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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'''.
  
[[Colloquia/Spring 2015 | Tentative schedule for Spring 2015]]
+
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].
  
== Fall 2014 ==
+
==Spring 2019==
  
 
{| 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)
 
|-
 
|-
|September 12
+
|Jan 25
| [http://mduchin.math.tufts.edu/index.html Moon Duchin] (Tufts University)
+
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW
| [[Colloquia#September 12:  Moon Duchin (Tufts University) | Geometry and counting in the Heisenberg group]]
+
|[[#Beata Randrianantoanina (Miami University Ohio) | Some nonlinear problems in the geometry of Banach spaces and their applications  ]]
| Dymarz and WIMAW
+
| Tullia Dymarz
 +
|
 +
|-
 +
|Jan 30 '''Wednesday'''
 +
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)
 +
|[[#Lillian Pierce (Duke University) |  Short character sums  ]]
 +
| Boston and Street
 +
|
 
|-
 
|-
|September 19
+
|Jan 31 '''Thursday'''
|[http://www.mast.queensu.ca/~ggsmith/ Gregory G. Smith] (Queen's University)
+
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)
|[[Colloquia#September 19: Gregory G. Smith (Queen's University) | Nonnegative sections and sums of squares]]
+
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations  ]]
|Erman
+
| Street
 +
|
 
|-
 
|-
|September 26
+
|Feb 1
|[http://www.math.uci.edu/~jxin/ Jack Xin] (UC Irvine)
+
| [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University)
|[[Colloquia#September 26: Jack Xin (UC Irvine) | G-equations and Front Motion in Fluid Flows]]
+
|[[# TBA|  TBA ]]
|Jin
+
| Qin
 +
|
 
|-
 
|-
|October 3
+
|Feb 5 '''Tuesday'''
|[http://math.arizona.edu/~tiep/ Pham Huu Tiep] (University of Arizona)
+
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)
|[[Colloquia#October 3: Pham Huu Tiep (Arizona) | Adequate subgroups]]
+
|[[# TBA| TBA  ]]
|Gurevich
+
| Denisov
 +
|
 
|-
 
|-
|October 10
+
|Feb 8
|[http://www.math.ubc.ca/~adem/ Alejandro Adem] (UBC)
+
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)
|[[Colloquia#October 10: Alejandro Adem (UBC) | Topology of Commuting Matrices]]
+
|[[#Aaron Naber (Northwestern) |   A structure theory for spaces with lower Ricci curvature bounds  ]]
|Yang
+
| Street
 +
|
 
|-
 
|-
|October 17
+
|Feb 15
|[http://www.icse.cornell.edu/ziagroup/ Roseanna Zia] (Cornell University)
+
|  
|[[Colloquia#October 17: Roseanna Zia (Cornell) | A micro-mechanical study of coarsening and rheology of colloidal gels: Cage building, cage hopping, and Smoluchowski’s ratchet]]
+
|[[# TBA| TBA  ]]
|Spagnolie
+
|  
 +
|
 
|-
 
|-
|October 24
+
|Feb 22
|[http://www.math.utoronto.ca/almut/ Almut Burchard] (Toronto)
+
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)
|[[Colloquia#October 24: Almut Burchard (Toronto) | Symmetrization, sharp inequalities, and geometric stability for integral functionals]]
+
|[[# TBA|  TBA ]]
|Stovall
+
| Erman and Corey
 +
|
 
|-
 
|-
|October 31
+
|March 4
|[http://www.math.uchicago.edu/~ngo/ Bao Chau Ngo] (Chicago)
+
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture
|[[Colloquia#October 31:  Bao Chau Ngo (Chicago) | L-Function, Trace Formula and Moduli Spaces]]
+
|[[# TBA| TBA ]]
|Gurevich
+
| Kim
 +
|
 
|-
 
|-
|November 7
+
|March 8
|Reserved for possible job interview
+
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)
 +
|[[# TBA|  TBA  ]]
 +
| Erman
 
|
 
|
 +
|-
 +
|March 15
 +
| Maksym Radziwill (Caltech)
 +
|[[# TBA|  TBA  ]]
 +
| Marshall
 
|
 
|
 
|-
 
|-
|November 14
+
|March 29
|Reserved for possible job interview
+
| Jennifer Park (OSU)
|  
+
|[[# TBA|  TBA  ]]
 +
| Marshall
 +
|
 
|-
 
|-
|November 21
+
|April 5
|[http://math.uchicago.edu/~hung/ Hung Tran](Univ. of Chicago)
+
| Ju-Lee Kim (MIT)
||[[Colloquia#November 21: Hung Tran (Univ. of Chicago) | Selection problems for a discounted degenerate viscous
+
|[[# TBA| TBA ]]
  Hamilton--Jacobi equation]]
+
| Gurevich
| Mikhail Feldman
 
 
|
 
|
 
|-
 
|-
|November 28
+
|April 12
|University holiday
+
| Evitar Procaccia (TAMU)
 +
|[[# TBA|  TBA  ]]
 +
| Gurevich
 
|
 
|
|
 
 
|-
 
|-
|December 5
+
|April 19
|Reserved for possible job interview
+
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)
 +
|[[# TBA|  TBA  ]]
 +
| Jean-Luc
 
|
 
|
|
 
 
|-
 
|-
|December 12
+
|April 26
| Reserved for possible job interview
+
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)
 +
|[[# TBA|  TBA  ]]
 +
| WIMAW
 
|
 
|
|
 
 
|-
 
|-
 +
|May 3
 +
| Tomasz Przebinda (Oklahoma)
 +
|[[# TBA|  TBA  ]]
 +
| Gurevich
 +
|
 
|}
 
|}
  
 
== Abstracts ==
 
== Abstracts ==
  
===September 12:  Moon Duchin (Tufts University)===
+
===Beata Randrianantoanina (Miami University Ohio)===
  
====Geometry and counting in the Heisenberg group====
+
Title: Some nonlinear problems in the geometry of Banach spaces and their applications.
  
The growth function of a finitely-generated group enumerates how many words can be spelled with each possible number of letters-- this should be thought of as a sort of volume growth in any geometric model of the group. A major theorem of Gromov tells us exactly which groups have growth in the polynomial range:  those that are (virtually) nilpotent. But we can still wonder how regular the growth of a nilpotent group is:  is it actually a polynomial?  Or could it exhibit some transcendentality together with pretty slow growth? 
+
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.
  
I'll talk about some themes and techniques in the study of group growth and outline a geometry of numbers for nilpotent groups, including a recent result with M. Shapiro settling a long-standing question:  the Heisenberg group -- the simplest non-abelian nilpotent group -- has rational growth in any generating set. 
+
===Lillian Pierce (Duke University)===
  
===September 19: Gregory G. Smith (Queen's University)===
+
Title: Short character sums
  
====Nonnegative sections and sums of squares====
+
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.
  
A polynomial with real coefficients is nonnegative if it takes on only nonnegative values.  For example, any sum of squares is obviously nonnegative.  For a homogeneous polynomial with respect to the standard grading, Hilbert famously characterized when the converse holds, that is when every nonnegative homogeneous polynomial is a sum of squares.  After reviewing some history of this problem, we will examine this converse in more general settings such as global sections of a line bundles.  This line of inquiry has unexpected connections to classical algebraic geometry and leads to new examples in which every nonnegative homogeneous polynomial is a sum of squares.  This talk is based on joint work with Grigoriy Blekherman and Mauricio Velasco.
+
===Dean Baskin (Texas A&M)===
  
===September 26: Jack Xin (UC Irvine)===
+
Title: Radiation fields for wave equations
  
====G-equations and Front Motion in Fluid Flows====
+
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.
  
G-equations are level set Hamilton-Jacobi equations (HJE) for modeling flame fronts in turbulent combustion where a fundamental problem is to characterize the turbulent flame speeds s_T.  The existence of s_T is connected with the homogenization of HJE, however classical theory does not apply due to the non-coercive and non-convex nature of the level set Hamiltonian. We shall illustrate the asymptotic properties of s_T from both Eulerian and Lagrangian perspectives in the case of two dimensional periodic incompressible flows, in particular cellular flows.
+
===Aaron Naber (Northwestern)===
  
Analytical and numerical results demonstrate that G-equations capture well the enhancement, slow down and quenching phenomena observed in fluid experiments. We also comment on s_T in chaotic flows. This is joint work with Yifeng Yu and Yu-Yu Liu.
+
Title: A structure theory for spaces with lower Ricci curvature bounds.
  
===October 3: Pham Huu Tiep (Arizona)===
+
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.
  
====Adequate subgroups====
 
  
The notion of adequate subgroups was introduced by Thorne. It is a weakening of the notion of big subgroups used in generalizations of the Taylor-Wiles method for proving the automorphy of certain Galois representations. Using this idea, Thorne was able to strengthen many automorphy lifting theorems. It was shown recently by Guralnick, Herzig, Taylor, and Thorne that if the degree is small compared to the characteristic then all absolutely irreducible representations are adequate. We will discuss extensions of this result obtained recently in joint work with R. M. Guralnick and F. Herzig. In particular, we show that almost all absolutely irreducible representations in characteristic p of degree less than p are adequate. We will also address a question of Serre about
+
== Past Colloquia ==
indecomposable modules in characteristic p of dimension less than 2p-2.
 
 
 
===October 10:  Alejandro Adem (UBC)===
 
 
 
====Topology of Commuting Matrices====
 
  
In this talk we will describe basic topological properties of the space of commuting unitary matrices. In particular we will show that they can be assembled to form a space which classifies commutativity for vector bundles and which has very interesting homotopy-theoretic properties.
+
[[Colloquia/Blank|Blank]]
  
===October 17: Roseanna Zia (Cornell) ===
+
[[Colloquia/Fall2018|Fall 2018]]
  
====A micro-mechanical study of coarsening and rheology of colloidal gels: Cage building, cage hopping, and Smoluchowski’s ratchet====
+
[[Colloquia/Spring2018|Spring 2018]]
  
Reconfigurable soft solids such as viscoelastic gels have emerged in the past decade as a promising material in numerous applications ranging from engineered tissue to drug delivery to injectable sensors. These include colloidal gels, which microscopically comprise a scaffoldlike network of interconnected particles embedded in a solvent. Network bonds can be permanent or reversible, depending on the nature and strength of interparticle attractions. When attractions are on the order of just a few kT, bonds easily rupture and reform. On a macroscopic scale, bond reversibility allows a gel to transition from solidlike behavior during storage, to liquidlike behavior during flow (e.g., injection or shear), and back to solidlike behavior in situ. On a microscopic scale, thermal fluctuations of the solvent are occasionally strong enough to break colloidal bonds, temporarily allowing particles to migrate and exchange neighbors before rebonding to the network, leading to structural evolution over time. Prior studies of colloidal gels have examined evolution of length scales and dynamics such as decorrelation times. Left open were additional questions such as how the particle-rich regions are structured (liquidlike, glassy, crystalline), how restructuring takes place (via bulk diffusion, surface migration, coalescence of large structures), and the impact of the evolution on rheology. In this talk I discuss these themes as explored in our recent dynamic simulations. We find that the network strands comprise a glassy, immobile interior near random-close packing, enclosed by a liquidlike surface along which the diffusive migration of particles drives structural coarsening. We show that coarsening is a three-step process of cage forming, cage hopping, and cage arrest, where particles migrate to ever-deeper energy wells via “Smoluchowski’s ratchet.” Both elastic and viscous high-frequency moduli are found to scale with the square-root of the frequency, similar to the perfectly viscoelastic behavior of non-hydrodynamically interacting, purely repulsive dispersions. But here, the behavior is elastic over all frequencies, with a quantitative offset between elastic and viscous moduli, which owes its origin to the hindrance of diffusion by particle attractions. Propagation of this elasticity via the network gives rise to age-stiffening as the gel coarsens. This simple phenomenological model suggests a rescaling of the moduli on dominant network length scale that collapses moduli for all ages onto a single curve. We propose a Rouse-like theoretical model and, from it, derive an analytical expression that predicts the effects of structural aging on rheology whereby linear response can be determined at any age by measurement of dominant network length scale—or vice versa.
+
[[Colloquia/Fall2017|Fall 2017]]
  
===October 24:  Almut Burchard (Toronto)===
+
[[Colloquia/Spring2017|Spring 2017]]
  
====Symmetrization, sharp inequalities, and geometric stability for integral functionals====
+
[[Archived Fall 2016 Colloquia|Fall 2016]]
  
Many integral functionals are maximized (under appropriate constraints) by radially symmetric functions.  For example, the Coulomb energy of a positive charge density --- the double integral of the Newton potential against the density --- increases under symmetrization.  The physical reason is that the interaction energy between the charges grows as the typical distance between the charges shrinks.  The energy increases strictly, unless the charge density is already radially decreasing about some point. Is this characterization of equality cases "stable"? In other words, must near-maximizers be close to maximizers?
+
[[Colloquia/Spring2016|Spring 2016]]
  
Such stability questions have been well-studied for the isoperimetric inequality and other functionals that involve gradients since the 1990's; the first results in that direction are due to Bonnesen in the 1920's. For example, the excess perimeter of a set (as compared to a ball of the same volume) controls its difference from a suitable translate of that ball.  Much less is known about convolutions and other multiple integrals that describe "non-local" interactions. In some cases, not even a complete list of maximizers is known. I will discuss very recent developments (due to M. Christ, Figalli, Jerison, and others), mention open problems, and present joint work with Greg Chambers on the Coulomb energy.
+
[[Colloquia/Fall2015|Fall 2015]]
  
 +
[[Colloquia/Spring2014|Spring 2015]]
  
===October 31:  Bao Chau Ngo (Chicago)===
+
[[Colloquia/Fall2014|Fall 2014]]
 
 
====L-function, trace formula, and moduli space====
 
 
 
In his PhD thesis, J. Tate recast the construction of Riemann's
 
zeta function in term of harmonic analysis on the group of ideles. This
 
construction was generalized by Godement and Jacquet to principal
 
L-function of automorphic forms. In a minimalistic view, Langlands program
 
consists in understanding analytic properties of all automorphic L-functions.
 
Braverman and Kazhdan proposed a generalization of Godement-Jacquet's
 
construction. I will talk about these construction in connection with the trace
 
formula and the geometry of certain moduli spaces.
 
 
 
 
 
===November 21: Hung Tran (Univ. of Chicago)===
 
 
 
====Selection problems for a discounted degenerate viscous
 
Hamilton--Jacobi equation====
 
 
 
I will give first a brief overview on the selection problem for solutions of Hamilton--Jacobi equations, which leads to the theory of viscosity solutions. Then I will describe the cell/ergodic problem of interest and its interesting phenomena. Finally, I will state the corresponding selection problem, the main result, and explain some key ideas. This is a joint work with Hiroyoshi Mitake.
 
 
 
== Past Colloquia ==
 
  
 
[[Colloquia/Spring2014|Spring 2014]]
 
[[Colloquia/Spring2014|Spring 2014]]

Latest revision as of 09:43, 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