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__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'''.


== Fall 2015  ==
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].
 
Go to next semester, [[Colloquia/Spring 2016|Spring 2016]].


==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 4'''
| [http://homepages.math.uic.edu/~isaac/  Isaac Goldbring] (UIC)   
| [[Colloquia#September 4:  Isaac Goldbring (UIC) | On Kirchberg's embedding problem]]
| Andrews/Lempp
|-
|-
| '''September 11'''  
|Jan 25
| [https://sites.google.com/site/doronpuder/ Doron Puder] (IAS)
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW
| [[Colloquia#September 11: Doron Puder (IAS) | Word-Measures on Groups]]
|[[#Beata Randrianantoanina (Miami University Ohio) |  Some nonlinear problems in the geometry of Banach spaces and their applications  ]]
| Gurevich
| 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
|
|-
|Jan 31 '''Thursday'''
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations  ]]
| Street
|
|-
|Feb 1
| [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University)
|[[# TBA| TBA  ]]
| Qin
|
|-
|-
| '''September 18'''  
|Feb 5 '''Tuesday'''
| [http://homepages.math.uic.edu/~coskun/ Izzet Coskun] (UIC)
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)
| [[Colloquia#September 18: Izzet Coskun (UIC) | The geometry of points in the plane]]  
|[[# TBA|  TBA ]]
| Erman
| Denisov
|
|-
|-
| '''September 25'''
|Feb 8
| [https://pantherfile.uwm.edu/ourmazd/www/ Abbas Ourmazd] (UW-Milwaukee)  
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)
|   [[Colloquia#September 25:  Abbas Ourmazd (UW-Milwaukee) | Structure and Dynamics from Random Observations]]
|[[#Aaron Naber (Northwestern) |   A structure theory for spaces with lower Ricci curvature bounds  ]]
| Mitchell
| Street
|
|-
|-
| '''October 2'''
|Feb 15
|
|  
|  
|[[# TBA|  TBA  ]]
|  
|  
|
|-
|-
| '''October 9'''
|Feb 22
| Chanwoo Kim 
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)
| [[Colloquia#October 9: Chanwoo Kim  | Coercivity of the Boltzmann equation ]]
|[[# TBA| TBA  ]]
|
| Erman and Corey
|
|-
|-
| '''October 16'''
|March 4
| [http://mysite.science.uottawa.ca/hsalmasi/ Hadi Salmasian] (Ottawa)  
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture
| [[Colloquia#October 16:  Hadi Salmasian (University of Ottawa) | The Capelli problem and spectrum of invariant differential operators]]
|[[# TBA| TBA ]]
| Gurevich
| Kim
|
|-
|-
| '''October 23'''
|March 8
| Lu Wang (UW)  <!-- [webpage Speaker Name] (University) -->   
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)
|   [[Colloquia#October23:  Lu Wang (UW) | Singularities of Mean Curvature Flow]]
|[[# TBA| TBA ]]
| <!-- host -->
| Erman
|
|-
|-
| '''October 30'''
|March 15
|   [http://people.brandeis.edu/~charney/Charney15.html Ruth Charney] (Brandeis)    
| Maksym Radziwill (Caltech)
| [[Colloquia#October 30: Ruth Charney (Brandeis) | Finding hyperbolic behavior in non-hyperbolic spaces]]
|[[# TBA|  TBA ]]
| Dymarz
| Marshall
|
|-
|-
| '''November 6'''
|March 29
| [http://people.seas.harvard.edu/~chr/ Chris Rycroft] (Harvard)  
| Jennifer Park (OSU)
| [[Colloquia#November 6: Chris Rycroft (Harvard) | Interfacial dynamics of dissolving objects in fluid flow]]
|[[# TBA|  TBA ]]
| Spagnolie
| Marshall
|
|-
|-
| '''November 13'''
|April 5
|   [http://pages.iu.edu/~fisherdm/ David Fisher] (Indiana)    
| Ju-Lee Kim (MIT)
| [[Colloquia#November 13: David Fisher (Indiana) | Rigidity of quasi-isometric embeddings]]
|[[# TBA|  TBA ]]
| Dymarz
| Gurevich
|
|-
|-
| '''November 20'''
|April 12
|  Avy Soffer (Rutgers)
|  Evitar Procaccia (TAMU)
|   [[Colloquia#November 20: Avy Soffer (Rutgers) | Nonlinear Long Range Scattering and Normal Form Analysis]]
|[[# TBA|  TBA ]]
| Minh Binh Tran
| Gurevich
|
|-
|-
| '''November 27'''
|April 19
| University Holiday
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)
|  No Colloquium
|[[# TBA|  TBA  ]]
| Jean-Luc
|
|
|-
|-
| '''December 4'''
|April 26
| Charlie Smart (Uchicago)
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)
| [[Colloquia#December 4: Charlie Smart (Uchicago) | The Abelian Sandpile and Circle Packings]]
|[[# TBA| TBA  ]]
| Street
| WIMAW
|
|-
|-
| '''December 11'''
|May 3
| [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] (UW Madison)
| Tomasz Przebinda (Oklahoma)
| [[Colloquia#December 11: Jean-Luc Thiffeault (UW Madison) | A Mathematical History of Taffy Pullers]]
|[[# TBA| TBA  ]]
| Gurevich
|
|
|}
|}
Line 94: Line 118:
== Abstracts ==
== Abstracts ==


===September 4: Isaac Goldbring (UIC) ===
===Beata Randrianantoanina (Miami University Ohio)===
Title: On Kirchberg's embedding problem


Abstract: In his seminal work on the classification program for nuclear C*-algebras, Kirchberg showed that a particular C*-algebra, the Cuntz algebra O2, plays a seminal role. Subsequent work with Chris Phillips showed that O2 also plays a prominent role in regards to the wider class of exact C*-algebras, and this led Kirchberg to conjecture that every C*-algebra is finitely representable in O2, that is, is embeddable in an ultrapower of O2. The main goal of this talk is to sketch a proof of a local finitary reformulation of this conjecture of Kirchberg. The proof uses model theory and in particular the notion of model-theoretic forcing. No knowledge of C*-algebras or model theory will be assumed. This is joint work with Thomas Sinclair.
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.


===September 11: Doron Puder (IAS) ===
===Lillian Pierce (Duke University)===
Title: Word-Measures on Groups.


Abstract: Let w be a word in the free group on k generators, and let G be a finite (compact) group. The word w induces a measure on G by substituting the letters of w with k independent uniformly (Haar) chosen random elements of G and evaluating the product. Questions about word-measures on groups attracted attention in recent years both for their own sake and as a tool to analyze random walks on groups.
Title: Short character sums


We will explain some properties of word-measure, give examples and state conjectures. We will also talk about recent results regarding word-measures on symmetric groups and word-measures on unitary groups.
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.
====  ====


===September 18: Izzet Coskun (UIC) ===
===Dean Baskin (Texas A&M)===
Title:  The geometry of points in the plane


Abstract: Grothendieck's Hilbert scheme of points is a smooth  compactification of the configuration space of points in the plane. It has close connections with combinatorics, representation theory, mathematical physics and algebraic geometry. In this talk, I will survey some of the basic properties of this beautiful space. If time permits, I will discuss joint work with Arcara, Bertram and Huizenga on codimension one subvarieties of the Hilbert scheme.
Title: Radiation fields for wave equations
====  ====


===September 25: Ourmazd (UW-Milwaukee) ===
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.
Title:  Structure and Dynamics from Random Observations


Abstract: At weddings, the bridal photo is taken under bright lights, with the happy couple holding still. Traditionally in science, the “best” observations are those with the largest signal from the most tightly controlled system. Like bridal photos, the results are not always exciting. In a wide range of phenomena – from the dance of proteins during their function, to the breaking of molecular bonds on the femtosecond scale – tight control is neither possible, nor desirable. Modern data-analytical techniques extract far more information from random sightings than usually obtained from set-piece experiments.
===Aaron Naber (Northwestern)===
I will describe on-going efforts to extract structural and dynamical information from noisy, random snapshots. Examples will include YouTube videos, the structure and conformations of molecular machines such as the ribosome, and the ultrafast dynamics of bond-breaking in small molecules like nitrogen.


==== October 9: Chanwoo Kim ====
Title:  A structure theory for spaces with lower Ricci curvature bounds.
Title: Coercivity in the Boltzmann equation


Abstract: The Boltzmann equation is a fundamental equation of rarefied gas. Around the natural steady state, so called Maxwellian, a linearized operator is degenerated coercive. In this talk we will see how to recover this degenerated part so that the linearized operator is coercive effectively.
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.


=== October 16: Hadi Salmasian (Ottawa)===
Title: The Capelli problem and spectrum of invariant differential operators


Abstract: The Capelli identity is a mysterious result in classical invariant theory with a long history. It was demystified by Roger Howe, who used it in an ingenious and elegant fashion in the modern theory of representations of real reductive groups. In this talk, I will introduce the Capelli identity, and exhibit the relationship between an extension of this identity with certain polynomials which describe the spectrum of invariant differential operators on symmetric superspaces. These polynomials are analogs of the Jack and Knop-Sahi/Okounkov-Olshanski polynomials. This talk is based on a joint project with Siddhartha Sahi.
== Past Colloquia ==
 
=== October 23: Lu Wang===
 
Title: Singularities of Mean Curvature Flow
 
Abstract: Mean curvature flow (MCF) of hypersurfaces is the gradient flow of volume functional, which decreases the volume in its steepest way. Any compact MCF will develop singularities in finite time, which are modeled by self-shrinkers, a special class of solutions of MCF. Recently, Colding-Minicozzi proposed a dynamical approach to study the singularities formation of MCF. In this talk, I will survey some progress in the classification of self-shrinkers (from different point views) as well as some major open problems. Part of the work is joint with Jacob Bernstein.
 
===October 30: Ruth Charney (Brandeis)===
 
Title: Finding hyperbolic behavior in non-hyperbolic spaces
 
Abstract: In the early 90’s, Gromov introduced a notion of hyperbolicity for geodesic metric spaces.  The study of groups of isometries of such spaces has been an underlying theme of much of the work in geometric group theory since that time.  Many geodesic metric spaces, while not hyperbolic in the sense of Gromov, nonetheless display some hyperbolic-like behavior.  I will discuss a new invariant, the Morse boundary of a space, designed to capture this behavior.  This is joint work with Harold Sultan, together with recent work of my students Matt Cordes and Devin Murray.
 
===November 6: Chris Rycroft (Harvard)===
 
Title: Interfacial dynamics of dissolving objects in fluid flow
 
Abstract: An advection--diffusion-limited dissolution model of an object being eroded by a two-dimensional potential flow will be presented. By taking advantage of conformal invariance of the model, a numerical method will be introduced that tracks the evolution of the object boundary in terms of a time-dependent Laurent series. Simulations of several dissolving objects will be shown, all of which show collapse to a single point in finite time. The simulations reveal a surprising connection between the position of the collapse point and the initial Laurent coefficients, which was subsequently derived analytically using residue calculus.
 
===November 13: David Fisher (Indiana)===
 
Title: Rigidity of quasi-isometric embeddings
 
Abstract:  In geometric group theory, one defines a metric
on finitely generated groups and then asks when algebraic
properties are related to metric ones.  The most famous
example is Gromov's theorem on polynomial growth
which state that a group has polynomial growth iff
it has a finite index subgroup which is nilpotent.
In this talk I will focus on when a geometric mapping
is in fact algebraic and so an isomorphism or homomorphism. 
For the case of isomorphisms, this phenomena was first
discovered by Schwartz, with other examples followed in work of
Farb-Schwartz and Eskin.  I will talk about the first results
of this kind for homomorphisms that are not onto;  this
is joint work with Thang Nguyen.  The talk will be accessible
to graduate students.
 
===November 20: Avy Soffer (Rutgers)===
 
Title Nonlinear Long Range Scattering and Normal Form Analysis"


Abstract
[[Colloquia/Blank|Blank]]


First I will describe the source and nature of long range dynamics in general.
[[Colloquia/Fall2018|Fall 2018]]
This fundamental effect is responsible to the change in the asymptotic behavior of the system at large times.
It is present in Coulomb and Gravitational dynamics, in theories with mass-less particles (gauge theories) and in low power nonlinear dispersive and hyperbolic equations.
Then, I will describe new results and new Normal Form techniques to deal with the nonlinear Klein-Gordon equation in one dimension, with quadratic and variable coefficient cubic nonlinearity. This problem exhibits a striking resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the solutions. We prove global existence and (in L-infinity) scattering as well as a certain kind of strong smoothness for the solution at time-like infinity; it is based on several new classes of normal-form transformations. The analysis also shows the limited smoothness of the solution, in the presence of the resonances. In particular we observe the phenomena of growth of some Invariant Sobolev norm of high order. This seems to be generic for such nonlinear systems.


===December 4: Charlie Smart (Uchicago)===
[[Colloquia/Spring2018|Spring 2018]]


Title: The Abelian Sandpile and Circle Packings
[[Colloquia/Fall2017|Fall 2017]]


Abstract: The Abelian sandpile is a simple and deterministic diffusion process on graphs, devised as a model of self-organized criticality by Bak, Tang, and Weisenfeld. 
[[Colloquia/Spring2017|Spring 2017]]
The scaling limit of the sandpile on a periodic graph is a nonlinear elliptic partial differential equation with complicated algebraic structure.  I will discuss the sandpile, the algebraic structure of its scaling limit, and the fractal pictures it produces.


===December 11: Jean-Luc Thiffeault (UW Madison)===
[[Archived Fall 2016 Colloquia|Fall 2016]]


Title: A Mathematical History of Taffy Pullers
[[Colloquia/Spring2016|Spring 2016]]


Abstract: Taffy is a type of candy made by repeated 'pulling' (streching and folding) a mass of heated sugar.  The purpose of pulling is to get air bubbles into the taffy, which gives it a nicer texture.  Until the late 19th century, taffy was pulled by hand, an arduous task.  The early 20th century saw an avalanche of new devices to mechanize the process.  These devices have fascinating connections to the topological dynamics of surfaces, in particular with pseudo-Anosov maps.  "Special" algebraic integers such as the Golden ratio and the lesser-known Silver ratio make an apperance, as well as more exotic numbers.  After discussing the history and examining the designs from a mathematical angle, we ask the question: can modern mathematics help us improve on these designs?
[[Colloquia/Fall2015|Fall 2015]]
 
== Past Colloquia ==


[[Colloquia/Spring2014|Spring 2015]]
[[Colloquia/Spring2014|Spring 2015]]

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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