Uri Andrews] (University of Wisconsin)
|
|
|-
|Sept 20
|[http://www.math.neu.edu/people/profile/valerio-toledano-laredo Valerio Toledano Laredo] (Northeastern)
|
|Gurevich
|-
|'''Wed, Sept 25, 2:30PM'''
|[http://mypage.iu.edu/~alindens/ Ayelet Lindenstrauss]
|
|Meyer
|-
|'''Wed, Sept 25''' (Distinguished lecture)
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)
|
|Gurevich
|-
|'''Thurs, Sept 26''' (Distinguished lecture)
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)
|
|Gurevich
|-
|Sept 27 (Distinguished lecture)
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)
|
|Gurevich
|-
|Oct 4
|[http://www.math.tamu.edu/~sottile/ Frank Sottile] (Texas A&M)
|
|Caldararu
|-
|Oct 11
|[http://math.uchicago.edu/~wilkinso/ Amie Wilkinson] (Chicago)
|
|WIMAW (Cladek)
|-
|Oct 15
|Reserved for a distinguished lecture
|
|Valko
|-
|<strike>Oct 18</strike>
|No colloquium due to the distinguished lecture
|
|
|-
|Oct 25
|[http://www.math.umn.edu/~garrett/ Paul Garrett] (Minnesota)
|
|Gurevich
|
|
|-
|Nov 1
|[http://www.cs.utexas.edu/~alewko/ Allison Lewko] (Microsoft Research New England)
|
|
|Stovall
|-
|-
|Nov 8
|Jan 30 '''Wednesday'''
|[http://www.math.cornell.edu/~riley/ Tim Riley] (Cornell)
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)
|[[#Lillian Pierce (Duke University) |  Short character sums  ]]
| Boston and Street
|
|
|Dymarz
|-
|-
|Nov 15 and later
|Jan 31 '''Thursday'''
|Reserved
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations  ]]
| Street
|
|
|Street
|}
== Spring 2014 ==
{| cellpadding="8"
!align="left" | date
!align="left" | speaker
!align="left" | title
!align="left" | host(s)
|-
|-
|Jan 24
|Feb 1
|
| [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University)
|
|[[# TBA|  TBA  ]]
| Qin
|
|
|-
|-
|Jan 31
|Feb 5 '''Tuesday'''
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)
|[[# TBA|  TBA  ]]
| Denisov
|
|
|Gurevich
|-
|-
|Feb 7
|Feb 8
|David Treumann (Boston College)
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)
|[[#Aaron Naber (Northwestern) |  A structure theory for spaces with lower Ricci curvature bounds  ]]
| Street
|
|
|Street
|-
|-
|Feb 14
|Feb 15
|
|  
|
|[[# TBA|  TBA  ]]
|  
|
|
|-
|-
|Feb 21
|Feb 22
|
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)
|
|[[# TBA|  TBA  ]]
| Erman and Corey
|
|
|-
|-
|Feb 28
|March 4
|
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture
|
|[[# TBA| TBA ]]
| Kim
|
|
|-
|-
|March 7
|March 8
|
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)
|
|[[# TBA|  TBA  ]]
| Erman
|
|
|-
|-
|March 14
|March 15
|
| Maksym Radziwill (Caltech)
|
|[[# TBA| TBA  ]]
|
| Marshall
|-
|<strike>March 21</strike>
|'''Spring Break'''
|No Colloquium
|
|
|-
|-
|March 28
|March 29
|[http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)
| Jennifer Park (OSU)
|The Two Weight Inequality for the Hilbert Transform
|[[# TBA| TBA  ]]
|Street
| Marshall
|-
|April 4
|[https://sites.google.com/site/katejuschenko/ Kate Jushchenko] (Northwestern)
|
|
|Dymarz
|-
|-
|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
|
|
|A. 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
|-
|-
|May 2
|April 26
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)
|[[# TBA|  TBA  ]]
| WIMAW
|
|
|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 ==


===Sep 6: Matt Baker (GA Tech) ===
===Beata Randrianantoanina (Miami University Ohio)===
''Riemann-Roch for Graphs and Applications''
 
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 ==
 
[[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]]


We will begin by formulating the Riemann-Roch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a Riemann-Roch theorem for tropical curves, proved by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof of the Brill-Noether theorem in algebraic geometry (work of by Cools-Draisma-Payne-Robeva), a "volume-theoretic proof" of Kirchhoff's Matrix-Tree Theorem (work of An, Kuperberg, Shokrieh, and the speaker), and a new Chabauty-Coleman style bound for the number of rational points on an algebraic curve over the rationals (work of Katz and Zureick-Brown).
[[Colloquia/Fall2014|Fall 2014]]


===March 28: Michael Lacey (GA Tech) ===
[[Colloquia/Spring2014|Spring 2014]]
''The Two Weight Inequality for the Hilbert Transform ''


The individual two weight inequality for the Hilbert transform
[[Colloquia/Fall2013|Fall 2013]]
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 talks ==
[[Colloquia 2012-2013|Spring 2013]]


Last year's schedule: [[Colloquia 2012-2013]]
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]

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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