Difference between revisions of "Colloquia"

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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 ==
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== Fall 2018 ==
 +
 
  
 
{| cellpadding="8"
 
{| cellpadding="8"
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!align="left" | host(s)
 
!align="left" | host(s)
 
|-
 
|-
|January 29 (Monday)
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|Sep 12, 14
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)
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| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguish Lecture series
|[[#January 29 Li Chao (Columbia)|  Elliptic curves and Goldfeld's conjecture  ]]
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| Jordan Ellenberg
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|
+
|-
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|February 2 (Room: 911)
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| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)
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|[[#February 2 Thomas Fai (Harvard)|  The Lubricated Immersed Boundary Method ]]
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| Spagnolie, Smith
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|
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|-
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|February 5 (Monday, Room: 911)
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| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University)
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|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]
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| Ellenberg, Gurevitch
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|
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|-
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|February 6 (Tuesday 2 pm, Room 911)
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| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University)
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|[[#February 6 Alex Lubotzky (Hebrew University)|  Groups' approximation, stability and high dimensional expanders ]]
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| Ellenberg, Gurevitch
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|
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|-
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|February 9
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| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)
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|[[#February 9 Wes Pegden (CMU)|  The fractal nature of the Abelian Sandpile ]]
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| Roch
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|
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|-
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|March 2
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| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)
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|[[#March 2 Aaron Bertram (Utah)| Stability in Algebraic Geometry ]]
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| Caldararu
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|
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|-
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| March 16
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|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)
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|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
| WIMAW
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| Li
 
|
 
|
 
|-
 
|-
|April 4 (Wednesday)
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|Sep 21
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)
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| Andrew Stuart (Caltech) LAA lecture
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
| Craciun
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| Jin
 
|
 
|
 
|-
 
|-
| April 6
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|Sep 28
| [https://www.math.purdue.edu/~egoins Edray Goins] (Purdue)
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| person (institution)
|[[# Edray Goins|  TBA  ]]
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| Melanie
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|
+
|-
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| April 13
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| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)
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|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
| WIMAW
+
| hosting faculty
 
|
 
|
 
|-
 
|-
| April 20
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|Oct 5
| Xiuxiong Chen(Stony Brook University)
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| person (institution)
|[[# Xiuxiong Chen|  TBA  ]]
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| Bing Wang
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|
+
|-
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| April 25 (Wednesday)
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| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Waseda University) Wasow lecture
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|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
| Tran
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| hosting faculty
 
|
 
|
 
|-
 
|-
|date
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|Oct 12
 
| person (institution)
 
| person (institution)
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
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|-
 
|-
|date
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|Oct 19
| person (institution)
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| Jeremy Teitelbaum (U Connecticut)
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
| hosting faculty
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| Boston
 
|
 
|
 
|-
 
|-
|date
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|Oct 26
 
| person (institution)
 
| person (institution)
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
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|
 
|-
 
|-
|date
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|Nov 2
 
| person (institution)
 
| person (institution)
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
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|date
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|Nov 9
 
| person (institution)
 
| person (institution)
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
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|date
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|Nov 16
 
| person (institution)
 
| person (institution)
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
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|date
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|Nov 30
 
| person (institution)
 
| person (institution)
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
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|date
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|Dec 7
 
| person (institution)
 
| person (institution)
 
|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
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|[[# TBA|  TBA  ]]
 
|[[# TBA|  TBA  ]]
 
| hosting faculty
 
| hosting faculty
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 +
|-
 +
|March 4
 +
| Vladimir Sverak (Minnesota) Wasow lecture
 +
|[[# TBA| TBA ]]
 +
| Kim
 
|
 
|
 
|}
 
|}
  
== Spring Abstracts ==
+
== Abstracts ==
  
 +
=== <DATE>: <PERSON> (INSTITUTION) ===
 +
Title: <TITLE>
  
===January 29 Li Chao (Columbia)===
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Abstract: <ABSTRACT>
  
Title: Elliptic curves and Goldfeld's conjecture
 
  
Abstract:
 
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.
 
  
=== February 2 Thomas Fai (Harvard) ===
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== Past Colloquia ==
  
Title: The Lubricated Immersed Boundary Method
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[[Colloquia/Blank|Blank]]
 
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Abstract:
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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.
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===February 5 Alex Lubotzky (Hebrew University)===
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Title:  High dimensional expanders: From Ramanujan graphs to Ramanujan complexes
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Abstract:
+
 
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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.
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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.
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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.
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+
 
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===February 6 Alex Lubotzky (Hebrew University)===
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Title:  Groups' approximation, stability and high dimensional expanders
+
 
+
Abstract:
+
 
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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.
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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.
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All notions will be explained.      Joint work with M, De Chiffre, L. Glebsky and A. Thom.
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===February 9 Wes Pegden (CMU)===
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Title: The fractal nature of the Abelian Sandpile
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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.
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+
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.
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===March 2 Aaron Bertram (Utah)===
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Title: Stability in Algebraic Geometry
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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.
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+
===April 6 Edray Goins (Purdue)===
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Title: Toroidal Belyi Pairs, Toroidal Graphs, and their Monodromy Groups
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Abstract: A Belyi 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 Belyi 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 Belyi 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>
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+
This project seeks to create a database of such Belyi pairs, their corresponding Dessins d'Enfant, and their monodromy groups.  For each positive integer N, there are only finitely many toroidal Belyi 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 Belyi 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.
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+
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.
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== Past Colloquia ==
+
  
[[Colloquia/Blank|Blank Colloquia]]
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[[Colloquia/Spring2018|Spring 2018]]
  
 
[[Colloquia/Fall2017|Fall 2017]]
 
[[Colloquia/Fall2017|Fall 2017]]

Latest revision as of 01:48, 18 June 2018

Mathematics Colloquium

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

Fall 2018

date speaker title host(s)
Sep 12, 14 Gunther Uhlmann (Univ. of Washington) Distinguish Lecture series TBA Li
Sep 21 Andrew Stuart (Caltech) LAA lecture TBA Jin
Sep 28 person (institution) TBA hosting faculty
Oct 5 person (institution) TBA hosting faculty
Oct 12 person (institution) TBA hosting faculty
Oct 19 Jeremy Teitelbaum (U Connecticut) TBA Boston
Oct 26 person (institution) TBA hosting faculty
Nov 2 person (institution) TBA hosting faculty
Nov 9 person (institution) TBA hosting faculty
Nov 16 person (institution) TBA hosting faculty
Nov 30 person (institution) TBA hosting faculty
Dec 7 person (institution) TBA hosting faculty
date person (institution) TBA hosting faculty
March 4 Vladimir Sverak (Minnesota) Wasow lecture TBA Kim

Abstracts

<DATE>: <PERSON> (INSTITUTION)

Title: <TITLE>

Abstract: <ABSTRACT>


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