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<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == -->
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == -->


== Spring 2017 ==
==Fall 2017==
 
 
{| 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)
|-
|-
|'''Monday, January 9, 9th floor'''
|September 8
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)
|[[#Monday, January 9: Miklos Racz (Microsoft) |  ''Statistical inference in networks and genomics'' ]]
|[[#September 8: Tess Anderson (Madison) |  A Spherical Maximal Function along the Primes ]]
| Valko
| Tonghai Yang
|
|
|-
|-
|January 13, B239
|September 15
|  [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) |  ''Two dimensional water waves''  ]]
|  Angenent
|
|
|-
|[[#|   ]]
|'''Tuesday, January 17, B139'''
|  [https://web.math.princeton.edu/~fabiop/ Fabio Pusateri] (Princeton)
|[[#Tuesday, January 17:  Fabio Pusateri (Princeton) | ''The Water Waves problem''  ]]
|  Angenent
|
|
|-
|January 20, B239
|  [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)
|[[#Friday, January 20: Sam Raskin (MIT) |  Tempered local geometric Langlands  ]]
|  Arinkin
|
|
|-
|'''Monday, January 23, B239'''
|  [http://www.math.umd.edu/~tdarvas/ Tamas Darvas] (Maryland)
|[[#Monday, January 23: Tamas Darvas (Maryland) |  Geometry on the space of Kahler metrics and applications to canonical metrics ]]
|  Viaclovsky
|
|
|-
|-
|January 27
|September 22, '''9th floor'''
|Reserved for possible job talks
| Jaeyoung Byeon (KAIST)
|[[# |   ]]
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces  ]]
|
| Paul Rabinowitz & Chanwoo Kim
|
|
|-
|February 3, 9th floor
| Melanie Matchett Wood (UW-, Madison)
|[[#Friday, February 3: Melanie Matchett Wood (UW-Madison) | Random groups from generators and relations ]]
|
|
|
|
|-
|-
|Monday, February 6, B239 (Wasow lecture)
|October 6, '''9th floor'''
| Benoit Perthame (University of Paris VI)
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)
|[[#Monday, February 6: Benoit Perthame (University of Paris VI)| Models for neural networks; analysis, simulations and behaviour ]]  
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]
| Jin
| Nigel Boston
|
|  
|-
|-
|February 10 (WIMAW lecture), B239
|October 13, '''9th floor'''
| Alina Chertock (NC State Univ.)
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)
|[[#February 10: Alina Chertock (NC State Univ.) | Numerical Method for Chemotaxis and Related Models ]]  
|[[#October 13: Tomoko Kitagawa (Berkeley) |  A Global History of Mathematics from 1650 to 2017 ]]
| WIMAW
| Laurentiu Maxim
|
|
|-
|-
|February 17, 9th floor
|October 20
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU)  
| [[#Friday, February 17: Gustavo Ponce(UCSB) The Korteweg-de Vries equation vs. the Benjamin-Ono equation ]]  
|[[#October 13: Pierre Germain (Courant, NYU) |  Stability of the Couette flow in the Euler and Navier-Stokes equations ]]
| Minh-Binh Tran
| Minh-Binh Tran
|
|
|-
|-
|Monday, February 20, 9th floor
|October 27
| [https://lsa.umich.edu/math/people/postdoc-faculty/cochraam.html/ Amy Cochran] (Michigan)
|Stefanie Petermichl (Toulouse)
| [[#Monday, February 20, Amy Cochran (Michigan) |  Mathematical Classification of Bipolar Disorder ]]
|[[#October 27: Stefanie Petermichl (Toulouse) Higher order Journé commutators  ]]
| Smith
| Betsy Stovall, Andreas Seeger
|
|
|-
|-
|February 24
|November 1 (Wednesday)
|  
|[http://pages.iu.edu/~shaoguo/  Shaoming Guo] (Indiana)
|   |  
|[[#November 1: Shaoming Guo (Indiana)|  Parsell-Vinogradov systems in higher dimensions  ]]
|  
|Andreas Seeger
|
|
|
|
|-
|March 3, B239
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)
|[[#Friday, March 3, Ken Bromberg (Utah) | Renormalized volume for hyperbolic 3-manifolds ]]
|Dymarz
|
|
|-
|'''Tuesday, March 7, 4PM, 9th floor (Distinguished Lecture) '''
| [http://pages.iu.edu/~temam/  Roger Temam] (Indiana University)
|[[#Tuesday, March 7: Roger Temam (Indiana University)  |  On the mathematical  modeling of the humid atmosphere  ]]
|Smith
|
|
|-
|-
|'''Wednesday, March 8, 4PM, B239 '''
|November 17
| [http://pages.iu.edu/~temamRoger Temam] (Indiana University)  
| [http://math.mit.edu/~ylioYevgeny Liokumovich] (MIT)
|[[#Wednesday, March 8: Roger Temam (Indiana University) |  Weak solutions of the Shigesada-Kawasaki-Teramoto system. ]]
|[[#November 17:Yevgeny Liokumovich (MIT)|  Recent progress in Min-Max Theory ]]
|Smith
|Sean Paul
|
|-
|-
|March 10
|November 21, '''9th floor'''
| '''No Colloquium'''  
| [https://web.stanford.edu/~mkemeny/homepage.html  Michael Kemeny] (Stanford)
|[[# |   ]]
|[[#November 21:Michael Kemeny (Stanford)| The equations defining curves and moduli spaces  ]]
|
|Jordan Ellenberg
|
|
|-
|-
|'''Wednesday, March 15, 4PM, 9th floor'''
|November 24
|  [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)
|'''Thanksgiving break'''
|[[#Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) | Control and numerics: Recent progress and challenges ]]
| Jin & Minh-Binh Tran
|
|
|-
|March 17, B239
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)
|[[#Friday, March 17: Lillian Pierce (Duke University) | p-torsion in class groups of number fields of arbitrary degree ]]
| M. Matchett Wood
|
|
|-
|-
|March 24
|November 27,
'''Spring Break'''
| [http://www.math.harvard.edu/~tcollins/homepage.html Tristan Collins] (Harvard)
|[[# |   ]]
|[[#November 27:Tristan Collins (Harvard)| The J-equation and stability  ]]
|Sean Paul
|
|
|
|
|-
|-
|'''Wednesday, March 29  at 3:30PM (Wasow)'''
|December 5 (Tuesday)
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU)  
| [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)
|[[ #Wednesday, March 29: Sylvia Serfaty (NYU) | Microscopic description of Coulomb-type systems ]]
|[[#December 5: Ryan Hynd (U Penn)| Adhesion dynamics and the sticky particle system]]
|Tran
|Sigurd Angenent
|
|
|-
|-
|March 31
|December 8 (Friday)
| '''No Colloquium'''
| [https://cims.nyu.edu/~chennan/  Nan Chen] (Courant, NYU)
|[[# |   ]]
|[[#December 8: Nan Chen (Courant, NYU)| A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems  ]]
|Leslie Smith
|
|
|
|
|-
|-
|April 7
|December 11 (Monday)
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]
| [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)
|[[#Schenck Hyperplane Arrangements: Algebra, Combinatorics, Topology  ]]
|[[#December 11: Connor Mooney (ETH Zurich)Regularity vs. Singularity for Elliptic and Parabolic Systems]]
|Erman
|Sigurd Angenent
|
|
|-
|-
|April 14
|December 13 (Wednesday)
| Wilfrid Gangbo
| [http://math.mit.edu/~blwilson/ Bobby Wilson] (MIT)
|[[# |   ]]
|[[#December 13: Bobby Wilson (MIT) | Projections in Banach Spaces and Harmonic Analysis ]]
|Feldman & Tran
|Andreas Seeger
|
|
|-
|-
|April 17
|December 15 (Friday) '''9th floor'''
| [http://math.stanford.edu/~vakil/ Ravi Vakil]
| [http://roy.lederman.name/ Roy Lederman] (Princeton)
|[[#Doodling | The Mathematics of Doodling (Public Lecture) ]]
|[[#December 15: Roy Lederman (Princeton) | Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM) ]]
|Erman
|Leslie Smith
|
|
|-
|-
|April 18
|December 18 (Monday) '''B115'''
| [http://math.stanford.edu/~vakil/ Ravi Vakil]
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)
|[[#CutPaste Cutting and Pasting in Algebraic Geometry  ]]
|[[#December 18: Jenny Wilson (Stanford)Stability in the homology of configuration spaces]]
|Erman
|Jordan Ellenberg
|
|-
|April 21
|
|
|
|
|-
|-
|April 28
|December 19 (Tuesday) '''9th floor'''
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou]
| [https://web.stanford.edu/~amwright/ Alex Wright] (Stanford)
|[[# TBATBA  ]]
|[[#December 19: Alex Wright (Stanford)Dynamics, geometry, and the moduli space of Riemann surfaces]]
|Li
|Jordan Ellenberg
|}
|}


==Fall 2017==
== Fall 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.
 
 
=== September 22: Jaeyoung Byeon (KAIST) ===
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.
 
===October 6: Jonathan Hauenstein (Notre Dame) ===
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.
 
===October 13: Tomoko Kitagawa (Berkeley) ===
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?
 
 
 
===October 20: Pierre Germain (Courant, NYU) ===
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).
 
===October 27: Stefanie Petermichl (Toulouse)===
Title: Higher order Journé commutators
 
Abstract: We consider questions that stem from operator theory via Hankel and
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.
 
 
===November 27:Tristan Collins (Harvard)===
Title: The J-equation and stability
 
Abstract: Donaldson and Chen introduced the J-functional in '99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point.  The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equation.  I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation.
 
===December 5: Ryan Hynd (U Penn)===
Title: Adhesion dynamics and the sticky particle system.
 
Abstract:  The sticky particle system expresses the conservation of mass and
momentum for a collection of particles that only interact via perfectly inelastic collisions. 
The equations were first considered in astronomy in a model for the expansion of
matter without pressure. These equations also play a central role in the theory of optimal
transport.  Namely, the geodesics in an appropriately metrized space of probability
measures correspond to solutions of the sticky particle system.  We will survey what is
known about solutions and discuss connections with Hamilton-Jacobi equations.
 
===December 8: Nan Chen (Courant, NYU)===
Title: A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems
 
Abstract:
A conditional Gaussian framework for uncertainty quantification, data assimilation and prediction of nonlinear turbulent dynamical systems will be introduced in this talk. Despite the conditional Gaussianity, the dynamics remain highly nonlinear and are able to capture strongly non-Gaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the real-time data assimilation and prediction.
 
The talk will include three applications of such conditional Gaussian framework. In the first part, a physics-constrained nonlinear stochastic model is developed, and is applied to predicting the Madden-Julian oscillation indices with strongly non-Gaussian intermittent features. The second part regards the state estimation and data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers. Rigorous analysis shows that an exponential increase in the number of tracers is required for reducing the uncertainty by a fixed amount. This indicates a practical information barrier. In the last part of the talk, an efficient statistically accurate algorithm is developed that is able to solve a rich class of high dimensional Fokker-Planck equation with strong non-Gaussian features and beat the curse of dimensions.
 
===December 11: Connor Mooney (ETH Zurich)===
Title: Regularity vs. Singularity for Elliptic and Parabolic Systems
 
Abstract:
Hilbert's 19th problem asks if minimizers of &ldquo;natural&rdquo; variational integrals are smooth. For the past century, this problem inspired fundamental regularity results for elliptic and parabolic PDEs. It also led to the construction of several beautiful counterexamples to regularity. The dichotomy of regularity vs. singularity is related to that of single PDE (the scalar case) vs. system of PDEs (the vectorial case), and low dimension vs. high dimension. I will discuss some interesting recent counterexamples to regularity in low-dimensional vectorial cases, as well as outstanding open problems. Some of this is joint work with O. Savin.
 
===December 13: Bobby Wilson (MIT)===
Title:  Projections in Banach Spaces and Harmonic Analysis
 
Abstract: In this talk, we will discuss the measure theoretic principles of orthogonal projections that follow from the classical Besicovitch-Federer projection theorem. The Besicovitch-Federer projection theorem offers a characterization of rectifiability of one-dimensional sets in R^d by the size of their projections to lines. We will focus on the validity of analogues to the Besicovitch-Federer projection theorem with respect to such sets in general Banach spaces. In particular, we will show that the projection theorem is false when the Banach space is infinite-dimensional and discuss related applications to questions in Harmonic Analysis. This is joint work with Marianna Csornyei and David Bate.
 
===December 15: Roy Lederman (Princeton)===
Title: Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM)
 
Abstract:
Cryo-EM is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson “for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution".
Cryo-electron microscopes produce a large number of very noisy two-dimensional projection images of individual frozen molecules. Unlike related methods, such as computed tomography (CT), the viewing direction of each image is unknown. The unknown directions, together with extreme levels of noise and additional technical factors, make the determination of the structure of molecules challenging.
While other methods for structure determination, such as x-ray crystallography and nuclear magnetic resonance (NMR), measure ensembles of molecules together, cryo-EM produces measurements of individual molecules. Therefore, cryo-EM could potentially be used to study mixtures of different conformations of molecules. Indeed, current algorithms have been very successful at analyzing homogeneous samples, and can recover some distinct conformations mixed in solutions, but, the determination of multiple conformations, and in particular, continuums of similar conformations (continuous heterogeneity), remains one of the open problems in cryo-EM.
I will discuss a one-dimensional discrete model problem, Heterogeneous Multireference Alignment, which captures many of the group properties and other mathematical properties of the cryo-EM problem. I will then discuss different components which we are introducing in order to address the problem of continuous heterogeneity in cryo-EM: 1. “hyper-molecules,” the mathematical formulation of truly continuously heterogeneous molecules, 2. computational and numerical tools for formulating associated priors, and 3. Bayesian algorithms for inverse problems with an unsupervised-learning component for recovering such hyper-molecules in cryo-EM.
 
===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"
{| cellpadding="8"
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!align="left" | host(s)
!align="left" | host(s)
|-
|-
|September 8
| March 16
| Tess Anderson (Madison)
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)
|[[# TBA|  TBA  ]]
| Yang
|
|-
|September 15
|
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| WIMAW
|
|
|-
|-
| '''Wednesday, September 20, LAA lecture
|April 4 (Wednesday)
| Andrew Stuart (Caltech)
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| Jin
| Craciun
|
|
|-
|-
|September 22
| April 6
|
| Reserved
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| Melanie
|
|
|-
|-
|September 29
| April 13
|
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| WIMAW
|
|
|-
|-
|October 6
| April 25 (Wednesday)
|
| Hitoshi Ishii (Waseda University) Wasow lecture
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| Tran
|
|
|-
|-
|October 13
|date
|
| person (institution)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| hosting faculty
|
|
|-
|-
|October 20
|date
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU)  
| person (institution)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| Minh-Binh Tran
| hosting faculty
|
|
|-
|-
|October 27
|date
|
| person (institution)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| hosting faculty
|
|
|-
|-
|November 3
|date
|
| person (institution)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| hosting faculty
|
|
|-
|-
|November 10
|date
| Reserved for possible job talks
| person (institution)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| hosting faculty
|
|
|-
|-
|November 17
|date
| Reserved for possible job talks
| person (institution)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| hosting faculty
|
|
|-
|-
|November 24
|date
|'''Thanksgiving break'''
| person (institution)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| hosting faculty
|
|
|-
|-
|December 1
|date
| Reserved for possible job talks
| person (institution)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| hosting faculty
|
|
|-
|-
|December 8
|date
| Reserved for possible job talks
| person (institution)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| hosting faculty
|
|
|
|-
|}
|}


== Abstracts ==
== Spring Abstracts ==
=== September 16: Po-Shen Loh (CMU) ===
Title: Directed paths: from Ramsey to Pseudorandomness


Abstract: Starting from an innocent Ramsey-theoretic question regarding directed
=== <DATE>: <PERSON> (INSTITUTION) ===
paths in graphs, we discover a series of rich and surprising connections
Title: <TITLE>
that lead into the theory around a fundamental result in Combinatorics:
Szemeredi's Regularity Lemma, which roughly states that every graph (no
matter how large) can be well-approximated by a bounded-complexity
pseudorandom object.  Using these relationships, we prove that every
coloring of the edges of the transitive N-vertex tournament using three
colors contains a directed path of length at least sqrt(N) e^{log^* N}
which entirely avoids some color.  The unusual function log^* is the
inverse function of the tower function (iterated exponentiation).


=== September 23: Gheorghe Craciun (UW-Madison) ===
Abstract: <ABSTRACT>
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture


Abstract:  The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics.


The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.
== Past Colloquia ==
 
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality.
 
=== September 30: Akos Magyar (University of Georgia) ===
Title: Geometric Ramsey theory
 
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.
 
=== October 14: Ling Long (LSU) ===
Title: Hypergeometric functions over finite fields
 
Abstract: Hypergeometric functions are special functions with lot of
symmetries.  In this talk, we will introduce hypergeometric functions over finite
fields, originally due to Greene, Katz and McCarthy, in a way that is
parallel to the classical hypergeometric functions, and discuss their
properties and applications to character sums and the arithmetic of
hypergeometric abelian varieties.
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.
 
=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===
Title: Three Miracles in Analysis
 
Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).
 
=== October 28: Linda Reichl (UT Austin) ===
Title: Microscopic hydrodynamic modes in a binary mixture
 
Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.
 
===Monday, October 31: Kathryn Mann (Berkeley) ===
Title: Groups acting on the circle
 
Abstract:  Given a group G and a manifold M, can one describe all the actions of G on M?  This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. 
 
In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others.  We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. 
 
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===
Title: Siegel's problem on small volume lattices
 
Abstract: We outline in very general terms the history and the proof of the identification
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3
Coxeter group extended by the involution preserving the symmetry of this
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.
This solves (in three dimensions) a problem posed by Siegel in 1945.  Siegel solved this problem in two dimensions by deriving the
signature formula identifying the (2,3,7)-triangle group as having minimal
co-area.
There are strong connections with arithmetic hyperbolic geometry in
the proof, and the result has applications in the maximal symmetry groups
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem
and Siegel's result do.
 
===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===
Title: Shapes of Julia Sets
 
Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded.  William Thurston asked "What are the possible shapes of polynomial Julia sets?"  For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name?  It turns out the answer to all of these is "yes!"  I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.
 
===November 18: Andrew Snowden (University of Michigan)===
Title: Recent progress in representation stability
 
Abstract:  Representation stability is a relatively new field that studies
somewhat exotic algebraic structures and exploits their properties to
prove results (often asymptotic in nature) about objects of interest.
I will describe some of the algebraic structures that appear (and
state some important results about them), give a sampling of some
notable applications (in group theory, topology, and algebraic
geometry), and mention some open problems in the area.
 
===Monday, November 21:  Mariya Soskova (University of Wisconsin-Madison)===
Title:  Definability in degree structures
 
Abstract:  Some incomputable sets are more incomputable than others. We use
Turing reducibility and enumeration reducibility to measure the
relative complexity of incomputable sets. By identifying sets of the
same complexity, we can associate to each reducibility a degree
structure: the partial order of the Turing degrees and the partial
order of the enumeration degrees. The two structures are related in
nontrivial ways. The first has an isomorphic copy in the second and
this isomorphic copy is an automorphism base. In 1969, Rogers asked a
series of questions about the two degree structures with a common
theme: definability. In this talk I will introduce the main concepts
and describe the work that was motivated by these questions.
 
===Friday, December 2:  Hao Shen (Columbia)===
Title:  Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?
 
Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.
 
===Monday, December 5:  Botong Wang (UW-Madison)===
Title:  Enumeration of points, lines, planes, etc.
 
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.
 
=== Friday, December 9: Aaron Brown (U Chicago) ===
''Lattice actions and recent progress in the Zimmer program''
 
Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds.  For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions.  In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. 
 
I will present some background, motivation, and selected previous results in the Zimmer program.  I will then explain two of my results within the Zimmer program:
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).
 
=== Monday, December 19: Andrew Zimmer (U Chicago) ===
''Metric spaces of non-positive curvature and applications in several complex variables''
 
Abstract:  In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps. Some of what I will talk about is joint work with Gautam Bharali.
 
=== Monday, January 9: Miklos Racz (Microsoft) ===
''Statistical inference in networks and genomics''
 
Abstract: From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas.
 
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.
 
=== Friday, January 13: Mihaela Ifrim (Berkeley) ===
''Two dimensional water waves''
 
The classical water-wave problem consists of solving the Euler equations in the presence of a free fluid surface (e.g the water-air interface). This talk will provide an overview of recent developments concerning the motion of a two dimensional incompressible fluid with a free surface. There is a wide range of problems that fall under the heading of water waves, depending on a number of assumptions that can be applied: surface tension, gravity, finite bottom, infinite bottom, rough bottom, etc., and combinations thereof. We will present the physical motivation for studying such problems, followed by the discussion of several interesting mathematical questions related to them. The first step in the analysis is the choice of coordinates, where multiple choices are available. Once the equations are derived we will discuss the main issues arising when analysing local well-posedness, as well as the long time behaviour of solutions with small, or small and localized data. In the last part of the talk we will introduce a new, very robust method which allows one to obtain enhanced lifespan bounds for the solutions. If time permits we will also introduce an alternative method to the scattering theory, which in some cases yields a straightforward route to proving global existence results and obtaining an asymptotic description of solutions. This is joint work with Daniel Tataru, and in part with John Hunter.
 
=== Tuesday, January 17:  Fabio Pusateri (Princeton) ===
''The Water Waves problem''
 
We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.
 
=== Friday, January 20: Sam Raskin (MIT) === 
''Tempered local geometric Langlands ''
 
The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local.
 
Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately explored.
 
The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture.
 
=== Monday, January 23: Tamas Darvas (Maryland) ===
''Geometry on the space of Kahler metrics and applications to canonical metrics''
 
A basic problem in Kahler geometry, going back to Calabi in the 50's, is to find Kahler
metrics with the best curvature properties, e.g., Einstein metrics. Such special metrics are
minimizers of well known functionals on the space of all Kahler metrics H. However these
functionals become convex only if an adequate geometry is chosen on H. One such choice of
Riemannian geometry was proposed by Mabuchi in the 80's, and was used to address a number of
uniqueness questions in the theory. In this talk I will present more general Finsler geometries on
H, that still enjoy many of the  properties that Mabuchi's geometry has, and I will give
applications related to existence of special Kahler metrics, including the recent resolution of
Tian's related properness conjectures. 
 
 
=== Friday, February 3: Melanie Matchett Wood (UW-Madison) ===
''Random groups from generators and relations''
 
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations.  We discuss this model in the case of abelian groups (starting with a free abelian group), and its relationship to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields.  We will explain a universality theorem, an analog of the central limit theorem for random groups, that says the resulting distribution of random groups is largely insensitive to the distribution from which the relations are chosen.  Finally, we discuss joint work with Yuan Liu on the non-abelian random groups built in this way, including the existence of a limit of the random groups as n goes to infinity. 
 
=== Monday, February 6: Benoit Perthame (University of Paris VI) ===
''Models for neural networks; analysis, simulations and behaviour''
 
Neurons exchange informations via discharges, propagated
by membrane potential,  which trigger firing of the many connected
neurons. How to describe large networks of such neurons? What are the properties of these mean-field equations?
How can such a network generate a spontaneous activity?
Such questions can be tackled using nonlinear integro-differential
equations. These are now classically used in the neuroscience community to describe
neuronal networks or neural assemblies. Among them, the best known is certainly
Wilson-Cowan's equation which
describe spiking rates arising in different brain locations.
 
Another classical model is the integrate-and-fire equation that describes
neurons through their voltage using a particular type of Fokker-Planck equations. Several mathematical results will be presented concerning existence, blow-up, convergence to steady state,
for the excitatory and inhibitory neurons, with or without refractory states. Conditions for the transition to spontaneous activity (periodic solutions) will be discussed.
 
One can also describe directly the spike time
distribution which seems to encode more directly the neuronal information. 
This leads to a structured population equation that describes
at time $t$ the probability to find a neuron with time $s$
elapsed since its last discharge.  Here, we can 
show that small or large connectivity
leads to desynchronization. For intermediate regimes, sustained
periodic activity occurs.
A common mathematical tool is the use of the relative entropy method.
 
This talk is based on works with K. Pakdaman and D. Salort, M. Caceres, J. A. Carrillo and D. Smets.
 
=== February 10: Alina Chertock (NC State Univ.) ===
''Numerical Method for Chemotaxis and Related Models''
 
Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.
 
In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxis–fluid system and will also be discussed.
 
 
=== Friday, February 17: Gustavo Ponce(UCSB) ===
 
''The Korteweg-de Vries equation vs. the Benjamin-Ono equation''
 
In this talk we shall study the <math>k</math>-generalized Korteweg-de Vries <math>(k</math>-KdV) equation
 
<math>\partial_t u + \partial_x^3u +u^k\,\partial_xu=0,\;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+, </math>
 
and the <math>k</math>-generalized Benjamin-Ono (<math>k</math>-BO) equation
 
<math>\partial_t u-\partial_x^2\mathcal {H} u+u^k\,\partial_x u=0, \;\;\;\;\;\;\;x,t\in\Bbb R,\, k\in \Bbb Z^+,</math>
 
where <math>\mathcal {H}</math> denotes the Hilbert transform,
 
<math>\mathcal {H} f(x)=\frac{1}{\pi}\, {p.v.}\big(\frac{1}{x}\ast f\big)(x)=(-i\,sgn(\xi) \widehat{f}(\xi))^{\vee}(x).</math>
 
The goal is to review and analyze results concerning solutions of the initial value properties associated to these equations.
These include a comparison of the  local and global well-posedness and unique continuation properties
as well as special features of the special solutions of these models.
 
=== Monday, February 20, Amy Cochran (Michigan) ===
''Mathematical Classification of Bipolar Disorder''
 
Bipolar disorder is a chronic disease of mood instability. Longitudinal patterns of mood are central to any patient description, but are condensed into simple attributes and categories. Although these provide a common language for clinicians, they are not supported by empirical evidence.  In this talk, I present patient-specific models of mood in  bipolar disorder that incorporate existing longitudinal data.  In the first part, I will describe mood as a Bayesian nonparametric hierarchical model that includes latent classes and patient-specific mood dynamics given by discrete-time Markov chains. These models are fit to weekly mood data, revealing three patient classes that differ significantly in attempted suicide rates, disability, and symptom chronicity. In the second part of the talk, I discuss how combined statistical inferences from a population do not support widely held assumptions (e.g. mood is one-dimensional, rhythmic, and/or multistable). I then present a stochastic differential equation model that does not make any of these assumptions.  I show that this model accurately describes the data and that it can be personalized to an individual.  Taken together, this work moves forward data-driven modeling approaches that can guide future research into precise clinical care and disease causes.
 
=== Friday, March 3, Ken Bromberg (Utah)===
"Renormalized volume for hyperbolic 3-manifolds"
 
Motivated by ideas in physics Krasnov and Schlenker defined the renormalized volume of a hyperbolic 3-manifold. This is a way of assigning a finite volume to a hyperbolic 3-manifold that has infinite volume in the usual sense. We will begin with some basic background on hyperbolic geometry and hyperbolic 3-manifolds before defining renormalized volume with the aim of explaining why this is a natural quantity to study from a mathematician’s perspective. At the end will discuss some joint results with M. Bridgeman and J. Brock.
 
=== Tuesday, March 7: Roger Temam (Indiana University) ===
''On the mathematical  modeling of the humid atmosphere''
 
The humid atmosphere is a multi-phase system, made of air, water vapor, cloud-condensate, and rain water (and possibly ice / snow, aerosols and other components). The possible changes of phase  due to evaporation and condensation make the equations nonlinear, non-continuous (and non-monotone) in the framework of nonlinear partial differential equations.
We will discuss some modeling aspects, and some issues of existence, uniqueness and regularity for the solutions of the considered problems, making use of convex analysis, variational inequalities, and quasi-variational inequalities.
 
=== Wednesday, March 8: Roger Temam (Indiana University) ===
''Weak solutions of the Shigesada-Kawasaki-Teramoto system''
 
We will present a result of existence of weak solutions to the Shigesada-Kawasaki-Teramoto system, in all dimensions. The method is based on new a priori estimates, the construction of approximate solutions and passage to the limit. The proof of existence is completely self-contained and does not rely on any earlier result.
Based on an article with Du Pham, to appear in Nonlinear Analysis.
 
=== Wednesday, March 15: Enrique Zuazua (Universidad Autónoma de Madrid) ===
''Control and numerics: Recent progress and challenges''
 
In most real life applications Mathematics not only face the challenge of modelling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design.
 
And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art on Mathematical and Numerical Analysis. Rather, it requires specific tools, adapted to the very features of the problems under consideration, since stable numerical methods for the forward resolution of a given model, do not necessarily lead to stable solvers of control and design problems.
 
In this lecture we will summarize some of the recent work developed in our group, motivated by different applications, that have led to different analytical and numerical methodologies to circumvent these difficulties.
 
The examples we shall consider are motivated by problems of different nature and lead to various new mathematical developments. We shall mainly focus on the following three topics:
 
- Inverse design for hyperbolic conservation laws,
 
- The turnpike property: control in long time intervals,
 
- Collective behavior: guidance by repulsion.
 
We shall also briefly discuss the convenience of using greedy algorithms when facing parameter-dependence problems.
 
This lecture has been conceived for a broad audience. Accordingly, unnecessary technicalities will be avoided.


[[Colloquia/Blank|Blank Colloquia]]


=== Friday, March 17: Lillian Pierce (Duke University) ===
[[Colloquia/Spring2017|Spring 2017]]
''P-torsion in class groups of number fields of arbitrary degree''
 
Abstract: Fix a number field K of degree n over the rationals, and a prime p, and consider the p-torsion subgroup of the class group of K. How big is it? It is conjectured that this p-torsion subgroup should be very small (in an appropriate sense), relative to the absolute discriminant of the field; this relates to the Cohen-Lenstra heuristics and various other arithmetic problems. So far it has proved extremely difficult even to beat the trivial bound, that is, to show that the p-torsion subgroup is noticeably smaller than the full class group. In 2007, Ellenberg and Venkatesh shaved a power off the trivial bound by assuming GRH. This talk will discuss several new, contrasting, methods that recover or improve on this bound for almost all members of certain infinite families of fields, without assuming GRH.
 
===  Wednesday, March 29: Sylvia Serfaty (NYU) ===
''Microscopic description of Coulomb-type systems''
 
We are interested in systems of points with Coulomb, logarithmic
or more generally Riesz interactions (i.e. inverse powers of the distance). They arise in various settings: an instance is the classical Coulomb gas which in some cases happens
to be a random matrix ensemble, another is vortices in the Ginzburg-Landau
model of superconductivity, where one observes in certain regimes the emergence of densely packed point vortices forming perfect triangular lattice patterns named
Abrikosov lattices, a third is the study of Fekete points which arise in approximation theory. After reviewing the motivations, we will take a point of view based on the detailed expansion of the interaction energy to describe the microscopic behavior of the systems. In particular a Central Limit Theorem for fluctuations and a Large Deviations Principle for the microscopic point processes are given.
This allows to observe the effect of the temperature as it gets very large or very small, and to connect with crystallization questions.
The main results are joint with Thomas Leblé and also based on previous works with Etienne Sandier, Nicolas Rougerie and Mircea Petrache.
 
 
===  Friday, April 7: Hal Schenck (UIUC) ===
''Hyperplane Arrangements: Algebra, Combinatorics, Topology''
 
A hyperplane arrangement is a collection of hyperplanes in affine space, usually the real or complex numbers. 
The complement X of the hypersurfaces has
very interesting topology. In 1980 Orlik and Solomon determined
that the cohomology ring is a quotient of an
exterior algebra, with a generator for each hyperplane.
Surprisingly, all relations are determined by the combinatorics
of the arrangement. Nevertheless, there remain many interesting
open questions, which involve a beautiful interplay of algebra,
combinatorics, geometry, and topology. I'll spend much of the
talk discussing this interplay, and close by discussing several
conjectures in the field, along with recent progress on those
conjectures, where the Bernstein-Gelfand-Gelfand correspondence
plays a key role. Joint work with Dan Cohen (LSU) and Alex
Suciu (Northeastern).
 
 
===  Monday, April 17: Ravi Vakil (Stanford) ===
''The Mathematics of Doodling''
 
Doodling has many mathematical aspects: patterns, shapes,  numbers, and more.  Not surprisingly, there is often some sophisticated and fun mathematics buried inside common doodles.  I'll begin by doodling, and see where it takes us.  It looks like play, but it reflects what mathematics is really about:  finding patterns in nature, explaining them, and extending them.  By the end, we'll have seen some important notions in geometry, topology, physics, and elsewhere; some fundamental ideas guiding the development of mathematics over the course of the last century;  and ongoing work continuing today.
 
 
===  Tuesday, April 18: Ravi Vakil (Stanford) ===
''Cutting and pasting in (algebraic) geometry''
 
Given some class of "geometric space", we can make a ring as follows.
 
<b> Additive Structure:</b>  When U is an open subset of X we set [X] = [U] + [U \ X].
 
<b> Multiplicative Structure:</b>  [X x Y] = [X][Y]
 
In the algebraic setting, this ring (the "Grothendieck ring of varieties") contains surprising "stabilization" structure, connecting geometry to arithmetic and topology.  I will discuss some remarkable statements about this ring (both known and conjectural), and present new statements (again, both known and conjectural).  A motivating example will be polynomials in one variable. This talk is intended for a broad audience.  This is joint work with Melanie Matchett Wood.
 
== Past Colloquia ==


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

Revision as of 19:56, 7 December 2017


Mathematics Colloquium

All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.


Fall 2017

Date Speaker Title Host(s)
September 8 Tess Anderson (Madison) A Spherical Maximal Function along the Primes Tonghai Yang
September 15
September 22, 9th floor Jaeyoung Byeon (KAIST) Patterns formation for elliptic systems with large interaction forces Paul Rabinowitz & Chanwoo Kim
October 6, 9th floor Jonathan Hauenstein (Notre Dame) Real solutions of polynomial equations Nigel Boston
October 13, 9th floor Tomoko L. Kitagawa (Berkeley) A Global History of Mathematics from 1650 to 2017 Laurentiu Maxim
October 20 Pierre Germain (Courant, NYU) Stability of the Couette flow in the Euler and Navier-Stokes equations Minh-Binh Tran
October 27 Stefanie Petermichl (Toulouse) Higher order Journé commutators Betsy Stovall, Andreas Seeger
November 1 (Wednesday) Shaoming Guo (Indiana) Parsell-Vinogradov systems in higher dimensions Andreas Seeger
November 17 Yevgeny Liokumovich (MIT) Recent progress in Min-Max Theory Sean Paul
November 21, 9th floor Michael Kemeny (Stanford) The equations defining curves and moduli spaces Jordan Ellenberg
November 24 Thanksgiving break
November 27, Tristan Collins (Harvard) The J-equation and stability Sean Paul
December 5 (Tuesday) Ryan Hynd (U Penn) Adhesion dynamics and the sticky particle system Sigurd Angenent
December 8 (Friday) Nan Chen (Courant, NYU) A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems Leslie Smith
December 11 (Monday) Connor Mooney (ETH Zurich) Regularity vs. Singularity for Elliptic and Parabolic Systems Sigurd Angenent
December 13 (Wednesday) Bobby Wilson (MIT) Projections in Banach Spaces and Harmonic Analysis Andreas Seeger
December 15 (Friday) 9th floor Roy Lederman (Princeton) Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM) Leslie Smith
December 18 (Monday) B115 Jenny Wilson (Stanford) Stability in the homology of configuration spaces Jordan Ellenberg
December 19 (Tuesday) 9th floor Alex Wright (Stanford) Dynamics, geometry, and the moduli space of Riemann surfaces Jordan Ellenberg

Fall 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.


September 22: Jaeyoung Byeon (KAIST)

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.

October 6: Jonathan Hauenstein (Notre Dame)

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.

October 13: Tomoko Kitagawa (Berkeley)

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?


October 20: Pierre Germain (Courant, NYU)

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).

October 27: Stefanie Petermichl (Toulouse)

Title: Higher order Journé commutators

Abstract: We consider questions that stem from operator theory via Hankel and 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.


November 27:Tristan Collins (Harvard)

Title: The J-equation and stability

Abstract: Donaldson and Chen introduced the J-functional in '99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point. The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equation. I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation.

December 5: Ryan Hynd (U Penn)

Title: Adhesion dynamics and the sticky particle system.

Abstract: The sticky particle system expresses the conservation of mass and momentum for a collection of particles that only interact via perfectly inelastic collisions. The equations were first considered in astronomy in a model for the expansion of matter without pressure. These equations also play a central role in the theory of optimal transport. Namely, the geodesics in an appropriately metrized space of probability measures correspond to solutions of the sticky particle system. We will survey what is known about solutions and discuss connections with Hamilton-Jacobi equations.

December 8: Nan Chen (Courant, NYU)

Title: A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems

Abstract: A conditional Gaussian framework for uncertainty quantification, data assimilation and prediction of nonlinear turbulent dynamical systems will be introduced in this talk. Despite the conditional Gaussianity, the dynamics remain highly nonlinear and are able to capture strongly non-Gaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the real-time data assimilation and prediction.

The talk will include three applications of such conditional Gaussian framework. In the first part, a physics-constrained nonlinear stochastic model is developed, and is applied to predicting the Madden-Julian oscillation indices with strongly non-Gaussian intermittent features. The second part regards the state estimation and data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers. Rigorous analysis shows that an exponential increase in the number of tracers is required for reducing the uncertainty by a fixed amount. This indicates a practical information barrier. In the last part of the talk, an efficient statistically accurate algorithm is developed that is able to solve a rich class of high dimensional Fokker-Planck equation with strong non-Gaussian features and beat the curse of dimensions.

December 11: Connor Mooney (ETH Zurich)

Title: Regularity vs. Singularity for Elliptic and Parabolic Systems

Abstract: Hilbert's 19th problem asks if minimizers of “natural” variational integrals are smooth. For the past century, this problem inspired fundamental regularity results for elliptic and parabolic PDEs. It also led to the construction of several beautiful counterexamples to regularity. The dichotomy of regularity vs. singularity is related to that of single PDE (the scalar case) vs. system of PDEs (the vectorial case), and low dimension vs. high dimension. I will discuss some interesting recent counterexamples to regularity in low-dimensional vectorial cases, as well as outstanding open problems. Some of this is joint work with O. Savin.

December 13: Bobby Wilson (MIT)

Title: Projections in Banach Spaces and Harmonic Analysis

Abstract: In this talk, we will discuss the measure theoretic principles of orthogonal projections that follow from the classical Besicovitch-Federer projection theorem. The Besicovitch-Federer projection theorem offers a characterization of rectifiability of one-dimensional sets in R^d by the size of their projections to lines. We will focus on the validity of analogues to the Besicovitch-Federer projection theorem with respect to such sets in general Banach spaces. In particular, we will show that the projection theorem is false when the Banach space is infinite-dimensional and discuss related applications to questions in Harmonic Analysis. This is joint work with Marianna Csornyei and David Bate.

December 15: Roy Lederman (Princeton)

Title: Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM)

Abstract: Cryo-EM is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson “for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution".

Cryo-electron microscopes produce a large number of very noisy two-dimensional projection images of individual frozen molecules. Unlike related methods, such as computed tomography (CT), the viewing direction of each image is unknown. The unknown directions, together with extreme levels of noise and additional technical factors, make the determination of the structure of molecules challenging.

While other methods for structure determination, such as x-ray crystallography and nuclear magnetic resonance (NMR), measure ensembles of molecules together, cryo-EM produces measurements of individual molecules. Therefore, cryo-EM could potentially be used to study mixtures of different conformations of molecules. Indeed, current algorithms have been very successful at analyzing homogeneous samples, and can recover some distinct conformations mixed in solutions, but, the determination of multiple conformations, and in particular, continuums of similar conformations (continuous heterogeneity), remains one of the open problems in cryo-EM.

I will discuss a one-dimensional discrete model problem, Heterogeneous Multireference Alignment, which captures many of the group properties and other mathematical properties of the cryo-EM problem. I will then discuss different components which we are introducing in order to address the problem of continuous heterogeneity in cryo-EM: 1. “hyper-molecules,” the mathematical formulation of truly continuously heterogeneous molecules, 2. computational and numerical tools for formulating associated priors, and 3. Bayesian algorithms for inverse problems with an unsupervised-learning component for recovering such hyper-molecules in cryo-EM.

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

date speaker title host(s)
March 16 Anne Gelb (Dartmouth) TBA WIMAW
April 4 (Wednesday) John Baez (UC Riverside) TBA Craciun
April 6 Reserved TBA Melanie
April 13 Jill Pipher (Brown) TBA WIMAW
April 25 (Wednesday) Hitoshi Ishii (Waseda University) Wasow lecture TBA Tran
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Spring Abstracts

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Past Colloquia

Blank Colloquia

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Spring 2015

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012