Difference between revisions of "Colloquia"

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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'''.
  
== Spring 2018 ==
+
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].
 +
 
 +
== Fall 2018 ==
 +
 
  
 
{| cellpadding="8"
 
{| cellpadding="8"
Line 11: Line 14:
 
!align="left" | host(s)
 
!align="left" | host(s)
 
|-
 
|-
|January 29 (Monday)
+
|Sep 12    '''Room 911'''
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)
+
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series
|[[#January 29 Li Chao (Columbia)|  Elliptic curves and Goldfeld's conjecture ]]
+
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)|  Harry Potter's Cloak via Transformation Optics ]]
| Jordan Ellenberg
+
| Li
 
|
 
|
 
|-
 
|-
|February 2 (Room: 911)
+
|Sep 14    '''Room 911'''
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)
+
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series
|[[#February 2 Thomas Fai (Harvard)|  The Lubricated Immersed Boundary Method ]]
+
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) |  Journey to the Center of the Earth  ]]
| Spagnolie, Smith
+
| Li
 
|
 
|
 
|-
 
|-
|February 5 (Monday, Room: 911)
+
|Sep 21    '''Room 911'''
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University)  
+
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]
+
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman  ]]
| Ellenberg, Gurevitch
+
| Jin
 
|
 
|
 
|-
 
|-
|February 6 (Tuesday 2 pm, Room 911)
+
|Sep 28
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University)  
+
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)
|[[#February 6 Alex Lubotzky (Hebrew University)| Groups' approximation, stability and high dimensional expanders ]]
+
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]
| Ellenberg, Gurevitch
+
| Thiffeault
 
|
 
|
 
 
|-
 
|-
|February 9
+
|Oct 5
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)
+
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)
|[[#February 9 Wes Pegden (CMU)|  The fractal nature of the Abelian Sandpile ]]
+
|[[#Oct 5: Eyal Subag (Penn State)|  Symmetries of the hydrogen atom and algebraic families  ]]
| Roch
+
| Gurevich
 
|
 
|
 
|-
 
|-
| March 16
+
|Oct 12
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)
+
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)
|[[# TBA| TBA ]]
+
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]
| WIMAW
+
| ...
 
|
 
|
 
|-
 
|-
|April 4 (Wednesday)
+
|Oct 19
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)
+
| [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 ]]
| Craciun
+
| Boston
 
|
 
|
 
|-
 
|-
| April 6
+
|Oct 26
| Reserved
+
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)
|[[# TBA| TBA  ]]
+
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]
| Melanie
+
| Yang
 
|
 
|
 
|-
 
|-
| April 13
+
|Nov 2  '''Room 911'''
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)
+
| [https://sites.google.com/view/ruixiang-zhang/home?authuser=0# Ruixiang Zhang] (Madison)
|[[# TBATBA ]]
+
|[[#Nov 2: Ruixiang Zhang (Madison) The Fourier extension operator ]]
| WIMAW
+
|  
 
|
 
|
 
|-
 
|-
| April 25 (Wednesday)
+
|Nov 7  '''Wednesday'''
| Hitoshi Ishii (Waseda University) Wasow lecture
+
| [http://math.mit.edu/~lspolaor/ Luca Spolaor] (MIT)
|[[# TBATBA ]]
+
|[[#Nov 7: Luca Spolaor (MIT) (Log)-Epiperimetric Inequality and the Regularity of Variational Problems ]]
| Tran
+
| Feldman
 
|
 
|
 
|-
 
|-
|date
+
|Nov 12  '''Monday'''
| person (institution)
+
| [http://www.math.tamu.edu/~annejls/ Anne Shiu] (Texas A&M)
|[[# TBATBA ]]
+
|[[#Nov 9: Anne Shiu (Texas A&M) Dynamics of biochemical reaction systems ]]
| hosting faculty
+
| Craciun, Stechmann
 
|
 
|
 
|-
 
|-
|date
+
|Nov 19 '''Monday'''
| person (institution)
+
| [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 ]]
| hosting faculty
+
| Boston, Gurevitch
 
|
 
|
 
|-
 
|-
|date
+
|Nov 20 '''Tuesday'''
| person (institution)
+
| [http://http://www.math.uchicago.edu/~drh/ Denis Hirschfeldt] (University of Chicago)
|[[# TBATBA ]]
+
|[[#Nov 20: Denis Hirschfeldt (University of Chicago)Computability and Ramsey Theory ]]
| hosting faculty
+
| Andrews
 
|
 
|
 
|-
 
|-
|date
+
|Nov 30
| person (institution)
+
| Reserved for job talk
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
 
| hosting faculty
 
| hosting faculty
 
|
 
|
 
|-
 
|-
|date
+
|Dec 7
| person (institution)
+
| Reserved for job talk
|[[# TBA|  TBA  ]]
+
| hosting faculty
+
|
+
|-
+
|date
+
| person (institution)
+
|[[# TBA|  TBA  ]]
+
| hosting faculty
+
|
+
|-
+
|date
+
| person (institution)
+
|[[# TBA|  TBA  ]]
+
| hosting faculty
+
|
+
|-
+
|date
+
| person (institution)
+
|[[# TBA|  TBA  ]]
+
| hosting faculty
+
|
+
|-
+
|date
+
| person (institution)
+
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
 
| hosting faculty
 
| hosting faculty
Line 127: Line 105:
 
|}
 
|}
  
== Spring Abstracts ==
+
== Abstracts ==
  
 +
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===
 +
Harry Potter's Cloak via Transformation Optics
  
===January 29 Li Chao (Columbia)===
+
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.
  
Title: Elliptic curves and Goldfeld's conjecture
+
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===
 +
Journey to the Center of the Earth
  
Abstract:
+
We will consider the inverse problem of determining the sound
An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family y^2=x^3-d), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our recent work (with D. Kriz) towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.
+
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.
  
=== February 2 Thomas Fai (Harvard) ===
+
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.
  
Title: The Lubricated Immersed Boundary Method
+
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.
  
Abstract:
+
=== Sep 21: Andrew Stuart (Caltech) ===
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.
+
  
===February 5 Alex Lubotzky (Hebrew University)===
+
The Legacy of Rudolph Kalman
  
Title:  High dimensional expanders: From Ramanujan graphs to Ramanujan complexes
+
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.
  
Abstract:  
+
=== Sep 28: Gautam Iyer (CMU) ===
  
Expander graphs in general, and Ramanujan graphs , in particular,  have played a major role in  computer science in the last 5 decades  and more recently also in pure math. The first explicit construction of bounded degree expanding graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders.
+
Stirring and Mixing
  
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d>1.
+
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:
  
This question was answered recently affirmatively (by  T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological expanders. We will describe these developments and the general area of high dimensional expanders.  
+
1. How efficiently can stirring "mix"?
  
 +
2. What is the interaction between diffusion and mixing.
  
===February 6 Alex Lubotzky (Hebrew University)===
+
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.
  
Title: Groups' approximation, stability and high dimensional expanders
+
=== Oct 5: Eyal Subag (Penn State)===
  
Abstract:
+
Symmetries of the hydrogen atom and algebraic families
  
Several well-known open questions, such as: are all groups sofic or hyperlinear?,  have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the  unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms.  We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.
+
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.
  
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability  and using  high dimensional expanders, it is shown that  some non-residually finite groups  (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated.
+
=== Oct 12: Andrei Caldararu (Madison)===
  
All notions will be explained.      Joint work with M, De Chiffre, L. Glebsky and A. Thom.
+
Mirror symmetry and derived categories
  
===February 9 Wes Pegden (CMU)===
+
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: The fractal nature of the Abelian Sandpile
+
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).
  
Abstract: The Abelian Sandpile is a simple diffusion process on the integer lattice, in which configurations of chips disperse according to a simple rule: when a vertex has at least 4 chips, it can distribute one chip to each neighbor.
+
===  Oct 19:   Jeremy Teitelbaum (U Connecticut)===
 +
Lessons Learned and New Perspectives:
 +
From Dean and Provost to aspiring Data Scientist
  
Introduced in the statistical physics community in the 1980s, the Abelian sandpile exhibits striking fractal behavior which long resisted rigorous mathematical analysis (or even a plausible explanation)We now have a relatively robust mathematical understanding of this fractal nature of the sandpile, which involves surprising connections between integer superharmonic functions on the lattice, discrete tilings of the plane, and Apollonian circle packings.  In this talk, we will survey our work in this area, and discuss avenues of current and future research.
+
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 positionI 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 ==
 
== Past Colloquia ==
  
[[Colloquia/Blank|Blank Colloquia]]
+
[[Colloquia/Blank|Blank]]
 +
 
 +
[[Colloquia/Spring2018|Spring 2018]]
  
 
[[Colloquia/Fall2017|Fall 2017]]
 
[[Colloquia/Fall2017|Fall 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

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Spring 2015

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012