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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'''.
  
== Fall 2013 ==
+
== Spring 2018 ==
  
 
{| 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)
 
|-
 
|-
|Sept 13
+
|January 29 (Monday)
|
+
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)
|
+
|[[#January 29 Li Chao (Columbia)|  Elliptic curves and Goldfeld's conjecture  ]]
 +
| Jordan Ellenberg
 
|
 
|
 
|-
 
|-
|Sept 20
+
|February 2 (Room: 911)
|[http://www.math.neu.edu/people/profile/valerio-toledano-laredo Valerio Toledano Laredo] (Northeastern)
+
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)
 +
|[[#February 2 Thomas Fai (Harvard)|  The Lubricated Immersed Boundary Method ]]
 +
| Spagnolie, Smith
 
|
 
|
|Gurevich
 
 
|-
 
|-
|Sept 27 (Distinguished lecture)
+
|February 5 (Monday, Room: 911)
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)
+
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University)  
 +
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]
 +
| Ellenberg, Gurevitch
 
|
 
|
|Gurevich
 
 
|-
 
|-
|Oct 4
+
|February 6 (Tuesday 2 pm, Room 911)
|[http://www.math.tamu.edu/~sottile/ Frank Sottile] (Texas A&M)
+
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University)  
 +
|[[#February 6 Alex Lubotzky (Hebrew University)|  Groups' approximation, stability and high dimensional expanders ]]
 +
| Ellenberg, Gurevitch
 
|
 
|
|Caldararu
 
 
|-
 
|-
|Oct 11
+
|February 9
|
+
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)
|
+
|[[#February 9 Wes Pegden (CMU)|  The fractal nature of the Abelian Sandpile ]]
 +
| Roch
 
|
 
|
 
|-
 
|-
|Oct 15
+
|March 2
|Reserved for a distinguished lecture
+
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)
 +
|[[# TBA|  TBA  ]]
 +
| Caldararu
 
|
 
|
|Valko
 
 
|-
 
|-
|<strike>Oct 18</strike>
+
| March 16
|No colloquium due to the distinguished lecture
+
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)
|
+
|[[# TBA|  TBA  ]]
 +
| WIMAW
 
|
 
|
 
|-
 
|-
|Oct 25
+
|April 4 (Wednesday)
|[http://www.math.umn.edu/~garrett/ Paul Garrett] (Minnesota)
+
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)
|
+
|[[# TBA| TBA  ]]
|Gurevich
+
| Craciun
|
+
 
|
 
|
 
|-
 
|-
|Nov 1
+
| April 6
|[http://www.cs.utexas.edu/~alewko/ Allison Lewko] (Microsoft Research New England)
+
| Reserved
 +
|[[# TBA|  TBA  ]]
 +
| Melanie
 
|
 
|
|Stovall
 
 
|-
 
|-
|Nov 8
+
| April 13
 +
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)
 +
|[[# TBA|  TBA  ]]
 +
| WIMAW
 
|
 
|
|
 
|}
 
 
== Spring 2014 ==
 
 
{| cellpadding="8"
 
!align="left" | date
 
!align="left" | speaker
 
!align="left" | title
 
!align="left" | host(s)
 
 
|-
 
|-
|Jan 24
+
| April 20
|
+
| Xiuxiong Chen(Stony Brook University)
|
+
|[[# Xiuxiong Chen|  TBA  ]]
 +
| Bing Wang
 
|
 
|
 
|-
 
|-
|Jan 31
+
| April 25 (Wednesday)
|
+
| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Waseda University) Wasow lecture
|
+
|[[# TBA|  TBA  ]]
 +
| Tran
 
|
 
|
 
|-
 
|-
|Feb 7
+
|date
|
+
| person (institution)
|
+
|[[# TBA|  TBA  ]]
 +
| hosting faculty
 
|
 
|
 
|-
 
|-
|Feb 14
+
|date
|
+
| person (institution)
|
+
|[[# TBA|  TBA  ]]
 +
| hosting faculty
 
|
 
|
 
|-
 
|-
|Feb 21
+
|date
|
+
| person (institution)
|
+
|[[# TBA|  TBA  ]]
 +
| hosting faculty
 
|
 
|
 
|-
 
|-
|Feb 28
+
|date
|
+
| person (institution)
|
+
|[[# TBA|  TBA  ]]
 +
| hosting faculty
 
|
 
|
 
|-
 
|-
|March 7
+
|date
|
+
| person (institution)
|
+
|[[# TBA|  TBA  ]]
 +
| hosting faculty
 
|
 
|
 
|-
 
|-
|March 14
+
|date
|
+
| person (institution)
|
+
|[[# TBA| TBA  ]]
|
+
| hosting faculty
|-
+
|<strike>March 21</strike>
+
|'''Spring Break'''
+
|No Colloquium
+
 
|
 
|
 
|-
 
|-
|March 28
+
|date
|
+
| person (institution)
|
+
|[[# TBA|  TBA  ]]
 +
| hosting faculty
 
|
 
|
 
|-
 
|-
|April 4
+
|date
|
+
| person (institution)
|
+
|[[# TBA|  TBA  ]]
 +
| hosting faculty
 
|
 
|
 
|-
 
|-
|April 11
+
|date
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)
+
| person (institution)
 +
|[[# TBA|  TBA  ]]
 +
| hosting faculty
 
|
 
|
|Gurevich
 
|-
 
|April 18 (Wasow Lecture)
 
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)
 
|
 
|A. Seeger
 
|-
 
|April 25
 
|
 
|
 
|
 
|-
 
|May 2
 
|
 
|
 
|
 
|-
 
|May 9
 
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)
 
|
 
|WIMAW
 
 
|}
 
|}
  
== Past talks ==
+
== Spring Abstracts ==
 +
 
 +
 
 +
===January 29 Li Chao (Columbia)===
 +
 
 +
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) ===
 +
 
 +
Title: The Lubricated Immersed Boundary Method
 +
 
 +
Abstract:
 +
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)===
 +
 
 +
Title:  High dimensional expanders: From Ramanujan graphs to Ramanujan complexes
 +
 
 +
Abstract:
 +
 
 +
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.
 +
 
 +
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.
 +
 
 +
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.
 +
 
 +
 
 +
===February 6 Alex Lubotzky (Hebrew University)===
 +
 
 +
Title:  Groups' approximation, stability and high dimensional expanders
 +
 
 +
Abstract:
 +
 
 +
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 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.
 +
 
 +
All notions will be explained.      Joint work with M, De Chiffre, L. Glebsky and A. Thom.
 +
 
 +
===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.
 +
 
 +
 
 +
== Past Colloquia ==
 +
 
 +
[[Colloquia/Blank|Blank Colloquia]]
 +
 
 +
[[Colloquia/Fall2017|Fall 2017]]
 +
 
 +
[[Colloquia/Spring2017|Spring 2017]]
 +
 
 +
[[Archived Fall 2016 Colloquia|Fall 2016]]
 +
 
 +
[[Colloquia/Spring2016|Spring 2016]]
 +
 
 +
[[Colloquia/Fall2015|Fall 2015]]
 +
 
 +
[[Colloquia/Spring2014|Spring 2015]]
 +
 
 +
[[Colloquia/Fall2014|Fall 2014]]
 +
 
 +
[[Colloquia/Spring2014|Spring 2014]]
 +
 
 +
[[Colloquia/Fall2013|Fall 2013]]
 +
 
 +
[[Colloquia 2012-2013|Spring 2013]]
  
Last year's schedule: [[Colloquia 2012-2013]]
+
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]

Revision as of 11:32, 9 February 2018

Mathematics Colloquium

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

Spring 2018

date speaker title host(s)
January 29 (Monday) Li Chao (Columbia) Elliptic curves and Goldfeld's conjecture Jordan Ellenberg
February 2 (Room: 911) Thomas Fai (Harvard) The Lubricated Immersed Boundary Method Spagnolie, Smith
February 5 (Monday, Room: 911) Alex Lubotzky (Hebrew University) High dimensional expanders: From Ramanujan graphs to Ramanujan complexes Ellenberg, Gurevitch
February 6 (Tuesday 2 pm, Room 911) Alex Lubotzky (Hebrew University) Groups' approximation, stability and high dimensional expanders Ellenberg, Gurevitch
February 9 Wes Pegden (CMU) The fractal nature of the Abelian Sandpile Roch
March 2 Aaron Bertram (University of Utah) TBA Caldararu
March 16 Anne Gelb (Dartmouth) TBA WIMAW
April 4 (Wednesday) John Baez (UC Riverside) TBA Craciun
April 6 Reserved TBA Melanie
April 13 Jill Pipher (Brown) TBA WIMAW
April 20 Xiuxiong Chen(Stony Brook University) TBA Bing Wang
April 25 (Wednesday) Hitoshi Ishii (Waseda University) Wasow lecture TBA Tran
date person (institution) TBA hosting faculty
date person (institution) TBA hosting faculty
date person (institution) TBA hosting faculty
date person (institution) TBA hosting faculty
date person (institution) TBA hosting faculty
date person (institution) TBA hosting faculty
date person (institution) TBA hosting faculty
date person (institution) TBA hosting faculty
date person (institution) TBA hosting faculty

Spring Abstracts

January 29 Li Chao (Columbia)

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)

Title: The Lubricated Immersed Boundary Method

Abstract: 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)

Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes

Abstract:

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.

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.

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.


February 6 Alex Lubotzky (Hebrew University)

Title: Groups' approximation, stability and high dimensional expanders

Abstract:

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 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.

All notions will be explained. Joint work with M, De Chiffre, L. Glebsky and A. Thom.

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.


Past Colloquia

Blank Colloquia

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Spring 2015

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012