Difference between revisions of "Colloquia"

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= Mathematics Colloquium =
 
= Mathematics Colloquium =
  
 
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.
 
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.
  
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == -->
+
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].
 +
 
 +
== Fall 2018 ==
  
==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 8
+
|Sep 12    '''Room 911'''
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)
+
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series
|[[#September 8: Tess Anderson (Madison) |  A Spherical Maximal Function along the Primes ]]
+
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)|  Harry Potter's Cloak via Transformation Optics ]]
| Yang
+
| Li
 
|
 
|
 
|-
 
|-
|September 15
+
|Sep 14    '''Room 911'''
|
+
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series
|[[#|   ]]
+
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth  ]]
 +
| Li
 
|
 
|
 +
|-
 +
|Sep 21    '''Room 911'''
 +
| [http://stuart.caltech.edu/  Andrew Stuart] (Caltech) LAA lecture
 +
|[[#Sep 21: Andrew Stuart (Caltech) |  The Legacy of Rudolph Kalman  ]]
 +
| Jin
 
|
 
|
 +
|-
 +
|Sep 28
 +
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)
 +
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]
 +
| Thiffeault
 
|
 
|
 
|-
 
|-
|September 22, '''9th floor'''
+
|Oct 5
| Jaeyoung Byeon (KAIST)
+
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)
|[[#September 22: Jaeyoung Byeon (KAIST) |  Patterns formation for elliptic systems with large interaction forces ]]
+
|[[#Oct 5: Eyal Subag (Penn State)|  Symmetries of the hydrogen atom and algebraic families ]]
| Rabinowitz & Kim
+
| Gurevich
 
|
 
|
 
|-
 
|-
|September 29
+
|Oct 12
|
+
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)
|[[# TBA| TBA ]]
+
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]
|
+
| ...
 
|
 
|
 
|-
 
|-
|October 6,  '''9th floor'''
+
|Oct 19
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)
+
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)
|[[#October 6: Jonathan Hauenstein (Notre Dame) |  Real solutions of polynomial equations ]]
+
|[[#Oct 19:   Jeremy Teitelbaum (U Connecticut)|  Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist  ]]
 
| Boston
 
| Boston
|
 
|-
 
|October 13, '''9th floor'''
 
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)
 
|[[#October 13: Tomoko Kitagawa (Berkeley) |  A Global History of Mathematics from 1650 to 2017 ]]
 
| Max
 
 
|
 
|
 
|-
 
|-
|October 20
+
|Oct 26
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU)  
+
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]
+
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]
| Minh-Binh Tran
+
| Yang
 
|
 
|
 
|-
 
|-
|October 27
+
|Nov 2  '''Room 911'''
|Stefanie Petermichl (Toulouse)
+
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)
|[[#October 27: Stefanie Petermichl (Toulouse) Higher order Journé commutators ]]
+
|[[#Nov 2: Ruixiang Zhang (Madison) |  The Fourier extension operator ]]
| Stovall, Seeger
+
|  
 
|
 
|
 
|-
 
|-
|We, November 1, B239
+
|Nov 7  '''Wednesday'''
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)
+
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)
|[[# November 1: Shaoming Guo (Indiana)|  Parsell-Vinogradov systems in higher dimensions ]]
+
|[[#Nov 7: Luca Spolaor (MIT) |  (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]
|Seeger
+
| Feldman
 
|
 
|
 
|-
 
|-
|November 3
+
|Nov 12  '''Monday'''
|[[# TBATBA ]]
+
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)
|
+
|[[#Nov 9: Anne Shiu (Texas A&M) Dynamics of biochemical reaction systems ]]
 +
| Craciun, Stechmann
 
|
 
|
 
|-
 
|-
|November 10
+
|Nov 19 '''Monday'''
| Reserved for possible job talks
+
| [https://sites.google.com/site/ayomdin/ Alexander Yom Din] (Caltech)
|[[# TBA| TBA ]]
+
|[[#Nov 19: Alexander Yom Din (Caltech) | From analysis to algebra to geometry - an example in representation theory of real groups ]]
|
+
| Boston, Gurevitch
 
|
 
|
 
|-
 
|-
|November 17
+
|Nov 20 '''Tuesday'''
| Reserved for possible job talks
+
| [http://http://www.math.uchicago.edu/~drh/ Denis Hirschfeldt] (University of Chicago)
|[[# TBATBA ]]
+
|[[#Nov 20: Denis Hirschfeldt (University of Chicago)Computability and Ramsey Theory ]]
|
+
| Andrews
 
|
 
|
 
|-
 
|-
|November 24
+
|Nov 30
|'''Thanksgiving break'''
+
| Reserved for job talk
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
|
+
| hosting faculty
 
|
 
|
 
|-
 
|-
|December 1
+
|Dec 7
| Reserved for possible job talks
+
| Reserved for job talk
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
 +
| hosting faculty
 
|
 
|
|
 
|-
 
|December 8
 
| Reserved for possible job talks
 
|[[# TBA|  TBA  ]]
 
|
 
|
 
|-
 
|December 11
 
| Connor Mooney (ETH Zurich)
 
|[[# December 11: Connor Mooney|  Finite time blowup for parabolic systems in the plane]]
 
|
 
|
 
|-
 
 
 
|}
 
|}
  
== Fall Abstracts ==
+
== Abstracts ==
=== September 8: Tess Anderson (Madison) ===
+
Title: A Spherical Maximal Function along the Primes
+
  
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example.  In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to.  We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory.  This is joint work with Cook, Hughes, and Kumchev.
+
=== 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.
  
=== September 22: Jaeyoung Byeon (KAIST) ===
+
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===
Title: Patterns formation for elliptic systems with large interaction forces
+
Journey to the Center of the Earth
  
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.
+
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.
  
===October 6: Jonathan Hauenstein (Notre Dame) ===
+
The problem can be recast as a geometric problem: Can one determine the
Title: Real solutions of polynomial equations
+
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.
  
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.
+
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.
  
===October 13: Tomoko Kitagawa (Berkeley) ===
+
=== Sep 21: Andrew Stuart (Caltech) ===
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?
+
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) ===
  
===October 20: Pierre Germain (Courant, NYU) ===
+
Stirring and Mixing
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).
+
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:
  
===October 27: Stefanie Petermichl (Toulouse)===
+
1. How efficiently can stirring "mix"?
Title: Higher order Journé commutators
+
  
Abstract: We consider questions that stem from operator theory via Hankel and
+
2. What is the interaction between diffusion and mixing.
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
+
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of
+
results, and talk about a few open problems.
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
+
=== Oct 5: Eyal Subag (Penn State)===
analysis, while preserving the Ansatz from classical operator theory.
+
  
===November 1: Shaoming Guo (Indiana) ===
+
Symmetries of the hydrogen atom and algebraic families
Title: Parsell-Vinogradov systems in higher dimensions
+
  
Abstract:
+
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.
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.
+
  
===December 11: Connor Mooney (ETH Zurich) ===
+
=== Oct 12: Andrei Caldararu (Madison)===
Title: Finite time blowup for parabolic systems in the plane
+
  
Abstract:
+
Mirror symmetry and derived categories
Hilbert's 19th problem asks about the smoothness of solutions to nonlinear elliptic PDE that arise in the calculus of variations. This problem leads naturally to the question of continuity for solutions to linear elliptic and parabolic systems with measurable coefficients. We will first discuss some classical results on this topic, including Morrey's result that solutions to linear elliptic systems in two dimensions are continuous. We will then discuss surprising recent examples of finite time blowup from smooth data for linear parabolic systems in two dimensions, and important open problems.
+
  
== Spring 2018 ==
+
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.
  
{| cellpadding="8"
+
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).
!align="left" | date 
+
 
!align="left" | speaker
+
=== Oct 19:   Jeremy Teitelbaum (U Connecticut)===
!align="left" | title
+
Lessons Learned and New Perspectives:
!align="left" | host(s)
+
From Dean and Provost to aspiring Data Scientist
|-
+
 
| March 16
+
After more than 10 years in administration, including 9 as Dean of
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)
+
Arts and Sciences and 1 as interim Provost at UConn, I have returned
|[[# TBA|  TBA  ]]
+
to my faculty position. I am spending a year as a visiting scientist
| WIMAW
+
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
|April 4 (Wednesday)
+
observations about being a mathematician and a high-level administrator, talk a bit about
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)
+
the research environment at an independent research institute like JAX-GM, outline
|[[# TBA|  TBA  ]]
+
a few problems that I've begun to learn about, and conclude with a
| Craciun
+
discussion of how these experiences have shaped my view of graduate training in mathematics.
|
+
 
|-
+
=== Oct 26: Douglas Ulmer (Arizona)===
| April 6
+
 
| Reserved
+
Rational numbers, rational functions, and rational points
|[[# TBA| TBA  ]]
+
 
| Melanie
+
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
| April 13
+
will explain the landscape of expectations and conjectures in this
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)
+
area, focusing on curves and their Jacobians over global fields
|[[# TBA|  TBA  ]]
+
(number fields and function fields), and then survey the progress made
| WIMAW
+
over the last decade in the function field case. The talk is intended
|
+
to be accessible to a wide audience.
|-
+
 
| April 25 (Wednesday)
+
=== Nov 2: Ruixiang Zhang (Madison)===
| Hitoshi Ishii (Waseda University) Wasow lecture
+
|[[# TBA| TBA  ]]
+
| Tran
+
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|[[# TBA|  TBA  ]]
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|[[# TBA|  TBA  ]]
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|[[# TBA| TBA  ]]
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|[[# TBA|  TBA  ]]
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|[[# TBA|  TBA  ]]
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|date
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|[[# TBA|  TBA  ]]
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|[[# TBA|  TBA ]]
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|[[# TBA| TBA  ]]
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|}
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== Spring Abstracts ==
+
The Fourier extension operator
  
=== <DATE>: <PERSON> (INSTITUTION) ===
+
I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.
Title: <TITLE>
+
  
Abstract: <ABSTRACT>
+
=== Nov 7: Luca Spolaor (MIT)===
  
 +
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems
 +
 +
In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents.
 +
Finally I will describe some future applications of this method both in regularity theory and in other settings.
 +
 +
=== Nov 9: Anne Shiu (Texas A&M)===
 +
 +
Dynamics of biochemical reaction systems
 +
 +
Reaction networks taken with mass-action kinetics arise in many settings,
 +
from epidemiology to population biology to systems of chemical reactions.
 +
This talk focuses on certain biological signaling networks, namely,
 +
phosphorylation networks, and their resulting dynamical systems. For many
 +
of these systems, the set of steady states admits a rational
 +
parametrization (that is, the set is the image of a map with
 +
rational-function coordinates). We describe how such a parametrization
 +
allows us to investigate the dynamics, including the emergence of
 +
bistability in a network underlying ERK regulation, and the capacity for
 +
oscillations in a mixed processive/distributive phosphorylation network.
 +
 +
=== Nov 19: Alexander Yom Din (Caltech)===
 +
 
 +
From analysis to algebra to geometry - an example in representation theory of real groups
 +
 +
Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation. Geometrization, again very roughly, reveals how algebraic objects have secret lives over spaces - thus more amenable to human intuition. In this talk, I will try to motivate and present one example - the calculation of the Casselman-Jacquet module of a principal series representation (I will explain the terms in the talk).
 +
 +
=== Nov 20: Denis Hirschfeldt (University of Chicago)===
 +
 +
Computability and Ramsey Theory
 +
 +
Computability theory can be seen as the study of the fine
 +
structure of definability. Much of its power relies on the deep
 +
connections between definability and computation. These connections can be seen in fundamental results such as Post's Theorem, which establishes a connection between the complexity of formulas needed to define a given set of natural numbers and its computability-theoretic strength. As has become increasingly clear, they can also be seen in the computability-theoretic analysis of objects whose definitions come from notions that arise naturally in combinatorics. The heuristic here is that
 +
computability-theoretically natural notions tend to be combinatorially
 +
natural, and vice-versa. I will discuss some results and open questions in
 +
the computability-theoretic analysis of combinatorial principles, in
 +
particular Ramsey-theoretic ones such as versions of Ramsey's Theorem for colorings of countably infinite sets, and versions of Hindman's Theorem, which states that for every coloring of the natural numbers with finitely many colors, there is an infinite set of numbers such that all nonempty sums of distinct elements of this set have the same color.
  
 
== Past Colloquia ==
 
== Past Colloquia ==
  
[[Colloquia/Blank|Blank Colloquia]]
+
[[Colloquia/Blank|Blank]]
 +
 
 +
[[Colloquia/Spring2018|Spring 2018]]
 +
 
 +
[[Colloquia/Fall2017|Fall 2017]]
  
 
[[Colloquia/Spring2017|Spring 2017]]
 
[[Colloquia/Spring2017|Spring 2017]]

Latest revision as of 15:34, 14 November 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 Room 911 Ruixiang Zhang (Madison) The Fourier extension operator
Nov 7 Wednesday Luca Spolaor (MIT) (Log)-Epiperimetric Inequality and the Regularity of Variational Problems Feldman
Nov 12 Monday Anne Shiu (Texas A&M) Dynamics of biochemical reaction systems Craciun, Stechmann
Nov 19 Monday Alexander Yom Din (Caltech) From analysis to algebra to geometry - an example in representation theory of real groups Boston, Gurevitch
Nov 20 Tuesday Denis Hirschfeldt (University of Chicago) Computability and Ramsey Theory Andrews
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)

Rational numbers, rational functions, and rational points

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.

Nov 2: Ruixiang Zhang (Madison)

The Fourier extension operator

I will present an integral operator that originated in the study of the Euclidean Fourier transform and is closely related to many problems in PDE, spectral theory, analytic number theory, and combinatorics. I will then introduce some recent developments in harmonic analysis concerning this operator. I will mainly focus on various new ways to "induct on scales" that played an important role in the recent solution in all dimensions to Carleson's a.e. convergence problem on free Schrödinger solutions.

Nov 7: Luca Spolaor (MIT)

(Log)-Epiperimetric Inequality and the Regularity of Variational Problems

In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents. Finally I will describe some future applications of this method both in regularity theory and in other settings.

Nov 9: Anne Shiu (Texas A&M)

Dynamics of biochemical reaction systems

Reaction networks taken with mass-action kinetics arise in many settings, from epidemiology to population biology to systems of chemical reactions. This talk focuses on certain biological signaling networks, namely, phosphorylation networks, and their resulting dynamical systems. For many of these systems, the set of steady states admits a rational parametrization (that is, the set is the image of a map with rational-function coordinates). We describe how such a parametrization allows us to investigate the dynamics, including the emergence of bistability in a network underlying ERK regulation, and the capacity for oscillations in a mixed processive/distributive phosphorylation network.

Nov 19: Alexander Yom Din (Caltech)

From analysis to algebra to geometry - an example in representation theory of real groups

Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation. Geometrization, again very roughly, reveals how algebraic objects have secret lives over spaces - thus more amenable to human intuition. In this talk, I will try to motivate and present one example - the calculation of the Casselman-Jacquet module of a principal series representation (I will explain the terms in the talk).

Nov 20: Denis Hirschfeldt (University of Chicago)

Computability and Ramsey Theory

Computability theory can be seen as the study of the fine structure of definability. Much of its power relies on the deep connections between definability and computation. These connections can be seen in fundamental results such as Post's Theorem, which establishes a connection between the complexity of formulas needed to define a given set of natural numbers and its computability-theoretic strength. As has become increasingly clear, they can also be seen in the computability-theoretic analysis of objects whose definitions come from notions that arise naturally in combinatorics. The heuristic here is that computability-theoretically natural notions tend to be combinatorially natural, and vice-versa. I will discuss some results and open questions in the computability-theoretic analysis of combinatorial principles, in particular Ramsey-theoretic ones such as versions of Ramsey's Theorem for colorings of countably infinite sets, and versions of Hindman's Theorem, which states that for every coloring of the natural numbers with finitely many colors, there is an infinite set of numbers such that all nonempty sums of distinct elements of this set have the same color.

Past Colloquia

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Spring 2018

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Spring 2015

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012