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= Mathematics Colloquium =
 
= Mathematics Colloquium =
  
 
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.
 
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.
  
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == -->
+
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].
 +
 
 +
== Fall 2018 ==
  
==Fall 2017==
 
  
 
{| cellpadding="8"
 
{| cellpadding="8"
!align="left" | Date    
+
!align="left" | date    
!align="left" | Speaker
+
!align="left" | speaker
!align="left" | Title
+
!align="left" | title
!align="left" | Host(s)
+
!align="left" | host(s)
 
|-
 
|-
|September 8
+
|Sep 12    '''Room 911'''
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)
+
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series
|[[#September 8: Tess Anderson (Madison) |  A Spherical Maximal Function along the Primes ]]
+
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)|  Harry Potter's Cloak via Transformation Optics ]]
| Yang
+
| Li
 
|
 
|
 
|-
 
|-
|September 15
+
|Sep 14    '''Room 911'''
|
+
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series
|[[#|   ]]
+
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth  ]]
 +
| Li
 
|
 
|
 +
|-
 +
|Sep 21    '''Room 911'''
 +
| [http://stuart.caltech.edu/  Andrew Stuart] (Caltech) LAA lecture
 +
|[[#Sep 21: Andrew Stuart (Caltech) |  The Legacy of Rudolph Kalman  ]]
 +
| Jin
 
|
 
|
 +
|-
 +
|Sep 28
 +
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)
 +
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]
 +
| Thiffeault
 
|
 
|
 
|-
 
|-
|September 22, '''9th floor'''
+
|Oct 5
| Jaeyoung Byeon (KAIST)
+
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)
|[[#September 22: Jaeyoung Byeon (KAIST) |  Patterns formation for elliptic systems with large interaction forces ]]
+
|[[#Oct 5: Eyal Subag (Penn State)|  Symmetries of the hydrogen atom and algebraic families ]]
| Rabinowitz & Kim
+
| Gurevich
 
|
 
|
 
|-
 
|-
|September 29
+
|Oct 12
|
+
| Arie Levit (Yale)
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
|
+
| Gurevich
 
|
 
|
 
|-
 
|-
|October 6,  '''9th floor'''
+
|Oct 19
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)
+
| Jeremy Teitelbaum (U Connecticut)
|[[#October 6: Jonathan Hauenstein (Notre Dame) Real solutions of polynomial equations ]]
+
|[[# TBATBA  ]]
 
| Boston
 
| Boston
|
 
|-
 
|October 13, '''9th floor'''
 
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)
 
|[[#October 13: Tomoko Kitagawa (Berkeley) |  A Global History of Mathematics from 1650 to 2017 ]]
 
| Max
 
 
|
 
|
 
|-
 
|-
|October 20
+
|Oct 26
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU)  
+
| Douglas Ulmer (Arizona)
|[[#October 13: Pierre Germain (Courant, NYU) |  Stability of the Couette flow in the Euler and Navier-Stokes equations ]]
+
|  Minh-Binh Tran
+
|
+
|-
+
|October 27
+
|Stefanie Petermichl (Toulouse)
+
|[[#October 27: Stefanie Petermichl (Toulouse)  |  Higher order Journé commutators  ]]
+
| Stovall, Seeger
+
|
+
|-
+
|We, November 1, B239
+
|[http://pages.iu.edu/~shaoguo/  Shaoming Guo] (Indiana)
+
|[[# November 1: Shaoming Guo (Indiana)|  Parsell-Vinogradov systems in higher dimensions  ]]
+
|Seeger
+
|
+
|-
+
|November 3
+
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
|
+
| Yang
 
|
 
|
 
|-
 
|-
|November 10
+
|Nov 2
| Reserved for possible job talks
+
| Reserved for job talk
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
|
+
| hosting faculty
 
|
 
|
 
|-
 
|-
|November 17
+
|Nov 9
| Reserved for possible job talks
+
| Reserved for job talk
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
|
+
| hosting faculty
 
|
 
|
 
|-
 
|-
|November 24
+
|Nov 16
|'''Thanksgiving break'''
+
| Reserved for job talk
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
|
+
| hosting faculty
 
|
 
|
 
|-
 
|-
|December 1
+
|Nov 30
| Reserved for possible job talks
+
| Reserved for job talk
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
|
+
| hosting faculty
 
|
 
|
 
|-
 
|-
|December 8
+
|Dec 7
| Reserved for possible job talks
+
| Reserved for job talk
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
 +
| hosting faculty
 
|
 
|
|
 
|-
 
|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) ===
+
== Past Colloquia ==
Title: Finite time blowup for parabolic systems in the plane
+
  
Abstract:
+
[[Colloquia/Blank|Blank]]
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 ==
+
[[Colloquia/Spring2018|Spring 2018]]
 
+
{| cellpadding="8"
+
!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  ]]
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| hosting faculty
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|
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|-
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|date
+
| person (institution)
+
|[[# TBA|  TBA  ]]
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| hosting faculty
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|
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|-
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|date
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| person (institution)
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|[[# TBA|  TBA  ]]
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| hosting faculty
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|
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|-
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|date
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| person (institution)
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|[[# TBA|  TBA  ]]
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| hosting faculty
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|-
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|date
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| person (institution)
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|[[# TBA|  TBA  ]]
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| hosting faculty
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|-
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|date
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| person (institution)
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|[[# TBA|  TBA  ]]
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| hosting faculty
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|-
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|date
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| person (institution)
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|[[# TBA|  TBA  ]]
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| hosting faculty
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|-
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|date
+
| person (institution)
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|[[# TBA|  TBA  ]]
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| hosting faculty
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|-
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|date
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| person (institution)
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|[[# TBA|  TBA  ]]
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| hosting faculty
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|
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|}
+
 
+
== Spring Abstracts ==
+
 
+
=== <DATE>: <PERSON> (INSTITUTION) ===
+
Title: <TITLE>
+
 
+
Abstract: <ABSTRACT>
+
 
+
 
+
== Past Colloquia ==
+
  
[[Colloquia/Blank|Blank Colloquia]]
+
[[Colloquia/Fall2017|Fall 2017]]
  
 
[[Colloquia/Spring2017|Spring 2017]]
 
[[Colloquia/Spring2017|Spring 2017]]

Latest revision as of 05:23, 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