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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
|
|
|-
|-
| '''Wednesday, September 20, LAA lecture
|Sep 21    '''Room 911'''
| Andrew Stuart (Caltech)
| [http://stuart.caltech.edu/  Andrew Stuart] (Caltech) LAA lecture
|[[# TBATBA ]]
|[[#Sep 21: Andrew Stuart (Caltech) The Legacy of Rudolph Kalman ]]
| Jin
| Jin
|
|
|-
|-
|September 22
|Sep 28
| Jaeyoung Byeon (KAIST)
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)
|[[# Patterns formation for elliptic systems with large interaction forces| Patterns formation for elliptic systems with large interaction forces  ]]
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]
| Rabinowitz & Kim
| Thiffeault
|
|
|-
|-
|September 29
|Oct 5
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)
|[[#Oct 5: Eyal Subag (Penn State)|  Symmetries of the hydrogen atom and algebraic families  ]]
| Gurevich
|
|
|-
|Oct 12
| Arie Levit (Yale)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| Gurevich
|
|
|-
|-
|October 6
|Oct 19
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)
| Jeremy Teitelbaum (U Connecticut)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| Boston
| Boston
|
|-
|October 13
|Tomoko L. Kitagawa (Berkeley)
|[[# TBA|  TBA  ]]
| Max
|
|
|-
|-
|October 20
|Oct 26
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU)  
| Douglas Ulmer (Arizona)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| Minh-Binh Tran
| Yang
|
|
|-
|-
|October 27
|Nov 2
|Stefanie Petermichl (Toulouse)
| Reserved for job talk
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| Stovall, Seeger
| hosting faculty
|
|
|-
|-
|November 3
|Nov 9
|Alexander Yom Din (Caltech)
| Reserved for job talk
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| hosting faculty
|
|
|-
|-
|November 10
|Nov 16
| Reserved for possible job talks
| Reserved for job talk
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| hosting faculty
|
|
|-
|-
|November 17
|Nov 30
| Reserved for possible job talks
| Reserved for job talk
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
|
| hosting faculty
|
|
|-
|-
|November 24
|Dec 7
|'''Thanksgiving break'''
| Reserved for job talk
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| hosting faculty
|
|
|
|}
|-
 
|December 1
== Abstracts ==
| Reserved for possible job talks
 
|[[# TBA|  TBA  ]]
=== 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
|December 8
fascination for millennia in Greek mythology, movies, science fiction,
| Reserved for possible job talks
etc. including the legend of Perseus versus Medusa and the more recent
|[[# TBA|  TBA  ]]
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.


== Fall Abstracts ==
We will also describe some recent results, join with Plamen Stefanov
=== September 8: Tess Anderson (Madison) ===
and Andras Vasy, on the partial data case, where you are making
Title: A Spherical Maximal Function along the Primes
measurements on a subset of the boundary. No previous knowledge of
Riemannian geometry will be assumed.


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 21: Andrew Stuart (Caltech) ===


The Legacy of Rudolph Kalman


=== September 22: Jaeyoung Byeon (KAIST) ===
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.
Title : Patterns formation for elliptic systems with large interaction forces


Abstract : Nonlinear elliptic systems coming from nonlinear Schroedinger systems have simple looking reaction terms whose corresponding energy can be expressed as quadratic forms in terms of density functions.  The entries of the matrix for the quadratic form represent interaction forces between components for a system. If  the signature of an entry is positive, the force between two components is attraction; on the other hand, if it is negative, it is repulsion. 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 general patterns formation structure for systems with large number of components, I would like to illustrate a phenomenon for systems with two components, and for systems with three components introduce some recent results of several phenomena depending on the network structure of attraction and repulsion between components.
=== 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:


== Spring 2018 ==
1. How efficiently can stirring "mix"?


{| cellpadding="8"
2. What is the interaction between diffusion and mixing.
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|}


== Spring Abstracts ==
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.


=== <DATE>: <PERSON> (INSTITUTION) ===
=== Oct 5: Eyal Subag (Penn State)===
Title: <TITLE>


Abstract: <ABSTRACT>
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.


== 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 10:23, 19 September 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 Arie Levit (Yale) TBA Gurevich
Oct 19 Jeremy Teitelbaum (U Connecticut) TBA Boston
Oct 26 Douglas Ulmer (Arizona) TBA 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.

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