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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"
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!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 2
+
|Oct 12
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)
+
| Arie Levit (Yale)
|[[#March 2 Aaron Bertram (Utah)| Stability in Algebraic Geometry ]]
+
| Caldararu
+
|
+
|-
+
| March 16
+
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)
+
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
| WIMAW
+
| Gurevich
 
|
 
|
 
|-
 
|-
|April 4 (Wednesday)
+
|Oct 19
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)
+
| Jeremy Teitelbaum (U Connecticut)
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
| Craciun
+
| Boston
|
+
|-
+
| April 6
+
| [https://www.math.purdue.edu/~egoins Edray Goins] (Purdue)
+
|[[# Edray Goins|  Toroidal Belyĭ Pairs, Toroidal Graphs, and their Monodromy Groups  ]]
+
| Melanie
+
 
|
 
|
 
|-
 
|-
| April 13
+
|Oct 26
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)
+
| Douglas Ulmer (Arizona)
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
| WIMAW
+
| Yang
 
|
 
|
 
|-
 
|-
| April 20
+
|Nov 2
| Xiuxiong Chen(Stony Brook University)
+
| Reserved for job talk
|[[# Xiuxiong Chen|  TBA  ]]
+
| Bing Wang
+
|
+
|-
+
| April 25 (Wednesday)
+
| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Waseda University) Wasow lecture
+
|[[# TBA|  TBA  ]]
+
| Tran
+
|
+
|-
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|date
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| person (institution)
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|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
 
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|date
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|Nov 9
| person (institution)
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| Reserved for job talk
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
 
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| hosting faculty
 
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|Nov 16
| person (institution)
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|[[# TBA|  TBA  ]]
 
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| hosting faculty
 
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|Nov 30
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|date
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|Dec 7
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|[[# TBA|  TBA  ]]
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|date
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|[[# TBA|  TBA  ]]
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== 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.
+
== Past Colloquia ==
  
All notions will be explained.      Joint work with M, De Chiffre, L. Glebsky and A. Thom.
+
[[Colloquia/Blank|Blank]]
 
+
===February 9 Wes Pegden (CMU)===
+
 
+
Title: The fractal nature of the Abelian Sandpile
+
 
+
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.
+
 
+
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.
+
 
+
===March 2 Aaron Bertram (Utah)===
+
 
+
Title: Stability in Algebraic Geometry
+
 
+
Abstract: Stability was originally introduced in algebraic geometry in the context of finding a projective quotient space for the action of an algebraic group on a projective manifold. This, in turn, led in the 1960s to a notion of slope-stability for vector bundles on a Riemann surface, which was an important tool in the classification of vector bundles. In the 1990s, mirror symmetry considerations led Michael Douglas to notions of stability for "D-branes" (on a higher-dimensional manifold) that corresponded to no previously known mathematical definition. We now understand each of these notions of stability as a distinct point of a complex "stability manifold" that is an important invariant of the (derived) category of complexes of vector bundles of a projective manifold. In this talk I want to give some examples to illustrate the various stabilities, and also to describe some current work in the area.
+
 
+
===April 6 Edray Goins (Purdue)===
+
 
+
Title: Toroidal Belyĭ  Pairs, Toroidal Graphs, and their Monodromy Groups
+
 
+
Abstract: A Bely&#301; map <math> \beta: \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C) </math> is a rational function with at most three critical values; we may assume these values are <math> \{ 0, \, 1, \, \infty \}. </math>  A Dessin d'Enfant is a planar bipartite graph obtained by considering the preimage of a path between two of these critical values, usually taken to be the line segment from 0 to 1.  Such graphs can be drawn on the sphere by composing with stereographic projection: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq \mathbb P^1(\mathbb C) \simeq S^2(\mathbb R). </math>  Replacing <math> \mathbb P^1 </math> with an elliptic curve E, there is a similar definition of a Bely&#301; map <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C). </math>  Since <math> E(\mathbb C) \simeq \mathbb T^2(\mathbb R) </math> is a torus, we call <math> (E, \beta) </math> a toroidal Bely&#301; pair.  The corresponding Dessin d'Enfant can be drawn on the torus by composing with an elliptic logarithm: <math> \beta^{-1} \bigl( [0,1] \bigr) \subseteq E(\mathbb C) \simeq \mathbb T^2(\mathbb R). </math>
+
 
+
This project seeks to create a database of such Bely&#301; pairs, their corresponding Dessins d'Enfant, and their monodromy groups.  For each positive integer N, there are only finitely many toroidal Bely&#301; pairs <math> (E, \beta) </math> with <math> \deg \, \beta = N. </math>  Using the Hurwitz Genus formula, we can begin this database by considering all possible degree sequences <math> \mathcal D </math> on the ramification indices as multisets on three partitions of N.  For each degree sequence, we compute all possible monodromy groups <math> G = \text{im} \, \bigl[ \pi_1 \bigl( \mathbb P^1(\mathbb C) - \{ 0, \, 1, \, \infty \} \bigr) \to S_N \bigr]; </math> they are the ``Galois closure'' of the group of automorphisms of the graph.  Finally, for each possible monodromy group, we compute explicit formulas for Bely&#301; maps <math> \beta: E(\mathbb C) \to \mathbb P^1(\mathbb C) </math> associated to some elliptic curve <math> E: \ y^2 = x^3 + A \, x + B. </math>  We will discuss some of the challenges of determining the structure of these groups, and present visualizations of group actions on the torus.
+
 
+
This work is part of PRiME (Purdue Research in Mathematics Experience) with Chineze Christopher, Robert Dicks, Gina Ferolito, Joseph Sauder, and Danika Van Niel with assistance by Edray Goins and Abhishek Parab.
+
 
+
== Past Colloquia ==
+
  
[[Colloquia/Blank|Blank Colloquia]]
+
[[Colloquia/Spring2018|Spring 2018]]
  
 
[[Colloquia/Fall2017|Fall 2017]]
 
[[Colloquia/Fall2017|Fall 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