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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 2017==
 
{| cellpadding="8"
!align="left" | Date 
!align="left" | Speaker
!align="left" | Title
!align="left" | Host(s)
|-
|September 8
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)
|[[#September 8: Tess Anderson (Madison) |  A Spherical Maximal Function along the Primes  ]]
| Yang
|
|-
|September 15
|
|[[#|  ]]
|
|
|
|-
|September 22, '''9th floor'''
| Jaeyoung Byeon (KAIST)
|[[#September 22: Jaeyoung Byeon (KAIST) |  Patterns formation for elliptic systems with large interaction forces  ]]
| Rabinowitz & Kim
|
|-
|September 29
|
|[[# TBA|  TBA  ]]
|
|
|-
|October 6,  '''9th floor'''
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)
|[[#October 6: Jonathan Hauenstein (Notre Dame) |  Real solutions of polynomial equations ]]
| Boston
|
|-
|October 13
|Tomoko L. Kitagawa (Berkeley)
|[[# TBA|  TBA  ]]
| Max
|
|-
|October 20
|  [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU)
|[[# TBA|  TBA  ]]
|  Minh-Binh Tran
|
|-
|October 27
|Stefanie Petermichl (Toulouse)
|[[# TBA|  TBA  ]]
| Stovall, Seeger
|
|-
|We, November 1
|Shaoming Guo (Indiana)
|[[# TBA|  TBA  ]]
|
|
|-
|November 3
|Robert Laugwitz  (Rutgers)
|[[# TBA|  TBA  ]]
|Dima Arinkin
|
|
|-
|November 10
| Reserved for possible job talks
|[[# TBA|  TBA  ]]
|
|
|-
|November 17
| Reserved for possible job talks
|[[# TBA|  TBA  ]]
|
|
|-
|November 24
|'''Thanksgiving break'''
|[[# TBA|  TBA  ]]
|
|
|-
|December 1
| Reserved for possible job talks
|[[# TBA|  TBA  ]]
|
|
|-
|December 8
| Reserved for possible job talks
|[[# TBA| TBA  ]]
|
|
|-
 
|}
 
== Fall Abstracts ==
=== September 8: Tess Anderson (Madison) ===
Title: A Spherical Maximal Function along the Primes
 
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior.  The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example.  In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to.  We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory.  This is joint work with Cook, Hughes, and Kumchev.
 
 
=== September 22: Jaeyoung Byeon (KAIST) ===
Title: Patterns formation for elliptic systems with large interaction forces
 
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions.  The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.


===October 6: Jonathan Hauenstein (Notre Dame) ===
== Fall 2018 ==
Title: Real solutions of polynomial equations


Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions.  Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application.  This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.
== Spring 2018 ==


{| cellpadding="8"
{| cellpadding="8"
Line 135: Line 14:
!align="left" | host(s)
!align="left" | host(s)
|-
|-
| March 30
|Sep 12    '''Room 911'''
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series
|[[# TBATBA ]]
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)Harry Potter's Cloak via Transformation Optics ]]
| WIMAW
| Li
|
|
|-
|-
| April 6
|Sep 14    '''Room 911'''
| Reserved
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series
|[[# TBATBA ]]
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) Journey to the Center of the Earth ]]
| Melanie
| Li
|
|
|-
|-
|date
|Sep 21    '''Room 911'''
| person (institution)
| [http://stuart.caltech.edu/  Andrew Stuart] (Caltech) LAA lecture
|[[# TBATBA ]]
|[[#Sep 21: Andrew Stuart (Caltech) The Legacy of Rudolph Kalman ]]
| hosting faculty
| Jin
|
|
|-
|-
|date
|Sep 28
| person (institution)
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)
|[[# TBA| TBA  ]]
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]
| hosting faculty
| Thiffeault
|
|
|-
|-
|date
|Oct 5
| person (institution)
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)
|[[# TBATBA ]]
|[[#Oct 5: Eyal Subag (Penn State)Symmetries of the hydrogen atom and algebraic families ]]
| hosting faculty
| Gurevich
|
|
|-
|-
|date
|Oct 12
| person (institution)
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)
|[[# TBA| TBA ]]
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]
| hosting faculty
| ...
|
|
|-
|-
|date
|Oct 19
| person (institution)
| [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 ]]
| hosting faculty
| Boston
|
|
|-
|-
|date
|Oct 26
| person (institution)
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)
|[[# TBA|  TBA  ]]
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]
| hosting faculty
| Yang
|
|-
|date
| person (institution)
|[[# TBA| TBA  ]]
| hosting faculty
|
|
|-
|-
|date
|Nov 2
| person (institution)
| Reserved for job talk
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| hosting faculty
| hosting faculty
|
|
|-
|-
|date
|Nov 9
| person (institution)
| Reserved for job talk
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| hosting faculty
| hosting faculty
|
|
|-
|-
|date
|Nov 16
| person (institution)
| Reserved for job talk
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| hosting faculty
| hosting faculty
|
|
|-
|-
|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  ]]
|[[# TBA|  TBA  ]]
| hosting faculty
| hosting faculty
Line 220: Line 93:
|}
|}


== Spring Abstracts ==
== 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.


=== <DATE>: <PERSON> (INSTITUTION) ===
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).
Title: <TITLE>


Abstract: <ABSTRACT>
===  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 ==
== 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]]

Revision as of 21:57, 17 October 2018

Mathematics Colloquium

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

The calendar for spring 2019 can be found here.

Fall 2018

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

Abstracts

Sep 12: Gunther Uhlmann (Univ. of Washington)

Harry Potter's Cloak via Transformation Optics

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

Sep 14: Gunther Uhlmann (Univ. of Washington)

Journey to the Center of the Earth

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

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

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

Sep 21: Andrew Stuart (Caltech)

The Legacy of Rudolph Kalman

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

Sep 28: Gautam Iyer (CMU)

Stirring and Mixing

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

1. How efficiently can stirring "mix"?

2. What is the interaction between diffusion and mixing.

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

Oct 5: Eyal Subag (Penn State)

Symmetries of the hydrogen atom and algebraic families

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

Oct 12: Andrei Caldararu (Madison)

Mirror symmetry and derived categories

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

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

Oct 19: Jeremy Teitelbaum (U Connecticut)

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

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

Oct 26: Douglas Ulmer (Arizona)

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

Past Colloquia

Blank

Spring 2018

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Spring 2015

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012