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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'''.


== Spring 2015  ==
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].
 
==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)
|-
|-
| '''January 12''' (special time: '''3PM''')
|Jan 25
| Botong Wang (Purdue)
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW
| Cohomology jump loci of algebraic varieties
|[[#Beata Randrianantoanina (Miami University Ohio) |  Some nonlinear problems in the geometry of Banach spaces and their applications  ]]
| Maxim
| Tullia Dymarz
|
|-
|-
| '''January 14''' (special time: '''11AM''')
|Jan 30 '''Wednesday'''
| Jayadev Athreya (UIUC)
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)
| Counting points for random (and not-so-random) geometric structures
|[[#Lillian Pierce (Duke University) |  Short character sums  ]]
| Ellenberg
| Boston and Street
|
|-
|-
| '''January 21'''
|Jan 31 '''Thursday'''
| Jun Kitagawa (Toronto)
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)
| TBA
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations  ]]
| Feldman
| Street
|
|-
|-
| January 23
|Feb 1
| Tentatively reserved for possible interview
| [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University)
|[[# TBA|  TBA  ]]
| Qin
|
|
|-
|Feb 5 '''Tuesday'''
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)
|[[# TBA|  TBA  ]]
| Denisov
|
|
|-
|-
| January 30
|Feb 8
| Tentatively reserved for possible interview
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)
|[[#Aaron Naber (Northwestern) |  A structure theory for spaces with lower Ricci curvature bounds  ]]
| Street
|
|
|-
|Feb 15
|
|[[# TBA|  TBA  ]]
|
|
|
|-
|-
| February 6
|Feb 22
| Morris Hirsch (UC Berkeley and UW Madison)
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)
| Fixed points of Lie group actions
|[[# TBA|  TBA  ]]
| Stovall
| Erman and Corey
|
|-
|-
| February 13
|March 4
| [http://www.math.ucsb.edu/~mputinar/ Mihai Putinar] (UC Santa Barbara, Newcastle University)
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture
| [[Colloquia#February 12: Mihai Putinar (UC Santa Barbara) | Quillen’s property of real algebraic varieties]]
|[[# TBA| TBA ]]
| Budišić
| Kim
|
|-
|-
| February 20
|March 8
| [http://www.mathcs.emory.edu/~dzb/ David Zureick-Brown] (Emory University)
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)
| TBA
|[[# TBA|  TBA  ]]
| Ellenberg
| Erman
|
|-
|-
| February 27
|March 15
| [http://www.math.rochester.edu/people/faculty/allan/ Allan Greenleaf] (University of Rochester)
| Maksym Radziwill (Caltech)
| TBA
|[[# TBA|  TBA ]]
| Seeger
| Marshall
|
|
|-
|-
| March 6
|March 29
| [http://math.mit.edu/~lguth/ Larry Guth] (MIT)
| Jennifer Park (OSU)
| TBA
|[[# TBA|  TBA ]]
| Stovall
| Marshall
|
|-
|-
| March 13
|April 5
|[http://www.ma.utexas.edu/text/webpages/gordon.html Cameron Gordon] (UT-Austin)
| Ju-Lee Kim (MIT)
| TBA
|[[# TBA|  TBA ]]
| Maxim
| Gurevich
|
|-
|-
| March 20
|April 12
|[http://banajim.myweb.port.ac.uk Murad Banaji] (University of Portsmouth)
| Evitar Procaccia (TAMU)
| TBA
|[[# TBA|  TBA ]]
| Craciun
| Gurevich
|
|-
|-
| March 27
|April 19
|[http://php.indiana.edu/~korr/ Kent Orr] (Indiana University at Bloomigton)
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)
| TBA
|[[# TBA|  TBA  ]]
| Maxim
| Jean-Luc
|
|-
|-
| April 3
|April 26
| University holiday
| [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
|
|
|-
| April 10
| [http://www-users.math.umn.edu/~jyfoo/ Jasmine Foo] (University of Minnesota)
|TBA
| Roch, WIMAW
|-
| April 17
| [http://www.math.uiuc.edu/~kkirkpat/ Kay Kirkpatrick] (University of Illinois-Urbana Champaign)
| TBA
| Stovall
|-
| April 24
| Marianna Csornyei (University of Chicago)
| TBA
| Seeger, Stovall
|-
| May 1
| [http://www.math.washington.edu/~bviray/ Bianca Viray] (University of Washington)
| TBA
| Erman
|-
| May 8
| [http://www.math.ucla.edu/~mroper/www/Home.html Marcus Roper] (UCLA)
| TBA
| Roch
|}
|}


== Abstracts ==
== Abstracts ==


===January 12:  Botong Wang===
===Beata Randrianantoanina (Miami University Ohio)===


====Cohomology jump loci of algebraic varieties====
Title: Some nonlinear problems in the geometry of Banach spaces and their applications.


In the moduli spaces of vector bundles (or local systems), cohomology jump loci are the algebraic sets where certain cohomology group has prescribed dimension. We will discuss some arithmetic and deformation theoretic aspects of cohomology jump loci. If time permits, we will also talk about some applications in algebraic statistics.
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.


===January 14:  Jayadev Athreya===
===Lillian Pierce (Duke University)===


====Counting points for random (and not-so-random) geometric structures====
Title: Short character sums


We describe a philosophy of how certain counting problems can be
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.
> studied by methods of probability theory and dynamics on appropriate moduli
> spaces. We focus on two particular cases:
>
> (1) Counting for Right-Angled Billiards: understanding the dynamics on and
> volumes of moduli spaces of meromorphic quadratic differentials yields
> interesting universality phenomenon for billiards in polygons with interior
> angles integer multiples of 90 degrees. This is joint work with A. Eskin
> and A. Zorich
>
> (2) Counting for almost every quadratic form: understanding the geometry of
> a random lattice allows yields striking diophantine and counting results
> for typical (in the sense of measure) quadratic (and other) forms. This is
> joint work with G. A. Margulis.


===February 12:  Mihai Putinar (UC Santa Barbara)===
===Dean Baskin (Texas A&M)===


====Quillen’s property of real algebraic varieties====
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.


A famous observation discovered by Fejer and Riesz a century ago
is the quintessential algebraic component of every spectral decomposition
result. It asserts that every non-negative polynomial on the unit circle is a
hermitian square. About half a century ago, Quillen proved that a positive polynomial
on an odd dimensional sphere is a sum of hermitian squares. Fact independently
rediscovered much later by D’Angelo and Catlin, respectively Athavale. The main subject of
the talk will be: on which real algebraic sub varieties of <math>\mathbb{C}^n</math> is Quillen theorem valid?
An interlace between real algebraic geometry, quantization techniques and complex
hermitian geometry will provide an answer to the above question, and more.
Based a recent work with Claus Scheiderer and John D’Angelo.


== Past Colloquia ==
== Past Colloquia ==
[[Colloquia/Blank|Blank]]
[[Colloquia/Fall2018|Fall 2018]]
[[Colloquia/Spring2018|Spring 2018]]
[[Colloquia/Fall2017|Fall 2017]]
[[Colloquia/Spring2017|Spring 2017]]
[[Archived Fall 2016 Colloquia|Fall 2016]]
[[Colloquia/Spring2016|Spring 2016]]
[[Colloquia/Fall2015|Fall 2015]]
[[Colloquia/Spring2014|Spring 2015]]


[[Colloquia/Fall2014|Fall 2014]]
[[Colloquia/Fall2014|Fall 2014]]

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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