Colloquia/Fall18: Difference between revisions

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


== Fall 2016  ==
==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)
|-
|-
|September 9
|September 8
|  
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)
|[[#  |    ]]
|[[#September 8: Tess Anderson (Madison) |  A Spherical Maximal Function along the Primes ]]
|
| Yang
|
|
|-
|-
|September 16
|September 15
|[http://www.math.cmu.edu/~ploh/ Po-Shen Loh] (CMU)
|Directed paths: from Ramsey to Pseudorandomness
|Ellenberg
|
|
|-
|[[#|   ]]
|September 23
| [http://www.math.wisc.edu/~craciun/ Gheorghe Craciun] (UW-Madison)
|Toric Differential Inclusions and a Proof of the Global Attractor Conjecture
| Street
|[[# |   ]]
|-
|September 30
|[http://math.uga.edu/~magyar/ Akos Magyar] (University of Georgia)
|Geometric Ramsey theory
| Cook
|
|
|-
|October 7
|
|[[# |    ]]
|
|
|
|
|-
|-
|October 14
|September 22, '''9th floor'''
| [https://www.math.lsu.edu/~llong/ Ling Long] (LSU)
| Jaeyoung Byeon (KAIST)
|Hypergeometric functions over finite fields
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces  ]]
| Yang
| Rabinowitz & Kim
|
|
|-
|-
|October 21
|September 29
|'''No colloquium this week'''
|
|[[#  |    ]]
|[[# TBA|  TBA ]]
|
|
|
|
|-
|-
|'''Tuesday, October 25, 9th floor'''
|October 6,  '''9th floor'''
|[http://users.math.yale.edu/users/steinerberger/ Stefan Steinerberger] (Yale)
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)
|Three Miracles in Analysis
|[[#October 6: Jonathan Hauenstein (Notre Dame) |  Real solutions of polynomial equations ]]
|Seeger
| 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 28, 9th floor
|October 20
|  [http://order.ph.utexas.edu/people/Reichl.htm Linda Reichl] (UT Austin)
|  [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU)  
|Microscopic hydrodynamic modes in a binary mixture
|[[#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, October 31, B239'''
|October 27
| [https://math.berkeley.edu/~kpmann/ Kathryn Mann] (Berkeley)
|Stefanie Petermichl (Toulouse)
|Groups acting on the circle
|[[# TBA|  TBA  ]]
|Smith
| Stovall, Seeger
|
|
|-
|-
|November 4
|We, November 1
|Shaoming Guo (Indiana)
|[[# TBA|  TBA  ]]
|
|
|
|
|  
|-
|November 3
|[[# TBA|  TBA  ]]
|
|
|-
|'''Monday, November 7 at 4:30, 9th floor''' ([http://www.ams.org/meetings/lectures/maclaurin-lectures AMS Maclaurin lecture])
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (New Zealand Institute for Advanced Study)
|Siegel's problem on small volume lattices
| Marshall
|
|
|-
|-
|November 11
|November 10
| Reserved for possible job talks
| Reserved for possible job talks
|[[# |   ]]
|[[# TBA| TBA  ]]
|
|
|
|
|-
|-
|'''Wednesday, November 16, 9th floor'''
|November 17
[http://math.uchicago.edu/~klindsey/ Kathryn Lindsey] (U Chicago)
| Reserved for possible job talks
|Shapes of Julia Sets
|[[# TBA|  TBA ]]
|Michell
|
|
|
|-
|-
|November 18, B239
|November 24
|[http://www-personal.umich.edu/~asnowden/ Andrew Snowden] (University of Michigan)
|'''Thanksgiving break'''
|Recent progress in representation stability
|[[# TBA| TBA  ]]
|Ellenberg
|
|
|-
|'''Monday, November 21, 9th floor'''
|[https://www.fmi.uni-sofia.bg/fmi/logic/msoskova/index.html Mariya Soskova] (University of Wisconsin-Madison)
|Definability in degree structures
|Smith
|
|
|-
|-
|November 25
|December 1
| '''Thanksgiving break'''
| Reserved for possible job talks
|[[# |   ]]
|[[# TBA| TBA  ]]
|
|
|
|
|-
|-
|December 2, 9th floor
|December 8
| [http://math.columbia.edu/~hshen/ Hao Shen] (Columbia)
| Reserved for possible job talks
|[[#Friday, December 2: Hao Shen (Columbia) | ''Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?'']]
|[[# TBA|  TBA ]]
|Roch
|
|
|-
|'''Monday, December 5, B239'''
|  [https://www.math.wisc.edu/~wang/ Botong Wang] (UW Madison)
|[[#Monday, December 5: Botong Wang  (UW-Madison) | ''Enumeration of points, lines, planes, etc.'']]
|Maxim
|
|
|-
|-
|December 9, B239
 
|  [http://math.uchicago.edu/~awbrown/ Aaron Brown] (U Chicago)
| [[#Friday, December 9: Aaron Brown  (U Chicago) | ''Lattice actions and recent progress in the Zimmer program'']]
|Kent
|-
|'''Monday, December 19, B115'''
|  [http://math.uchicago.edu/~andrew.zimmer/ Andrew Zimmer] (U Chicago)
| Metric spaces of non-positive curvature and applications in several complex variables
|Gong
|}
|}


== Spring 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 13: 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).
 
== Spring 2018 ==
 
{| cellpadding="8"
{| cellpadding="8"
!align="left" | date   
!align="left" | date   
Line 150: Line 143:
!align="left" | host(s)
!align="left" | host(s)
|-
|-
|'''Monday, January 9, 9th floor'''
| March 16
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)
|[[#Monday, January 9:  Miklos Racz (Microsoft) ''Statistical inference in networks and genomics'' ]]
|[[# TBATBA ]]
| Valko
| WIMAW
|
|
|-
|-
|January 13, B239
|April 4 (Wednesday)
| [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) ''Two dimensional water waves'' ]]
|[[# TBATBA ]]
| Angenent
| Craciun
|
|
|-
|-
|'''Tuesday, January 17, B139'''
| April 6
| [https://web.math.princeton.edu/~fabiop/ Fabio Pusateri] (Princeton)
| Reserved
|[[#Tuesday, January 17:  Fabio Pusateri (Princeton) ''The Water Waves problem'' ]]
|[[# TBATBA ]]
| Angenent
| Melanie
|
|
|-
|-
|January 20
| April 13
| [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)
|[[#Friday, January 20: Sam Raskin (MIT) |  Tempered local geometric Langlands  ]]
|[[# TBA|  TBA  ]]
|  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
|Reserved for possible job talks
|[[# |    ]]
|
|-
|February 3
|
|[[#  TBA|  TBA  ]]
|
|
|-
|February 6 (Wasow lecture)
| Benoit Perthame (University of Paris VI)
|[[# TBA|  TBA ]]
| Jin
|  
|-
|February 10 (WIMAW lecture)
| Alina Chertock (NC State Univ.)
|[[# |  ]]  
| WIMAW
| WIMAW
|
|
|-
|-
|February 17
|date
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)
| person (institution)
|[[#   |     ]]
|[[# TBA| TBA  ]]
| Minh-Binh Tran
| hosting faculty
|
|
|-
|-
|February 24
|date
|  
| person (institution)
|[[#  |    ]]
|[[# TBA|  TBA ]]
|  
| hosting faculty
|
|
|-
|-
|March 3
|date
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)
| person (institution)
|[[# |   ]]
|[[# TBA| TBA  ]]
|Dymarz
| hosting faculty
|
|
|-
|-
|Tuesday, March 7, 4PM (Distinguished Lecture)
|date
| [http://pages.iu.edu/~temam/  Roger Temam] (Indiana University)  
| person (institution)
|[[#  |    ]]
|[[# TBA|  TBA ]]
|Smith
| hosting faculty
|
|
|-
|-
|Wednesday, March 8, 2:25PM
|date
| [http://pages.iu.edu/~temam/  Roger Temam] (Indiana University)  
| person (institution)
|[[#  |    ]]
|[[# TBA|  TBA ]]
|Smith
| hosting faculty
|
|
|-
|-
|March 10
|date
| '''No Colloquium'''
| person (institution)
|[[# |   ]]
|[[# TBA| TBA  ]]
|
| hosting faculty
|
|
|-
|-
|Wednesday, March 15, 4PM
|date
| [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)
| person (institution)
|[[#   TBA|   TBA  ]]
|[[# TBA| TBA  ]]
| Jin & Minh-Binh Tran
| hosting faculty
|
|
|-
|-
|March 17
|date
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)  
| person (institution)
| TBA
|[[# TBA|  TBA ]]
| M. Matchett Wood
| hosting faculty
|
|
|-
|-
|March 24
|date
| '''Spring Break'''
| person (institution)
|[[# |   ]]
|[[# TBA| TBA  ]]
|
| hosting faculty
|
|
|-
|-
|Wednesday, March 29 (Wasow)
|date
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU)  
| person (institution)
|[[# TBA|   TBA]]
|[[# TBA| TBA  ]]
|Tran
| hosting faculty
|
|-
|March 31
| '''No Colloquium'''
|[[# |    ]]
|
|
|-
|April 7
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]
|[[# |    ]]
|Erman
|
|-
|April 14
| Wilfrid Gangbo
|[[# |    ]]
|Feldman & Tran
|
|
|-
|April 21
|  [http://www.math.stonybrook.edu/~mde/ Mark Andrea de Cataldo]  (Stony Brook)
|TBA
| Maxim
|
|-
|April 28
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] 
|[[# TBA|  TBA  ]]
|Li
|}
|}


== 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. 
[[Colloquia/Blank|Blank Colloquia]]


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. 
[[Colloquia/Spring2017|Spring 2017]]


===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===
[[Archived Fall 2016 Colloquia|Fall 2016]]
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. 
 
 
 
== Past Colloquia ==


[[Colloquia/Spring2016|Spring 2016]]
[[Colloquia/Spring2016|Spring 2016]]

Revision as of 20:30, 20 October 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 Yang
September 15
September 22, 9th floor Jaeyoung Byeon (KAIST) Patterns formation for elliptic systems with large interaction forces Rabinowitz & Kim
September 29 TBA
October 6, 9th floor Jonathan Hauenstein (Notre Dame) Real solutions of polynomial equations Boston
October 13, 9th floor Tomoko L. Kitagawa (Berkeley) A Global History of Mathematics from 1650 to 2017 Max
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) TBA Stovall, Seeger
We, November 1 Shaoming Guo (Indiana) TBA
November 3 TBA
November 10 Reserved for possible job talks TBA
November 17 Reserved for possible job talks TBA
November 24 Thanksgiving break TBA
December 1 Reserved for possible job talks TBA
December 8 Reserved for possible job talks TBA

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 13: 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).

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
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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