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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]].


==Fall 2017==
==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 8
|Jan 25
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW
|[[#September 8: Tess Anderson (Madison) |  A Spherical Maximal Function along the Primes ]]
|[[#Beata Randrianantoanina (Miami University Ohio) |  Some nonlinear problems in the geometry of Banach spaces and their applications ]]
| Yang
| Tullia Dymarz
|
|
|-
|-
|September 15
|Jan 30 '''Wednesday'''
|
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)
|[[#|  ]]
|[[#Lillian Pierce (Duke University) | Short character sums   ]]
|
| Boston and Street
|
|
|-
|Jan 31 '''Thursday'''
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations  ]]
| Street
|
|
|-
|-
|September 22, '''9th floor'''
|Feb 1
| Jaeyoung Byeon (KAIST)
| [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University)
|[[#September 22: Jaeyoung Byeon (KAIST) |  Patterns formation for elliptic systems with large interaction forces ]]
|[[# TBA|  TBA ]]
| Rabinowitz & Kim
| Qin
|
|
|-
|-
|September 29
|Feb 5 '''Tuesday'''
|
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| Denisov
|
|
|-
|Feb 8
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)
|[[#Aaron Naber (Northwestern) |  A structure theory for spaces with lower Ricci curvature bounds  ]]
| Street
|
|
|-
|-
|October 6
|Feb 15
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)
|[[#October 6: Jonathan Hauenstein (Notre Dame) |  Real solutions of polynomial equations ]]
| Boston
|  
|  
|[[# TBA|  TBA  ]]
|
|
|-
|-
|October 13
|Feb 22
|Tomoko L. Kitagawa (Berkeley)
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| Max
| Erman and Corey
|
|
|-
|-
|October 20
|March 4
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU)  
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture
|[[# TBA| TBA ]]
|[[# TBA| TBA ]]
| Minh-Binh Tran
| Kim
|
|
|-
|-
|October 27
|March 8
|Stefanie Petermichl (Toulouse)
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| Stovall, Seeger
| Erman
|
|
|-
|-
|We, November 1
|March 15
|Shaoming Guo (Indiana)
| Maksym Radziwill (Caltech)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| Marshall
|
|
|-
|-
|November 3
|March 29
|Robert Laugwitz  (Rutgers)
| Jennifer Park (OSU)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|Dima Arinkin
| Marshall
|
|
|
|-
|-
|November 10
|April 5
| Reserved for possible job talks
| Ju-Lee Kim (MIT)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| Gurevich
|
|
|-
|-
|November 17
|April 12
| Reserved for possible job talks
| Evitar Procaccia (TAMU)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| Gurevich
|
|
|-
|-
|November 24
|April 19
|'''Thanksgiving break'''
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| Jean-Luc
|
|
|-
|-
|December 1
|April 26
| Reserved for possible job talks
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| WIMAW
|
|
|-
|-
|December 8
|May 3
| Reserved for possible job talks
| Tomasz Przebinda (Oklahoma)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| Gurevich
|
|
|
|}
|-


|}
== Abstracts ==


== Fall Abstracts ==
===Beata Randrianantoanina (Miami University Ohio)===
=== September 8: Tess Anderson (Madison) ===
Title: A Spherical Maximal Function along the Primes


Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior.  The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example.  In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to.  We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory.  This is joint work with Cook, Hughes, and Kumchev.
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.


=== September 22: Jaeyoung Byeon (KAIST) ===
===Lillian Pierce (Duke University)===
Title: Patterns formation for elliptic systems with large interaction forces


Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions.  The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.
Title: Short character sums


===October 6: Jonathan Hauenstein (Notre Dame) ===
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.
Title: Real solutions of polynomial equations


Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions.  Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application.  This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.
===Dean Baskin (Texas A&M)===


== Spring 2018 ==
Title: Radiation fields for wave equations


{| cellpadding="8"
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.
!align="left" | date 
!align="left" | speaker
!align="left" | title
!align="left" | host(s)
|-
| April 6
| Reserved
|[[# TBA|  TBA  ]]
| Melanie
|
|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
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|date
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|[[# TBA|  TBA  ]]
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|}


== Spring Abstracts ==
===Aaron Naber (Northwestern)===


=== <DATE>: <PERSON> (INSTITUTION) ===
Title: A structure theory for spaces with lower Ricci curvature bounds.
Title: <TITLE>


Abstract: <ABSTRACT>
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 ==
== Past Colloquia ==


[[Colloquia/Blank|Blank Colloquia]]
[[Colloquia/Blank|Blank]]
 
[[Colloquia/Fall2018|Fall 2018]]
 
[[Colloquia/Spring2018|Spring 2018]]
 
[[Colloquia/Fall2017|Fall 2017]]


[[Colloquia/Spring2017|Spring 2017]]
[[Colloquia/Spring2017|Spring 2017]]

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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