Difference between revisions of "Colloquia"

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__NOTOC__
 
 
 
= Mathematics Colloquium =
 
= Mathematics Colloquium =
  
 
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.
 
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.
  
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == -->
+
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].
  
== Spring 2017  ==
+
== Fall 2018 ==
 
+
{| cellpadding="8"
+
!align="left" | date 
+
!align="left" | speaker
+
!align="left" | title
+
!align="left" | host(s)
+
|-
+
|'''Monday, January 9, 9th floor'''
+
|  [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)
+
|[[#Monday, January 9:  Miklos Racz (Microsoft) |  ''Statistical inference in networks and genomics''  ]]
+
|  Valko
+
|
+
|-
+
|January 13, B239
+
|  [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
+
|Reserved for possible job talks
+
|[[# |    ]]
+
+
|
+
|-
+
|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)
+
| Benoit Perthame (University of Paris VI)
+
|[[#Monday, February 6: Benoit Perthame (University of Paris VI)| Models for neural networks; analysis, simulations and behaviour ]]
+
| Jin
+
+
|-
+
|February 10 (WIMAW lecture), B239
+
| Alina Chertock (NC State Univ.)
+
|[[# |  ]]
+
| WIMAW
+
|
+
|-
+
|February 17, 9th floor
+
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)
+
| [[#Friday, February 17: Gustavo Ponce(UCSB)  |  The Korteweg-de Vries equation vs. the Benjamin-Ono equation ]]
+
| Minh-Binh Tran
+
|
+
|-
+
|February 24
+
| [http://acms.nd.edu/people/faculty/jonathan-hauenstein/ Jonathan Hauenstein] (Notre Dame)
+
|[[#February 24: Jonathan Hauenstein (Notre Dame) |  Real solutions of polynomial equations  ]]
+
| Boston
+
|
+
|-
+
|March 3
+
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)
+
|[[# |    ]]
+
|Dymarz
+
|
+
|-
+
|Tuesday, March 7, 4PM (Distinguished Lecture)
+
| [http://pages.iu.edu/~temam/  Roger Temam] (Indiana University)
+
|[[#  |    ]]
+
|Smith
+
|
+
|-
+
|'''Wednesday, March 8, 4PM, B239 '''
+
| [http://pages.iu.edu/~temam/  Roger Temam] (Indiana University)
+
|[[#  |    ]]
+
|Smith
+
|
+
|-
+
|March 10
+
| '''No Colloquium'''
+
|[[# |    ]]
+
|
+
|
+
|-
+
|'''Wednesday, March 15, 4PM '''
+
|  [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)
+
|[[#  TBA|  TBA  ]]
+
| Jin & Minh-Binh Tran
+
|
+
|-
+
|March 17
+
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)
+
| TBA
+
| M. Matchett Wood
+
|
+
|-
+
|March 24
+
|  '''Spring Break'''
+
|[[# |    ]]
+
|
+
|
+
|-
+
|'''Wednesday, March 29  at 3:30PM (Wasow)'''
+
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU)
+
|[[# TBA|  TBA]]
+
|Tran
+
|
+
|-
+
|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
+
|}
+
  
==Fall 2017==
 
  
 
{| cellpadding="8"
 
{| cellpadding="8"
Line 167: Line 14:
 
!align="left" | host(s)
 
!align="left" | host(s)
 
|-
 
|-
|September 8
+
|Sep 12    '''Room 911'''
|
+
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series
|[[# TBATBA ]]
+
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)Harry Potter's Cloak via Transformation Optics ]]
|
+
| Li
 
|
 
|
 
|-
 
|-
|September 15
+
|Sep 14    '''Room 911'''
|
+
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series
|[[# TBATBA ]]
+
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) Journey to the Center of the Earth ]]
|
+
| Li
 
|
 
|
 
|-
 
|-
| '''Wednesday, September 20, LAA lecture
+
|Sep 21    '''Room 911'''
| Andrew Stuart (Caltech)
+
| [http://stuart.caltech.edu/  Andrew Stuart] (Caltech) LAA lecture
|[[# TBATBA ]]
+
|[[#Sep 21: Andrew Stuart (Caltech) The Legacy of Rudolph Kalman ]]
 
| Jin
 
| Jin
 
|
 
|
 
|-
 
|-
|September 22
+
|Sep 28
|
+
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)
|[[# TBA| TBA  ]]
+
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]
|
+
| Thiffeault
 
|
 
|
 
|-
 
|-
|September 29
+
|Oct 5
|
+
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)
|[[# TBATBA ]]
+
|[[#Oct 5: Eyal Subag (Penn State)Symmetries of the hydrogen atom and algebraic families ]]
|
+
| Gurevich
 
|
 
|
 
|-
 
|-
|October 6
+
|Oct 12
|
+
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)
|[[# TBA| TBA ]]
+
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]
|
+
| ...
 
|
 
|
 
|-
 
|-
|October 13
+
|Oct 19
|
+
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)
|[[# TBATBA ]]
+
|[[#Oct 19:  Jeremy Teitelbaum (U Connecticut)Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]
|
+
| Boston
 
|
 
|
 
|-
 
|-
|October 20
+
|Oct 26
|
+
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)
|[[# TBA| TBA  ]]
+
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]
|
+
| Yang
 
|
 
|
 
|-
 
|-
|October 27
+
|Nov 2
|
+
| Reserved for job talk
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
|
+
| hosting faculty
 
|
 
|
 
|-
 
|-
|November 3
+
|Nov 9
|
+
| Reserved for job talk
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
|
+
| hosting faculty
 
|
 
|
 
|-
 
|-
|November 10
+
|Nov 16
| Reserved for possible job talks
+
| Reserved for job talk
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
|
+
| hosting faculty
 
|
 
|
 
|-
 
|-
|November 17
+
|Nov 30
| Reserved for possible job talks
+
| Reserved for job talk
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
|
+
| hosting faculty
 
|
 
|
 
|-
 
|-
|November 24
+
|Dec 7
|'''Thanksgiving break'''
+
| Reserved for job talk
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
 +
| hosting faculty
 
|
 
|
|
 
|-
 
|December 1
 
| Reserved for possible job talks
 
|[[# TBA|  TBA  ]]
 
|
 
|
 
|-
 
|December 8
 
| Reserved for possible job talks
 
|[[# TBA|  TBA  ]]
 
|
 
|
 
|-
 
 
 
|}
 
|}
  
 
== Abstracts ==
 
== Abstracts ==
=== September 16: Po-Shen Loh (CMU) ===
 
Title: Directed paths: from Ramsey to Pseudorandomness
 
  
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed
+
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===
paths in graphs, we discover a series of rich and surprising connections
+
Harry Potter's Cloak via Transformation Optics
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) ===
+
Can we make objects invisible? This has been a subject of human
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture
+
fascination for millennia in Greek mythology, movies, science fiction,
 +
etc. including the legend of Perseus versus Medusa and the more recent
 +
Star Trek and Harry Potter. In the last fifteen years or so there have been
 +
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion
 +
one of them, the so-called "traansformation optics"
 +
in a non-technical fashion n the so-called that has received the most attention in the
 +
scientific literature.
  
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.  
+
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===
 +
Journey to the Center of the Earth
  
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.
+
We will consider the inverse problem of determining the sound
 +
speed or index of refraction of a medium by measuring the travel times of
 +
waves going through the medium. This problem arises in global seismology
 +
in an attempt to determine the inner structure of the Earth by measuring
 +
travel times of earthquakes. It has also several applications in optics
 +
and medical imaging among others.
  
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.  
+
The problem can be recast as a geometric problem: Can one determine the
 +
Riemannian metric of a Riemannian manifold with boundary by measuring
 +
the distance function between boundary points? This is the boundary
 +
rigidity problem. We will also consider the problem of determining
 +
the metric from the scattering relation, the so-called lens rigidity
 +
problem. The linearization of these problems involve the integration
 +
of a tensor along geodesics, similar to the X-ray transform.
  
=== September 30: Akos Magyar (University of Georgia) ===
+
We will also describe some recent results, join with Plamen Stefanov
Title: Geometric Ramsey theory
+
and Andras Vasy, on the partial data case, where you are making
 +
measurements on a subset of the boundary. No previous knowledge of
 +
Riemannian geometry will be assumed.
  
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.
+
=== Sep 21: Andrew Stuart (Caltech) ===
  
=== October 14: Ling Long (LSU) ===
+
The Legacy of Rudolph Kalman
Title: Hypergeometric functions over finite fields
+
  
Abstract: Hypergeometric functions are special functions with lot of
+
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.
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) ===
+
=== Sep 28: Gautam Iyer (CMU) ===
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).
+
Stirring and Mixing
  
=== October 28: Linda Reichl (UT Austin) ===
+
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical
Title: Microscopic hydrodynamic modes in a binary mixture
+
aspects of mixing that arise in the context of fluid dynamics:
  
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.
+
1. How efficiently can stirring "mix"?
  
===Monday, October 31: Kathryn Mann (Berkeley) ===
+
2. What is the interaction between diffusion and mixing.
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.
+
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing
 +
results, and talk about a few open problems.
  
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. 
+
=== Oct 5: Eyal Subag (Penn State)===
  
===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===
+
Symmetries of the hydrogen atom and algebraic families
Title: Siegel's problem on small volume lattices
+
  
Abstract: We outline in very general terms the history and the proof of the identification
+
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetryIn this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modulesI will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system.  No prior knowledge on quantum mechanics or representation theory will be assumed.
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 1945Siegel 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) ===
+
=== Oct 12: Andrei Caldararu (Madison)===
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.
+
Mirror symmetry and derived categories
  
===November 18: Andrew Snowden (University of Michigan)===
+
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.
Title: Recent progress in representation stability
+
  
Abstract:  Representation stability is a relatively new field that studies
+
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).
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)===
+
===  Oct 19:  Jeremy Teitelbaum (U Connecticut)===
Title: Definability in degree structures
+
Lessons Learned and New Perspectives:
 +
From Dean and Provost to aspiring Data Scientist
  
Abstract:  Some incomputable sets are more incomputable than others. We use
+
After more than 10 years in administration, including 9 as Dean of
Turing reducibility and enumeration reducibility to measure the
+
Arts and Sciences and 1 as interim Provost at UConn, I have returned
relative complexity of incomputable sets. By identifying sets of the
+
to my faculty position. I am spending a year as a visiting scientist
same complexity, we can associate to each reducibility a degree
+
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,
structure: the partial order of the Turing degrees and the partial
+
Connecticut, trying to get a grip on some of the mathematical problems
order of the enumeration degrees. The two structures are related in
+
of interest to researchers in cancer genomics. In this talk, I will offer some personal
nontrivial ways. The first has an isomorphic copy in the second and
+
observations about being a mathematician and a high-level administrator, talk a bit about
this isomorphic copy is an automorphism base. In 1969, Rogers asked a
+
the research environment at an independent research institute like JAX-GM, outline
series of questions about the two degree structures with a common
+
a few problems that I've begun to learn about, and conclude with a
theme: definability. In this talk I will introduce the main concepts
+
discussion of how these experiences have shaped my view of graduate training in mathematics.
and describe the work that was motivated by these questions.
+
  
===Friday, December 2: Hao Shen (Columbia)===
+
=== Oct 26: Douglas Ulmer (Arizona)===
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.
+
One of the central concerns of arithmetic geometry is the study of
 +
solutions of systems of polynomial equations where the solutions are
 +
required to lie in a "small" field such as the rational numbers. I
 +
will explain the landscape of expectations and conjectures in this
 +
area, focusing on curves and their Jacobians over global fields
 +
(number fields and function fields), and then survey the progress made
 +
over the last decade in the function field case. The talk is intended
 +
to be accessible to a wide audience.
  
===Monday, December 5:  Botong Wang (UW-Madison)===
+
== Past Colloquia ==
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.
+
[[Colloquia/Blank|Blank]]
  
=== Friday, December 9: Aaron Brown (U Chicago) ===
+
[[Colloquia/Spring2018|Spring 2018]]
''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. 
+
[[Colloquia/Fall2017|Fall 2017]]
  
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:
+
[[Colloquia/Spring2017|Spring 2017]]
(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 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-KdV)</math> 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.
+
 
+
=== February 24: Jonathan Hauenstein (Notre Dame) ===
+
''Real solutions of polynomial equations''
+
 
+
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. 
+
 
+
 
+
== Past Colloquia ==
+
  
 
[[Archived Fall 2016 Colloquia|Fall 2016]]
 
[[Archived Fall 2016 Colloquia|Fall 2016]]

Latest revision as of 16:57, 17 October 2018

Mathematics Colloquium

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

The calendar for spring 2019 can be found here.

Fall 2018

date speaker title host(s)
Sep 12 Room 911 Gunther Uhlmann (Univ. of Washington) Distinguished Lecture series Harry Potter's Cloak via Transformation Optics Li
Sep 14 Room 911 Gunther Uhlmann (Univ. of Washington) Distinguished Lecture series Journey to the Center of the Earth Li
Sep 21 Room 911 Andrew Stuart (Caltech) LAA lecture The Legacy of Rudolph Kalman Jin
Sep 28 Gautam Iyer (CMU) Stirring and Mixing Thiffeault
Oct 5 Eyal Subag (Penn State) Symmetries of the hydrogen atom and algebraic families Gurevich
Oct 12 Andrei Caldararu (Madison) Mirror symmetry and derived categories ...
Oct 19 Jeremy Teitelbaum (U Connecticut) Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist Boston
Oct 26 Douglas Ulmer (Arizona) Rational numbers, rational functions, and rational points Yang
Nov 2 Reserved for job talk TBA hosting faculty
Nov 9 Reserved for job talk TBA hosting faculty
Nov 16 Reserved for job talk TBA hosting faculty
Nov 30 Reserved for job talk TBA hosting faculty
Dec 7 Reserved for job talk TBA hosting faculty

Abstracts

Sep 12: Gunther Uhlmann (Univ. of Washington)

Harry Potter's Cloak via Transformation Optics

Can we make objects invisible? This has been a subject of human fascination for millennia in Greek mythology, movies, science fiction, etc. including the legend of Perseus versus Medusa and the more recent Star Trek and Harry Potter. In the last fifteen years or so there have been several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion one of them, the so-called "traansformation optics" in a non-technical fashion n the so-called that has received the most attention in the scientific literature.

Sep 14: Gunther Uhlmann (Univ. of Washington)

Journey to the Center of the Earth

We will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes. It has also several applications in optics and medical imaging among others.

The problem can be recast as a geometric problem: Can one determine the Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between boundary points? This is the boundary rigidity problem. We will also consider the problem of determining the metric from the scattering relation, the so-called lens rigidity problem. The linearization of these problems involve the integration of a tensor along geodesics, similar to the X-ray transform.

We will also describe some recent results, join with Plamen Stefanov and Andras Vasy, on the partial data case, where you are making measurements on a subset of the boundary. No previous knowledge of Riemannian geometry will be assumed.

Sep 21: Andrew Stuart (Caltech)

The Legacy of Rudolph Kalman

In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.

Sep 28: Gautam Iyer (CMU)

Stirring and Mixing

Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical aspects of mixing that arise in the context of fluid dynamics:

1. How efficiently can stirring "mix"?

2. What is the interaction between diffusion and mixing.

Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing results, and talk about a few open problems.

Oct 5: Eyal Subag (Penn State)

Symmetries of the hydrogen atom and algebraic families

The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.

Oct 12: Andrei Caldararu (Madison)

Mirror symmetry and derived categories

Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.

In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).

Oct 19: Jeremy Teitelbaum (U Connecticut)

Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist

After more than 10 years in administration, including 9 as Dean of Arts and Sciences and 1 as interim Provost at UConn, I have returned to my faculty position. I am spending a year as a visiting scientist at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington, Connecticut, trying to get a grip on some of the mathematical problems of interest to researchers in cancer genomics. In this talk, I will offer some personal observations about being a mathematician and a high-level administrator, talk a bit about the research environment at an independent research institute like JAX-GM, outline a few problems that I've begun to learn about, and conclude with a discussion of how these experiences have shaped my view of graduate training in mathematics.

Oct 26: Douglas Ulmer (Arizona)

One of the central concerns of arithmetic geometry is the study of solutions of systems of polynomial equations where the solutions are required to lie in a "small" field such as the rational numbers. I will explain the landscape of expectations and conjectures in this area, focusing on curves and their Jacobians over global fields (number fields and function fields), and then survey the progress made over the last decade in the function field case. The talk is intended to be accessible to a wide audience.

Past Colloquia

Blank

Spring 2018

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Spring 2015

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012