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]].
 +
 
 +
== 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
|
+
 
|
 
|
 
|-
 
|-
|September 22, '''9th floor'''
+
|Sep 21    '''Room 911'''
| Jaeyoung Byeon (KAIST)
+
| [http://stuart.caltech.edu/  Andrew Stuart] (Caltech) LAA lecture
|[[#September 22: Jaeyoung Byeon (KAIST) |  Patterns formation for elliptic systems with large interaction forces ]]
+
|[[#Sep 21: Andrew Stuart (Caltech) |  The Legacy of Rudolph Kalman ]]
| Rabinowitz & Kim
+
| Jin
 
|
 
|
 
|-
 
|-
|September 29
+
|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
 
|
 
|
 
|-
 
|-
|October 6,  '''9th floor'''
+
|Oct 5
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)
+
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)
|[[#October 6: Jonathan Hauenstein (Notre Dame) |  Real solutions of polynomial equations ]]
+
|[[#Oct 5: Eyal Subag (Penn State)|  Symmetries of the hydrogen atom and algebraic families ]]
| Boston
+
| Gurevich
|
+
|-
+
|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 12
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU)  
+
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]
+
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories  ]]
| Minh-Binh Tran
+
| ...
 
|
 
|
 
|-
 
|-
|October 27
+
|Oct 19
|Stefanie Petermichl (Toulouse)
+
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)
|[[#October 27: Stefanie Petermichl (Toulouse) Higher order Journé commutators ]]
+
|[[#Oct 19:   Jeremy Teitelbaum (U Connecticut)|  Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]
| Stovall, Seeger
+
| Boston
 
|
 
|
 
|-
 
|-
|We, November 1, B239
+
|Oct 26
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)
+
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)
|[[#November 1: Shaoming Guo (Indiana)| Parsell-Vinogradov systems in higher dimensions  ]]
+
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]
|Seeger
+
| Yang
 
|
 
|
 
|-
 
|-
|November 3
+
|Nov 2
 +
| Reserved for job talk
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
|
+
| hosting faculty
 
|
 
|
 
|-
 
|-
|November 10
+
|Nov 9
| Reserved for possible job talks
+
| Reserved for job talk
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
|
+
| hosting faculty
 
|
 
|
 
|-
 
|-
|November 17
+
|Nov 16
| Reserved for possible job talks
+
| Reserved for job talk
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
|
+
| hosting faculty
 
|
 
|
 
|-
 
|-
|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
+
!align="left" | title
+
!align="left" | host(s)
+
|-
+
| March 16
+
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)
+
|[[# TBA|  TBA  ]]
+
| WIMAW
+
|
+
|-
+
|April 4 (Wednesday)
+
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)
+
|[[# TBA|  TBA  ]]
+
| Craciun
+
|
+
|-
+
| April 6
+
| Reserved
+
|[[# TBA|  TBA  ]]
+
| Melanie
+
|
+
|-
+
| April 13
+
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)
+
|[[# TBA|  TBA  ]]
+
| WIMAW
+
|
+
|-
+
| April 25 (Wednesday)
+
| Hitoshi Ishii (Waseda University) Wasow lecture
+
|[[# TBA|  TBA  ]]
+
| Tran
+
|
+
|-
+
|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  ]]
+
| hosting faculty
+
|
+
|-
+
|date
+
| person (institution)
+
|[[# TBA|  TBA  ]]
+
| hosting faculty
+
|
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|-
+
|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  ]]
+
| hosting faculty
+
|
+
|}
+
  
== Spring Abstracts ==
+
=== Oct 19:  Jeremy Teitelbaum (U Connecticut)===
 +
Lessons Learned and New Perspectives:
 +
From Dean and Provost to aspiring Data Scientist
  
=== <DATE>: <PERSON> (INSTITUTION) ===
+
After more than 10 years in administration, including 9 as Dean of
Title: <TITLE>
+
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.
  
Abstract: <ABSTRACT>
+
=== 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 ==
 
== 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 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

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