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__NOTOC__
= 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,  '''9th floor'''
|Feb 15
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)
|  
|[[#October 6: Jonathan Hauenstein (Notre Dame) |  Real solutions of polynomial equations ]]
|[[# TBA|  TBA  ]]
| Boston
|  
|  
|-
|October 13, '''9th floor'''
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)
|[[#October 13: Tomoko Kitagawa (Berkeley) |  A Global History of Mathematics from 1650 to 2017 ]]
| Max
|
|
|-
|-
|October 20
|Feb 22
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU)  
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)
|[[#October 13: Pierre Germain (Courant, NYU) |  Stability of the Couette flow in the Euler and Navier-Stokes equations ]]
|[[# TBA|  TBA  ]]
| Minh-Binh Tran
| Erman and Corey
|
|
|-
|-
|October 27
|March 4
|Stefanie Petermichl (Toulouse)
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture
|[[#October 27: Stefanie Petermichl (Toulouse)  | Higher order Journé commutators  ]]
|[[# TBA| TBA ]]
| Stovall, Seeger
| Kim
|
|
|-
|-
|We, November 1,
|March 8
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)
|[[#November 1: Shaoming Guo (Indiana)|  Parsell-Vinogradov systems in higher dimensions ]]
|[[# TBA|  TBA ]]
|Seeger
| Erman
|
|
|
|
|
|
|-
|-
|November 17
|March 15
| [http://math.mit.edu/~ylio/  Yevgeny Liokumovich] (MIT)
| Maksym Radziwill (Caltech)
|[[#November 17:Yevgeny Liokumovich (MIT)|  Recent progress in Min-Max Theory  ]]
|[[# TBA|  TBA ]]
|Sean Paul
| Marshall
|-
|November 21, '''9th floor'''
| [https://web.stanford.edu/~mkemeny/homepage.html  Michael Kemeny] (Stanford)
|[[#November 21:Michael Kemeny (Stanford)|  The equations defining curves and moduli spaces ]]
|Jordan Ellenberg
|
|
|-
|-
|November 24
|March 29
|'''Thanksgiving break'''
| Jennifer Park (OSU)
|
|[[# TBA|  TBA  ]]
|
| Marshall
|
|
|-
|-
|December 1
|April 5
| Reserved for possible job talks
| Ju-Lee Kim (MIT)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| Gurevich
|
|
|-
|-
|December 5 (Wednesday)
|April 12
| [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)
|  Evitar Procaccia (TAMU)
|[[#December 5: Ryan Hynd (U Penn)|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| Gurevich
|
|
|-
|-
|December 8
|April 19
| Reserved for possible job talks
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| Jean-Luc
|
|
|-
|-
|December 11 (Monday)
|April 26
| [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)
|[[#December 11: Connor Mooney (ETH Zurich)|  Finite time blowup for parabolic systems in the plane]]
|[[# TBA|  TBA  ]]
| WIMAW
|
|
|-
|-
|December 18 (Monday)
|May 3
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)
| Tomasz Przebinda (Oklahoma)
|[[#December 18: Jenny Wilson (Stanford)|  Stability in the homology of configuration spaces]]
|[[# TBA|  TBA  ]]
| Gurevich
|
|
|
|-
|December 19 (Tuesday)
| [https://web.stanford.edu/~amwright/  Alex Wright] (Stanford)
|[[#December 19: Alex Wright (Stanford)|  Dynamics, geometry, and the moduli space of Riemann surfaces]]
|Jordan Ellenberg
|}
|}


== Fall Abstracts ==
== Abstracts ==
=== 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.
===Beata Randrianantoanina (Miami University Ohio)===


Title: Some nonlinear problems in the geometry of Banach spaces and their applications.


=== September 22: Jaeyoung Byeon (KAIST) ===
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.
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.
===Lillian Pierce (Duke University)===


===October 6: Jonathan Hauenstein (Notre Dame) ===
Title: Short character sums
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.
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.


===October 13: Tomoko Kitagawa (Berkeley) ===
===Dean Baskin (Texas A&M)===
Title: A Global History of Mathematics from 1650 to 2017


Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?
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)===


===October 20: Pierre Germain (Courant, NYU) ===
Title: A structure theory for spaces with lower Ricci curvature bounds.
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations


Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).
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.


===October 27: Stefanie Petermichl (Toulouse)===
Title: Higher order Journé commutators


Abstract: We consider questions that stem from operator theory via Hankel and
== Past Colloquia ==
Toeplitz forms and target (weak) factorisation of Hardy spaces. In
more basic terms, let us consider a function on the unit circle in its
Fourier representation. Let P_+ denote the projection onto
non-negative and P_- onto negative frequencies. Let b denote
multiplication by the symbol function b. It is a classical theorem by
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and
only if b is in an appropriate space of functions of bounded mean
oscillation. The necessity makes use of a classical factorisation
theorem of complex function theory on the disk. This type of question
can be reformulated in terms of commutators [b,H]=bH-Hb with the
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such
as in the real variable setting, in the multi-parameter setting or
other, these classifications can be very difficult.
 
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of
spaces of bounded mean oscillation via L^p boundedness of commutators.
We present here an endpoint to this theory, bringing all such
characterisation results under one roof.
 
The tools used go deep into modern advances in dyadic harmonic
analysis, while preserving the Ansatz from classical operator theory.
 
===November 1: Shaoming Guo (Indiana) ===
Title: Parsell-Vinogradov systems in higher dimensions
 
Abstract:
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.
 
===November 17:Yevgeny Liokumovich (MIT)===
Title: Recent progress in Min-Max Theory
 
Abstract:
Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?
 
===November 21:Michael Kemeny (Stanford)===
Title: The equations defining curves and moduli spaces
 
Abstract:
A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in
algebraic geometry is to give a qualitative description of the equations defining a variety, together with
the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures
made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures,
which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.
 
 
===December 5: Ryan Hynd (U Penn)===
Title: TBA.
 
===December 11: Connor Mooney (ETH Zurich)===
Title: Finite time blowup for parabolic systems in the plane
 
Abstract:
Hilbert's 19th problem asks about the smoothness of solutions to nonlinear elliptic PDE that arise in the calculus of variations. This problem leads naturally to the question of continuity for solutions to linear elliptic and parabolic systems with measurable coefficients. We will first discuss some classical results on this topic, including Morrey's result that solutions to linear elliptic systems in two dimensions are continuous. We will then discuss surprising recent examples of finite time blowup from smooth data for linear parabolic systems in two dimensions, and important open problems.
 
 
===December 18: Jenny Wilson (Stanford)===
Title: Stability in the homology of configuration spaces
 
Abstract:
This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.
 
===December 19: Alex Wright (Stanford)===
Title: Dynamics, geometry, and the moduli space of Riemann surfaces
 
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel.
 
== Spring 2018 ==
 
{| cellpadding="8"
!align="left" | date 
!align="left" | speaker
!align="left" | title
!align="left" | host(s)
|-
| March 16
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)
|[[# TBA|  TBA  ]]
| WIMAW
|
|-
|April 4 (Wednesday)
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)
|[[# TBA|  TBA  ]]
| Craciun
|
|-
| April 6
| Reserved
|[[# TBA|  TBA  ]]
| Melanie
|
|-
| April 13
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)
|[[# TBA|  TBA  ]]
| WIMAW
|
|-
| April 25 (Wednesday)
| Hitoshi Ishii (Waseda University) Wasow lecture
|[[# TBA|  TBA  ]]
| Tran
|
|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
|
|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
|
|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
|
|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
|
|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
|
|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
|
|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
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|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
|
|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
|
|}
 
== Spring Abstracts ==


=== <DATE>: <PERSON> (INSTITUTION) ===
[[Colloquia/Blank|Blank]]
Title: <TITLE>


Abstract: <ABSTRACT>
[[Colloquia/Fall2018|Fall 2018]]


[[Colloquia/Spring2018|Spring 2018]]


== Past Colloquia ==
[[Colloquia/Fall2017|Fall 2017]]
 
[[Colloquia/Blank|Blank Colloquia]]


[[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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