Colloquia/Fall18: Difference between revisions

From UW-Math Wiki
Jump to navigation Jump to search
(255 intermediate revisions by 20 users not shown)
Line 1: Line 1:
__NOTOC__
= 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]] == -->
== Spring 2018 ==


== Fall 2016  ==
 
{| cellpadding="8"
{| cellpadding="8"
!align="left" | date   
!align="left" | date   
Line 15: Line 11:
!align="left" | host(s)
!align="left" | host(s)
|-
|-
|September 9
|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
|
|
|-
|-
|September 16
|February 2 (Room: 911)
|[http://www.math.cmu.edu/~ploh/ Po-Shen Loh] (CMU)
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)
|Directed paths: from Ramsey to Pseudorandomness
|[[#February 2 Thomas Fai (Harvard)|  The Lubricated Immersed Boundary Method ]]
|Ellenberg
| Spagnolie, Smith
|
|
|-
|-
|September 23
|February 5 (Monday, Room: 911)
| [http://www.math.wisc.edu/~craciun/ Gheorghe Craciun] (UW-Madison)
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University)  
|Toric Differential Inclusions and a Proof of the Global Attractor Conjecture
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]
| Street
| Ellenberg, Gurevitch
|[[# |    ]]
|-
|September 30
|[http://math.uga.edu/~magyar/ Akos Magyar]  (University of Georgia)
|Geometric Ramsey theory
| Cook
|
|
|-
|-
|October 7
|February 6 (Tuesday 2 pm, Room 911)
|  
| [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
|
|
|-
|-
|October 14
|February 9
| [https://www.math.lsu.edu/~llong/ Ling Long] (LSU)
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)
|Hypergeometric functions over finite fields
|[[#February 9 Wes Pegden (CMU)|  The fractal nature of the Abelian Sandpile ]]
| Yang
| Roch
|
|
|-
|-
|October 21
|March 2
|'''No colloquium this week'''
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)
|[[#  |    ]]
|[[# TBA|  TBA ]]
|
| Caldararu
|
|
|-
|-
|'''Tuesday, October 25, 9th floor'''
| March 16
|[http://users.math.yale.edu/users/steinerberger/ Stefan Steinerberger] (Yale)
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)
|Three Miracles in Analysis
|[[# TBA|  TBA  ]]
|Seeger
| WIMAW
|
|
|-
|-
|October 28, 9th floor
|April 4 (Wednesday)
| [http://order.ph.utexas.edu/people/Reichl.htm Linda Reichl] (UT Austin)
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)
|Microscopic hydrodynamic modes in a binary mixture
|[[# TBA|  TBA  ]]
|Minh-Binh Tran
| Craciun
|
|
|-
|-
|'''Monday, October 31, B239'''
| April 6
[https://math.berkeley.edu/~kpmann/ Kathryn Mann] (Berkeley)
| Reserved
|Groups acting on the circle
|[[# TBA|  TBA ]]
|Smith
| Melanie
|
|
|-
|-
|November 4
| April 13
|
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)
|
|[[# TBA|  TBA  ]]
|
|
|-
|'''Monday, November 7 at 4:30, 9th floor''' ([http://www.ams.org/meetings/lectures/maclaurin-lectures AMS Maclaurin lecture])
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (New Zealand Institute for Advanced Study)
|Siegel's problem on small volume lattices
| Marshall
|
|-
|November 11
|  Reserved for possible job talks
|[[# |    ]]
|
|
|-
|'''Wednesday, November 16, 9th floor'''
|  [http://math.uchicago.edu/~klindsey/ Kathryn Lindsey] (U Chicago)
|Shapes of Julia Sets
|Michell
|
|-
|November 18, B239
|[http://www-personal.umich.edu/~asnowden/ Andrew Snowden] (University of Michigan)
|Recent progress in representation stability
|Ellenberg
|
|-
|'''Monday, November 21, 9th floor'''
|[https://www.fmi.uni-sofia.bg/fmi/logic/msoskova/index.html Mariya Soskova] (University of Wisconsin-Madison)
|Definability in degree structures
|Smith
|
|-
|November 25
|  '''Thanksgiving break'''
|[[# |    ]]
|
|
|-
|December 2, 9th floor
|  [http://math.columbia.edu/~hshen/ Hao Shen] (Columbia)
|[[#Friday, December 2:  Hao Shen (Columbia) | ''Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?'']]
|Roch
|
|-
|'''Monday, December 5, B239'''
|  [https://www.math.wisc.edu/~wang/ Botong Wang] (UW Madison)
|[[#Friday, December 5: Botong Wang  (UW-Madison) | ''Enumeration of points, lines, planes, etc.'']]
|Maxim
|
|-
|December 9, B239
|  [http://math.uchicago.edu/~awbrown/ Aaron Brown] (U Chicago)
| [[#Friday, December 9: Aaron Brown (U Chicago) | ''Lattice actions and recent progress in the Zimmer program'']]
|Kent
|}
 
== Spring 2017  ==
 
{| cellpadding="8"
!align="left" | date 
!align="left" | speaker
!align="left" | title
!align="left" | host(s)
|-
|January 20
|Reserved for possible job talks 
|[[#  |    ]]
|
|-
|January 27
|Reserved for possible job talks
|[[# |    ]]
|
|
|-
|February 3
|
|[[#  |    ]]
|
|
|-
|February 6 (Wasow lecture)
| Benoit Perthame (University of Paris VI)
|[[# TBA|  TBA ]]
| Jin
|  
|-
|February 10 (WIMAW lecture)
| Alina Chertock (NC State Univ.)
|[[# |  ]]  
| WIMAW
| WIMAW
|
|
|-
|-
|February 17
| April 20
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)
| Xiuxiong Chen(Stony Brook University)
|[[#   |     ]]
|[[# Xiuxiong Chen| TBA  ]]
| Minh-Binh Tran
| Bing Wang
|
|
|-
|-
|February 24
| April 25 (Wednesday)
|  
| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Waseda University) Wasow lecture
|[[#  |    ]]
|[[# TBA|  TBA ]]
|  
| Tran
|
|
|-
|-
|March 3
|date
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)
| person (institution)
|[[# |   ]]
|[[# TBA| TBA  ]]
|Dymarz
| hosting faculty
|
|
|-
|-
|Tuesday, March 7, 4PM (Distinguished Lecture)
|date
| [http://pages.iu.edu/~temam/  Roger Temam] (Indiana University)  
| person (institution)
|[[#  |    ]]
|[[# TBA|  TBA ]]
|Smith
| hosting faculty
|
|
|-
|-
|Wednesday, March 8, 2:25PM
|date
| [http://pages.iu.edu/~temam/  Roger Temam] (Indiana University)  
| person (institution)
|[[#  |    ]]
|[[# TBA|  TBA ]]
|Smith
| hosting faculty
|
|
|-
|-
|March 10
|date
| '''No Colloquium'''
| person (institution)
|[[# |   ]]
|[[# TBA| TBA  ]]
|
| hosting faculty
|
|
|-
|-
|March 17
|date
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)  
| person (institution)
| TBA
|[[# TBA|  TBA ]]
| M. Matchett Wood
| hosting faculty
|
|
|-
|-
|March 24
|date
| '''Spring Break'''
| person (institution)
|[[# |   ]]
|[[# TBA| TBA  ]]
|
| hosting faculty
|
|
|-
|-
|Wednesday, March 29 (Wasow)
|date
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU)  
| person (institution)
|[[# TBA|   TBA]]
|[[# TBA| TBA ]]
|Tran
| hosting faculty
|
|
|-
|-
|March 31
|date
| '''No Colloquium'''
| person (institution)
|[[# |   ]]
|[[# TBA| TBA  ]]
|
| hosting faculty
|
|
|-
|-
|April 7
|date
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]
| person (institution)
|[[# |   ]]
|[[# TBA| TBA  ]]
|Erman
| hosting faculty
|
|
|-
|April 14
|  Wilfrid Gangbo
|[[# |    ]]
|Feldman & Tran
|
|-
|April 21
|  [http://www.math.stonybrook.edu/~mde/ Mark Andrea de Cataldo]  (Stony Brook)
|TBA
| Maxim
|
|-
|April 28
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] 
|[[# TBA|  TBA  ]]
|Li
|}
|}


== Abstracts ==
== Spring Abstracts ==
=== September 16: Po-Shen Loh (CMU) ===
Title: Directed paths: from Ramsey to Pseudorandomness


Abstract: Starting from an innocent Ramsey-theoretic question regarding directed
paths in graphs, we discover a series of rich and surprising connections
that lead into the theory around a fundamental result in Combinatorics:
Szemeredi's Regularity Lemma, which roughly states that every graph (no
matter how large) can be well-approximated by a bounded-complexity
pseudorandom object.  Using these relationships, we prove that every
coloring of the edges of the transitive N-vertex tournament using three
colors contains a directed path of length at least sqrt(N) e^{log^* N}
which entirely avoids some color.  The unusual function log^* is the
inverse function of the tower function (iterated exponentiation).


=== September 23: Gheorghe Craciun (UW-Madison) ===
===January 29 Li Chao (Columbia)===
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture


Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics.
Title: Elliptic curves and Goldfeld's conjecture


The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.
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.


We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality.
=== February 2 Thomas Fai (Harvard) ===


=== September 30: Akos Magyar (University of Georgia) ===
Title: The Lubricated Immersed Boundary Method
Title: Geometric Ramsey theory


Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.
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.


=== October 14: Ling Long (LSU) ===  
===February 5 Alex Lubotzky (Hebrew University)===
Title: Hypergeometric functions over finite fields


Abstract: Hypergeometric functions are special functions with lot of
TitleHigh dimensional expanders: From Ramanujan graphs to Ramanujan complexes
symmetries. In this talk, we will introduce hypergeometric functions over finite
fields, originally due to Greene, Katz and McCarthy, in a way that is
parallel to the classical hypergeometric functions, and discuss their
properties and applications to character sums and the arithmetic of
hypergeometric abelian varieties.
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.


=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===
Abstract:  
Title: Three Miracles in Analysis


Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).
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.  


=== October 28: Linda Reichl (UT Austin) ===
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.
Title: Microscopic hydrodynamic modes in a binary mixture


Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.
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.  


===Monday, October 31: Kathryn Mann (Berkeley) ===
Title: Groups acting on the circle


Abstract:  Given a group G and a manifold M, can one describe all the actions of G on M?  This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group. 
===February 6 Alex Lubotzky (Hebrew University)===


In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. 
Title: Groups' approximation, stability and high dimensional expanders


===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===
Abstract:  
Title: Siegel's problem on small volume lattices


Abstract: We outline in very general terms the history and the proof of the identification
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 normsWe 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.
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3
Coxeter group extended by the involution preserving the symmetry of this
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.
This solves (in three dimensions) a problem posed by Siegel in 1945.  Siegel solved this problem in two dimensions by deriving the
signature formula identifying the (2,3,7)-triangle group as having minimal
co-area.
   
There are strong connections with arithmetic hyperbolic geometry in
the proof, and the result has applications in the maximal symmetry groups
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem
and Siegel's result do.


===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===
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.
Title: Shapes of Julia Sets


Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes of polynomial Julia sets?"  For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name?  It turns out the answer to all of these is "yes!"  I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.
All notions will be explained.       Joint work with M, De Chiffre, L. Glebsky and A. Thom.


===November 18: Andrew Snowden (University of Michigan)===
===February 9 Wes Pegden (CMU)===
Title: Recent progress in representation stability


Abstract: Representation stability is a relatively new field that studies
Title: The fractal nature of the Abelian Sandpile
somewhat exotic algebraic structures and exploits their properties to
prove results (often asymptotic in nature) about objects of interest.
I will describe some of the algebraic structures that appear (and
state some important results about them), give a sampling of some
notable applications (in group theory, topology, and algebraic
geometry), and mention some open problems in the area.


===Monday, November 21:  Mariya Soskova (University of Wisconsin-Madison)===
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.
Title: Definability in degree structures


Abstract:  Some incomputable sets are more incomputable than others. We use
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.
Turing reducibility and enumeration reducibility to measure the
relative complexity of incomputable sets. By identifying sets of the
same complexity, we can associate to each reducibility a degree
structure: the partial order of the Turing degrees and the partial
order of the enumeration degrees. The two structures are related in
nontrivial ways. The first has an isomorphic copy in the second and
this isomorphic copy is an automorphism base. In 1969, Rogers asked a
series of questions about the two degree structures with a common
theme: definability. In this talk I will introduce the main concepts
and describe the work that was motivated by these questions.


===Friday, December 2:  Hao Shen (Columbia)===
Title:  Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?


Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.
== Past Colloquia ==


=== Friday, December 9: Aaron Brown (U Chicago) ===
[[Colloquia/Blank|Blank Colloquia]]
''Lattice actions and recent progress in the Zimmer program''


Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds.  For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions.  In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. 
[[Colloquia/Fall2017|Fall 2017]]


I will present some background, motivation, and selected previous results in the Zimmer program.  I will then explain two of my results within the Zimmer program:
[[Colloquia/Spring2017|Spring 2017]]
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).


== Past Colloquia ==
[[Archived Fall 2016 Colloquia|Fall 2016]]


[[Colloquia/Spring2016|Spring 2016]]
[[Colloquia/Spring2016|Spring 2016]]

Revision as of 16:32, 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