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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]].
 
==Spring 2019==


{| cellpadding="8"
{| cellpadding="8"
Line 11: Line 13:
!align="left" | host(s)
!align="left" | host(s)
|-
|-
|January 29 (Monday)
|Jan 25
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW
|[[#January 29 Li Chao (Columbia)|  Elliptic curves and Goldfeld's conjecture  ]]
|[[#Beata Randrianantoanina (Miami University Ohio) |  Some nonlinear problems in the geometry of Banach spaces and their applications ]]
| Jordan Ellenberg
| Tullia Dymarz
|
|-
|February 2 (Room: 911)
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)
|[[#February 2 Thomas Fai (Harvard)| The Lubricated Immersed Boundary Method ]]
| Spagnolie, Smith
|
|
|-
|-
|February 5 (Monday, Room: 911)
|Jan 30 '''Wednesday'''
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University)  
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)
|[[#February 5 Alex Lubotzky (Hebrew University)| High dimensional expanders: From Ramanujan graphs to Ramanujan complexes ]]
|[[#Lillian Pierce (Duke University) | Short character sums  ]]
| Ellenberg, Gurevitch
| Boston and Street
|
|
|-
|-
|February 6 (Tuesday 2 pm, Room 911)
|Jan 31 '''Thursday'''
| [http://www.ma.huji.ac.il/~alexlub/ Alex Lubotzky] (Hebrew University)  
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)
|[[#February 6 Alex Lubotzky (Hebrew University)|  Groups' approximation, stability and high dimensional expanders ]]
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations ]]
| Ellenberg, Gurevitch
| Street
|
|
|-
|-
|February 9
|Feb 1
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)
| [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University)
|[[#February 9 Wes Pegden (CMU)|  The fractal nature of the Abelian Sandpile ]]
| Roch
|
|-
|March 2
| [http://www.math.utah.edu/~bertram/ Aaron Bertram] (University of Utah)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| Caldararu
| Qin
|
|
|-
|-
| March 16
|Feb 5 '''Tuesday'''
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| WIMAW
| Denisov
|
|
|-
|-
|April 4 (Wednesday)
|Feb 8
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)
|[[# TBA| TBA ]]
|[[#Aaron Naber (Northwestern) |   A structure theory for spaces with lower Ricci curvature bounds ]]
| Craciun
| Street
|
|
|-
|-
| April 6
|Feb 15
| Reserved
|  
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| Melanie
|  
|
|
|-
|-
| April 13
|Feb 22
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| WIMAW
| Erman and Corey
|
|
|-
|-
| April 20
|March 4
| Reserved
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture
|[[# Xiuxiong Chen| TBA ]]
|[[# TBA| TBA ]]
| Bing Wang
| Kim
|
|
|-
|-
| April 25 (Wednesday)
|March 8
| [http://www.f.waseda.jp/hitoshi.ishii/ Hitoshi Ishii] (Waseda University) Wasow lecture
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| Tran
| Erman
|
|
|-
|-
|date
|March 15
| person (institution)
| Maksym Radziwill (Caltech)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| hosting faculty
| Marshall
|
|
|-
|-
|date
|March 29
| person (institution)
| Jennifer Park (OSU)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| hosting faculty
| Marshall
|
|
|-
|-
|date
|April 5
| person (institution)
| Ju-Lee Kim (MIT)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| hosting faculty
| Gurevich
|
|
|-
|-
|date
|April 12
| person (institution)
| Evitar Procaccia (TAMU)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| hosting faculty
| Gurevich
|
|
|-
|-
|date
|April 19
| person (institution)
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| hosting faculty
| Jean-Luc
|
|
|-
|-
|date
|April 26
| person (institution)
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| hosting faculty
| WIMAW
|
|
|-
|-
|date
|May 3
| person (institution)
| Tomasz Przebinda (Oklahoma)
|[[# TBA|  TBA  ]]
|[[# TBA|  TBA  ]]
| hosting faculty
| Gurevich
|
|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
|
|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
|
|
|}
|}


== Spring Abstracts ==
== Abstracts ==


===Beata Randrianantoanina (Miami University Ohio)===


===January 29 Li Chao (Columbia)===
Title: Some nonlinear problems in the geometry of Banach spaces and their applications.


Title: Elliptic curves and Goldfeld's conjecture
Abstract: Nonlinear problems in the geometry of Banach spaces have been studied since the inception of the field. In this talk I will outline some of the history, some of modern applications, and some open directions of research. The talk will be accessible to graduate students of any field of mathematics.


Abstract:
===Lillian Pierce (Duke University)===
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: Short character sums


Title: The Lubricated Immersed Boundary Method
Abstract: A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.


Abstract:
===Dean Baskin (Texas A&M)===
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: Radiation fields for wave equations


Title: High dimensional expanders: From Ramanujan graphs to Ramanujan complexes
Abstract: Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.


Abstract:
===Aaron Naber (Northwestern)===


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.  
Title: A structure theory for spaces with lower Ricci curvature bounds.


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.  
Abstract:  One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated.  It thus becomes a natural question, how well behaved or badly behaved can such spaces be?  This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like.  In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples.  The work discussed is joint with Cheeger, Jiang and with Li.


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.


== Past Colloquia ==


===February 6 Alex Lubotzky (Hebrew University)===
[[Colloquia/Blank|Blank]]
 
Title:  Groups' approximation, stability and high dimensional expanders


Abstract:
[[Colloquia/Fall2018|Fall 2018]]
 
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/Spring2018|Spring 2018]]


[[Colloquia/Fall2017|Fall 2017]]
[[Colloquia/Fall2017|Fall 2017]]

Latest revision as of 14:43, 24 January 2019

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.

Spring 2019

date speaker title host(s)
Jan 25 Beata Randrianantoanina (Miami University Ohio) WIMAW Some nonlinear problems in the geometry of Banach spaces and their applications Tullia Dymarz
Jan 30 Wednesday Lillian Pierce (Duke University) Short character sums Boston and Street
Jan 31 Thursday Dean Baskin (Texas A&M) Radiation fields for wave equations Street
Feb 1 Jianfeng Lu (Duke University) TBA Qin
Feb 5 Tuesday Alexei Poltoratski (Texas A&M University) TBA Denisov
Feb 8 Aaron Naber (Northwestern) A structure theory for spaces with lower Ricci curvature bounds Street
Feb 15 TBA
Feb 22 Angelica Cueto (Ohio State) TBA Erman and Corey
March 4 Vladimir Sverak (Minnesota) Wasow lecture TBA Kim
March 8 Jason McCullough (Iowa State) TBA Erman
March 15 Maksym Radziwill (Caltech) TBA Marshall
March 29 Jennifer Park (OSU) TBA Marshall
April 5 Ju-Lee Kim (MIT) TBA Gurevich
April 12 Evitar Procaccia (TAMU) TBA Gurevich
April 19 Jo Nelson (Rice University) TBA Jean-Luc
April 26 Kavita Ramanan (Brown University) TBA WIMAW
May 3 Tomasz Przebinda (Oklahoma) TBA Gurevich

Abstracts

Beata Randrianantoanina (Miami University Ohio)

Title: Some nonlinear problems in the geometry of Banach spaces and their applications.

Abstract: Nonlinear problems in the geometry of Banach spaces have been studied since the inception of the field. In this talk I will outline some of the history, some of modern applications, and some open directions of research. The talk will be accessible to graduate students of any field of mathematics.

Lillian Pierce (Duke University)

Title: Short character sums

Abstract: A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.

Dean Baskin (Texas A&M)

Title: Radiation fields for wave equations

Abstract: Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.

Aaron Naber (Northwestern)

Title: A structure theory for spaces with lower Ricci curvature bounds.

Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li.


Past Colloquia

Blank

Fall 2018

Spring 2018

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Spring 2015

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012

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