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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 2015  ==
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == -->


Go to next semester, [[Colloquia/Fall2015|Fall 2015]].
==Fall 2017==


{| 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 8
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)
|[[#September 8: Tess Anderson (Madison) |  A Spherical Maximal Function along the Primes  ]]
| Tonghai Yang
|
|-
|-
| '''January 12''' (special time: '''3PM''')
|September 15
| [http://math.nd.edu/people/visiting-faculty/botong-wang/ Botong Wang] (Notre Dame)
|
| [[Colloquia#January 12:  Botong Wang (Notre Dame) | Cohomology jump loci of algebraic varieties]]
|[[#|   ]]
| Maxim
|
|
|
|-
|-
| '''January 14''' (special time: '''11AM''')
|September 22, '''9th floor'''
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (UIUC)
| Jaeyoung Byeon (KAIST)
| [[Colloquia#January 14: Jayadev Athreya (UIUC) | Counting points for random (and not-so-random) geometric structures]]
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces  ]]
| Ellenberg
| Paul Rabinowitz & Chanwoo Kim
|
|
|
|-
|-
| '''January 15''' (special time: '''3PM''')
|October 6,  '''9th floor'''
| [http://www.math.sunysb.edu/~chili/ Chi Li] (Stony Brook)
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)
| [[Colloquia#January 15: Chi Li (Stony Brook) | On Kahler-Einstein metrics and K-stability]]
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]
| Sean Paul
| Nigel Boston
|
|-
|-
| '''January 21'''
|October 13, '''9th floor'''
| [http://www.math.utoronto.ca/cms/kitagawa-jun/ Jun Kitagawa] (Toronto)
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)
| [[Colloquia#January 21: Jun Kitagawa (Toronto) | Regularity theory for generated Jacobian equations: from optimal transport to geometric optics]]
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]
| Feldman
| Laurentiu Maxim
|
|-
|-
| '''January 23''' (special room/time: '''B135, 2:30PM''')
|October 20
| [http://math.duke.edu/~adding/ Nicolas Addington] (Duke)
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU)  
| [[Colloquia#January 23: Nicolas Addington (Duke) | Recent developments in rationality of cubic 4-folds]]
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]
Ellenberg
Minh-Binh Tran
|
|-
|-
| '''Monday January 26 4pm'''
|October 27
| [http://www.bcamath.org/en/people/minh-binh Minh Binh Tran] (CAM)
|Stefanie Petermichl (Toulouse)
| [[Colloquia#January 26: Minh Binh Tran (CAM) | Nonlinear approximation theory for the homogeneous Boltzmann
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators  ]]
equation]]
| Betsy Stovall, Andreas Seeger
| Jin
|
|-
|-
| January 30
|November 1 (Wednesday)
| Tentatively reserved for possible interview
|[http://pages.iu.edu/~shaoguo/  Shaoming Guo] (Indiana)
|[[#November 1: Shaoming Guo (Indiana)|  Parsell-Vinogradov systems in higher dimensions  ]]
|Andreas Seeger
|
|
|
|
|
|
|
|-
|-
| '''Monday, February 2 4pm'''
|November 17
| [https://web.math.princeton.edu/~ajsb/ Afonso Bandeira] (Princeton)
| [http://math.mit.edu/~ylio/ Yevgeny Liokumovich] (MIT)
| [[Colloquia#February 2: Afonso Bandeira (Princeton) | Tightness of convex relaxations for certain inverse problems on graphs]]
|[[#November 17:Yevgeny Liokumovich (MIT)| Recent progress in Min-Max Theory  ]]
| Ellenberg
|Sean Paul
|-
|-
| February 6
|November 21, '''9th floor'''
| Morris Hirsch (UC Berkeley and UW Madison)
| [https://web.stanford.edu/~mkemeny/homepage.html  Michael Kemeny] (Stanford)
| [[Colloquia#February 6: Morris Hirsch (UC Berkeley and UW Madison) | Fixed points of Lie transformation group, and zeros of Lie algebras of vector fields]]
|[[#November 21:Michael Kemeny (Stanford)|  The equations defining curves and moduli spaces ]]
| Stovall
|Jordan Ellenberg
|
|-
|-
| February 13
|November 24
| [http://www.math.ucsb.edu/~mputinar/ Mihai Putinar] (UC Santa Barbara, Newcastle University)
|'''Thanksgiving break'''
| [[Colloquia#February 13: Mihai Putinar (UC Santa Barbara) | Quillen’s property of real algebraic varieties]]
|
| Budišić
|
|-
|-
| February 20
|November 27,
| [http://www.mathcs.emory.edu/~dzb/ David Zureick-Brown] (Emory University)
| [http://www.math.harvard.edu/~tcollins/homepage.html  Tristan Collins] (Harvard)
| [[Colloquia#February 20: David Zureick-Brown (Emory University) | Diophantine and tropical geometry]]
|[[#November 27:Tristan Collins (Harvard)| The J-equation and stability  ]]
| Ellenberg
|Sean Paul
|
|
|-
|-
| '''Monday, February 23, 4pm'''
|December 5 (Tuesday)
|  [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (UIUC)
| [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)
|  [[Colloquia#'''Monday''' February 23:  Jayadev Athreya (UIUC) | The Erdos-Szusz-Turan distribution for equivariant point processes]]
|[[#December 5: Ryan Hynd (U Penn)| Adhesion dynamics and the sticky particle system]]
|  Mari-Beffa
|Sigurd Angenent
|-
| February 27
| [http://www.math.rochester.edu/people/faculty/allan/ Allan Greenleaf] (University of Rochester)
| [[Colloquia#February 27: Allan Greenleaf (University of Rochester) | Erdos-Falconer Configuration problems]]
| Seeger
|
|
|-
|-
| March 6
|December 8 (Friday)
| [http://math.mit.edu/~lguth/ Larry Guth] (MIT)
| [https://cims.nyu.edu/~chennan/ Nan Chen] (Courant, NYU)
| [[Colloquia#March 6: Larry Guth (MIT) | Introduction to incidence geometry]]
|[[#December 8: Nan Chen (Courant, NYU)| A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems  ]]
| Stovall
|Leslie Smith
|-
| March 13
|[http://www.ma.utexas.edu/text/webpages/gordon.html Cameron Gordon] (UT-Austin)
| Left-orderability and 3-manifold groups
| Maxim
|-
| March 20
| [http://www.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)
| TBA
| Paul
|-
| March 27
|[http://php.indiana.edu/~korr/ Kent Orr] (Indiana University at Bloomigton)
| TBA
| Maxim
|-
| April 3
| University holiday
|
|
|
|
|-
|-
| April 10
|December 11 (Monday)
| [http://www-users.math.umn.edu/~jyfoo/ Jasmine Foo] (University of Minnesota)
| [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)
|TBA
|[[#December 11: Connor Mooney (ETH Zurich)|  Regularity vs. Singularity for Elliptic and Parabolic Systems]]
| Roch, WIMAW
|Sigurd Angenent
|
|-
|-
| April 17
|December 13 (Wednesday)
| [http://www.math.uiuc.edu/~kkirkpat/ Kay Kirkpatrick] (University of Illinois-Urbana Champaign)
| [http://math.mit.edu/~blwilson/ Bobby Wilson] (MIT)
| TBA
|[[#December 13: Bobby Wilson (MIT) | Projections in Banach Spaces and Harmonic Analysis ]]
| Stovall
|Andreas Seeger
|
|-
|-
| April 24
|December 15 (Friday) '''9th floor'''
| Marianna Csornyei (University of Chicago)
| [http://roy.lederman.name/ Roy Lederman] (Princeton)
| TBA
|[[#December 15: Roy Lederman (Princeton) | Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM) ]]
| Seeger, Stovall
|Leslie Smith
|
|-
|-
| May 1
|December 18 (Monday) '''B115'''
| [http://www.math.washington.edu/~bviray/ Bianca Viray] (University of Washington)
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)
| TBA
|[[#December 18: Jenny Wilson (Stanford)|  Stability in the homology of configuration spaces]]
| Erman
|Jordan Ellenberg
|
|-
|-
| May 8
|December 19 (Tuesday) '''9th floor'''
| [http://www.math.ucla.edu/~mroper/www/Home.html Marcus Roper] (UCLA)
| [https://web.stanford.edu/~amwright/ Alex Wright] (Stanford)
| TBA
|[[#December 19: Alex Wright (Stanford)|  Dynamics, geometry, and the moduli space of Riemann surfaces]]
| Roch
|Jordan Ellenberg
|}
|}


== Abstracts ==
== Fall Abstracts ==
=== September 8: Tess Anderson (Madison) ===
Title: A Spherical Maximal Function along the Primes


===January 12Botong Wang (Notre Dame)===
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example.  In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to.  We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory.  This is joint work with Cook, Hughes, and Kumchev.


====Cohomology jump loci of algebraic varieties====


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.
=== September 22: Jaeyoung Byeon (KAIST) ===
Title: Patterns formation for elliptic systems with large interaction forces


===January 14: Jayadev Athreya (UIUC)===
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions.  The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.


====Counting points for random (and not-so-random) geometric structures====
===October 6: Jonathan Hauenstein (Notre Dame) ===
Title: Real solutions of polynomial equations


We describe a philosophy of how certain counting problems can be studied by methods of probability theory and dynamics on appropriate moduli spaces. We focus on two particular cases:
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions.  Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application.  This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.


(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
===October 13: Tomoko Kitagawa (Berkeley) ===
 
Title: A Global History of Mathematics from 1650 to 2017
(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.
 
===January 15: Chi Li (Stony Brook)===
====On Kahler-Einstein metrics and K-stability====


The existence of Kahler-Einstein metrics on Kahler manifolds is a basic problem in complex differential geometry. This problem has connections to other fields: complex algebraic geometry, partial differential equations and several complex variables. I will discuss the existence of Kahler-Einstein metrics on Fano manifolds and its relation to K-stability. I will mainly focus on the analytic part of the theory, discuss how to solve the related complex Monge-Ampere equations and provide concrete examples in both smooth and conical settings. If time permits, I will also say something about the algebraic part of the theory, including the study of K-stability using the Minimal Model Program (joint with Chenyang Xu) and the existence of proper moduli space of smoothable K-polystable Fano varieties (joint with Xiaowei Wang and Chenyang Xu).
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?


===January 21:  Jun Kitagawa (Toronto)===


====Regularity theory for generated Jacobian equations: from optimal transport to geometric optics====


Equations of Monge-Ampere type arise in numerous contexts, and solutions often exhibit very subtle qualitative and quantitative properties; this is owing to the highly nonlinear nature of the equation, and its degeneracy (in the sense of ellipticity). Motivated by an example from geometric optics, I will talk about the class of Generated Jacobian Equations; recently introduced by Trudinger, this class also encompasses, for example, optimal transport, the Minkowski problem, and the classical Monge-Ampere equation. I will present a new regularity result for weak solutions of these equations, which is new even in the case of equations arising from near-field reflector problems (of interest from a physical and practical point of view). This talk is based on joint works with N. Guillen.
===October 20: Pierre Germain (Courant, NYU) ===
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations


===January 23: Nicolas Addington (Duke)===
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).


====Recent developments in rationality of cubic 4-folds====
===October 27: Stefanie Petermichl (Toulouse)===
Title: Higher order Journé commutators


The question of which cubic 4-folds are rational is one of the foremost open problems in algebraic geometry. I'll start by explaining what this means and why it's interesting; then I'll discuss three approaches to solving it (including one developed in the last year), my own work relating the three approaches to one another, and the troubles that have befallen each approach.
Abstract: We consider questions that stem from operator theory via Hankel and
Toeplitz forms and target (weak) factorisation of Hardy spaces. In
more basic terms, let us consider a function on the unit circle in its
Fourier representation. Let P_+ denote the projection onto
non-negative and P_- onto negative frequencies. Let b denote
multiplication by the symbol function b. It is a classical theorem by
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and
only if b is in an appropriate space of functions of bounded mean
oscillation. The necessity makes use of a classical factorisation
theorem of complex function theory on the disk. This type of question
can be reformulated in terms of commutators [b,H]=bH-Hb with the
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such
as in the real variable setting, in the multi-parameter setting or
other, these classifications can be very difficult.


===January 26:  Minh Binh Tran (CAM)===
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of
spaces of bounded mean oscillation via L^p boundedness of commutators.
We present here an endpoint to this theory, bringing all such
characterisation results under one roof.


====Nonlinear approximation theory for the homogeneous Boltzmann equation====
The tools used go deep into modern advances in dyadic harmonic
analysis, while preserving the Ansatz from classical operator theory.


A challenging problem in solving the Boltzmann equation
===November 1: Shaoming Guo (Indiana) ===
numerically is that the velocity space is approximated by a finite region.
Title: Parsell-Vinogradov systems in higher dimensions
Therefore, most methods are based on a truncation technique and the
computational cost is then very high if the velocity domain is large.
Moreover, sometimes, non-physical conditions have to be imposed on the
equation in order to keep the velocity domain bounded. In this talk, we
introduce the first nonlinear approximation theory for the Boltzmann
equation. Our nonlinear wavelet approximation is non-truncated and based on
a nonlinear, adaptive spectral method associated with a new wavelet
filtering technique and a new formulation of the equation. The
approximation is proved to converge and perfectly preserve most of the
properties of the homogeneous Boltzmann equation. It could also be
considered as a general framework for approximating kinetic integral
equations.


===February 2: Afonso Bandeira (Princeton)===
Abstract:  
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.


====Tightness of convex relaxations for certain inverse problems on graphs====
===November 17:Yevgeny Liokumovich (MIT)===
Title: Recent progress in Min-Max Theory


Many maximum likelihood estimation problems are known to be
Abstract:
intractable in the worst case. A common approach is to consider convex
Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?
relaxations of the maximum likelihood estimator (MLE), and relaxations
based on semidefinite programming (SDP) are among the most popular. We
will focus our attention on a certain class of graph-based inverse
problems and show a couple of remarkable phenomena.


In some instances of these problems (such as community detection under
===November 21:Michael Kemeny (Stanford)===
the stochastic block model) the solution to the SDP matches the ground
Title: The equations defining curves and moduli spaces
truth parameters (i.e. achieves exact recovery) for information
theoretically optimal regimes. This is established using new
nonasymptotic bounds for the spectral norm of random matrices with
independent entries.


On other instances of these problems (such as angular
Abstract:
synchronization), the MLE itself tends to not coincide with the ground
A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in algebraic geometry is to give a qualitative description of the equations defining a variety, together with
truth (although maintaining favorable statistical properties).
the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures
Remarkably, these relaxations are often still tight (meaning that the
made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures,
solution of the SDP matches the MLE). For angular synchronization we
which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.
can understand this behavior by analyzing the solutions of certain
randomized Grothendieck problems. However, for many other problems,
such as the multireference alignment problem in signal processing,
this remains a fascinating open problem.


===February 6:  Morris Hirsch (UC Berkeley and UW Madison)===


====Fixed points of  Lie transformation group,  and zeros of Lie algebras of vector fields====
===November 27:Tristan Collins (Harvard)===
Title: The J-equation and stability


The following questions will be considered:
Abstract: Donaldson and Chen introduced the J-functional in '99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point.  The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equationI will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation.
When  a connected Lie group G acts effectively on a manifold M, what  general conditions on G,  M and the action  ensure that the action has a fixed point
If  g is a Lie algebra of  vector fields on M, what general conditions on g and M  ensure that g has a zero?
Old and new results will be discussedFor example:
Theorem: If G is nilpotent and M is a  compact surface of nonzero Euler characteristic, there is a fixed point.
   
Theorem:  Suppose G is supersoluble and M is as above.  Then every analytic action of G on M has a fixed point, but this is false for continuous actions, and for groups that are merely solvable.
Theorem:  Suppose M is a real or complex manifold that is 2-dimensional over the ground field, and g is a Lie algebra of analytic vector fields on M.  Assume  some element X in g spans a 1-dimensional ideal.  If  the zero set K of X is compact and the Poincar'e-Hopf index of X at K is nonzero,  then g vanishes at some point of K.
No special knowledge of Lie groups will be assumed.  


===February 13: Mihai Putinar (UC Santa Barbara)===
===December 5: Ryan Hynd (U Penn)===
Title: Adhesion dynamics and the sticky particle system.


====Quillen’s property of real algebraic varieties====
Abstract:  The sticky particle system expresses the conservation of mass and
momentum for a collection of particles that only interact via perfectly inelastic collisions. 
The equations were first considered in astronomy in a model for the expansion of
matter without pressure. These equations also play a central role in the theory of optimal
transport.  Namely, the geodesics in an appropriately metrized space of probability
measures correspond to solutions of the sticky particle system.  We will survey what is
known about solutions and discuss connections with Hamilton-Jacobi equations.


A famous observation discovered by Fejer and Riesz a century ago
===December 8: Nan Chen (Courant, NYU)===
is the quintessential algebraic component of every spectral decomposition
Title: A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems
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.


===February 20: David Zureick-Brown (Emory University)===
Abstract:
A conditional Gaussian framework for uncertainty quantification, data assimilation and prediction of nonlinear turbulent dynamical systems will be introduced in this talk. Despite the conditional Gaussianity, the dynamics remain highly nonlinear and are able to capture strongly non-Gaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the real-time data assimilation and prediction.


====Diophantine and tropical geometry====
The talk will include three applications of such conditional Gaussian framework. In the first part, a physics-constrained nonlinear stochastic model is developed, and is applied to predicting the Madden-Julian oscillation indices with strongly non-Gaussian intermittent features. The second part regards the state estimation and data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers. Rigorous analysis shows that an exponential increase in the number of tracers is required for reducing the uncertainty by a fixed amount. This indicates a practical information barrier. In the last part of the talk, an efficient statistically accurate algorithm is developed that is able to solve a rich class of high dimensional Fokker-Planck equation with strong non-Gaussian features and beat the curse of dimensions.


Diophantine geometry is the study of integral solutions to a polynomial equation. For instance, for integers
===December 11: Connor Mooney (ETH Zurich)===
<math>a,b,c \geq 2</math> satisfying <math>\tfrac1a + \tfrac1b + \tfrac1c > 1</math>, Darmon and Granville proved that the individual generalized Fermat equation <math>x^a + y^b = z^c</math> has only finitely many coprime integer solutions. Conjecturally something stronger is true: for <math>a,b,c \geq 3</math> there are no non-trivial solutions.
Title: Regularity vs. Singularity for Elliptic and Parabolic Systems


I'll discuss various other Diophantine problems, with a focus on the underlying intuition and conjectural framework. I will especially focus on the uniformity conjecture, and will explain new ideas from tropical geometry and our recent partial proof of the uniformity conjecture.
Abstract:
Hilbert's 19th problem asks if minimizers of &ldquo;natural&rdquo; variational integrals are smooth. For the past century, this problem inspired fundamental regularity results for elliptic and parabolic PDEs. It also led to the construction of several beautiful counterexamples to regularity. The dichotomy of regularity vs. singularity is related to that of single PDE (the scalar case) vs. system of PDEs (the vectorial case), and low dimension vs. high dimension. I will discuss some interesting recent counterexamples to regularity in low-dimensional vectorial cases, as well as outstanding open problems. Some of this is joint work with O. Savin.


==='''Monday''' February 23: Jayadev Athreya (UIUC)===
===December 13: Bobby Wilson (MIT)===
Title:  Projections in Banach Spaces and Harmonic Analysis


====The Erdos-Szusz-Turan distribution for equivariant point processes====
Abstract: In this talk, we will discuss the measure theoretic principles of orthogonal projections that follow from the classical Besicovitch-Federer projection theorem. The Besicovitch-Federer projection theorem offers a characterization of rectifiability of one-dimensional sets in R^d by the size of their projections to lines. We will focus on the validity of analogues to the Besicovitch-Federer projection theorem with respect to such sets in general Banach spaces. In particular, we will show that the projection theorem is false when the Banach space is infinite-dimensional and discuss related applications to questions in Harmonic Analysis. This is joint work with Marianna Csornyei and David Bate.


We generalize a problem of Erdos-Szusz-Turan on diophantine approximation to a variety of contexts, and use homogeneous dynamics to compute an associated probability distribution on the integers.
===December 15: Roy Lederman (Princeton)===
Title: Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM)


Abstract:
Cryo-EM is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson “for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution".
Cryo-electron microscopes produce a large number of very noisy two-dimensional projection images of individual frozen molecules. Unlike related methods, such as computed tomography (CT), the viewing direction of each image is unknown. The unknown directions, together with extreme levels of noise and additional technical factors, make the determination of the structure of molecules challenging.
While other methods for structure determination, such as x-ray crystallography and nuclear magnetic resonance (NMR), measure ensembles of molecules together, cryo-EM produces measurements of individual molecules. Therefore, cryo-EM could potentially be used to study mixtures of different conformations of molecules. Indeed, current algorithms have been very successful at analyzing homogeneous samples, and can recover some distinct conformations mixed in solutions, but, the determination of multiple conformations, and in particular, continuums of similar conformations (continuous heterogeneity), remains one of the open problems in cryo-EM.
I will discuss a one-dimensional discrete model problem, Heterogeneous Multireference Alignment, which captures many of the group properties and other mathematical properties of the cryo-EM problem. I will then discuss different components which we are introducing in order to address the problem of continuous heterogeneity in cryo-EM: 1. “hyper-molecules,” the mathematical formulation of truly continuously heterogeneous molecules, 2. computational and numerical tools for formulating associated priors, and 3. Bayesian algorithms for inverse problems with an unsupervised-learning component for recovering such hyper-molecules in cryo-EM.


===February 27: Allan Greenleaf (University of Rochester)===
===December 18: Jenny Wilson (Stanford)===
Title: Stability in the homology of configuration spaces


====Erdos-Falconer Configuration problems====
Abstract:
This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.


In discrete geometry, there is a large collection of problems due
===December 19: Alex Wright (Stanford)===
to Erdos and various coauthors starting in the 1940s, which have the
Title: Dynamics, geometry, and the moduli space of Riemann surfaces
following general form: Given a large finite set P of N points
in d-dimensional Euclidean space, and a geometric configuration (a line
segment of a given length, a triangle with given angles or a given area,
etc.), is there a lower bound on how many times that configuration must
occur among the points of P? Relatedly, is there an upper bound
on the number of times any single configuration can occur? One of the most
celebrated problems of this type, the Erdos distinct distances problem
in the plane, was essentially solved in 2010 by Guth and Katz, but for many
problems of this type only partial results are known.


In continuous geometry, there are analogous problems due to Falconer and
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel.
others. Here, one looks for results that say that if a set A is large enough (in
terms of a lower bound on its Hausdorff dimension, say), then the set of
configurations of a given type generated by the points of A  is large (has
positive measure, say).  
I will describe work on Falconer-type problems using some techniques from
harmonic analysis, including estimate for multilinear operators. In some
cases, these results can be discretized to obtain at least partial results
on Erdos-type problems.


== Spring 2018 ==


{| cellpadding="8"
!align="left" | date 
!align="left" | speaker
!align="left" | title
!align="left" | host(s)
|-
| March 16
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)
|[[# TBA|  TBA  ]]
| WIMAW
|
|-
|April 4 (Wednesday)
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)
|[[# TBA|  TBA  ]]
| Craciun
|
|-
| April 6
| Reserved
|[[# TBA|  TBA  ]]
| Melanie
|
|-
| April 13
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)
|[[# TBA|  TBA  ]]
| WIMAW
|
|-
| April 25 (Wednesday)
| Hitoshi Ishii (Waseda University) Wasow lecture
|[[# TBA|  TBA  ]]
| Tran
|
|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
|
|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
|
|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
|
|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
|
|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
|
|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
|
|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
|
|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
|
|-
|date
| person (institution)
|[[# TBA|  TBA  ]]
| hosting faculty
|
|}


===March 6:  Larry Guth (MIT)===
== Spring Abstracts ==


====Introduction to incidence geometry====
=== <DATE>: <PERSON> (INSTITUTION) ===
Title: <TITLE>


Incidence geometry is a branch of combinatorics that studies the possible intersection patterns of lines, circles, and other simple shapes.  For example, suppose that we have a set of L lines in the plane.  An r-rich point is a point that lies in at least r of these lines.  For a given L, r, how many r-rich points can we make?  This is a typical question in the field, and there are many variations.  What if we replace lines with circles?  What happens in higher dimensions?  We will give an introduction to this field, describing some of the important results, tools, and open problems.
Abstract: <ABSTRACT>


We will discuss two important tools used in the area.  One tool is to apply topology to the problem.  This tool allows us to prove results in R^2 that are stronger than what happens over finite fields.  The second tool is to look for algebraic structure in the problem by studying low-degree polynomials that vanish on the points we are studying.  We will also discuss some of the (many) open problems in the field and try to describe the nature of the difficulties in approaching them.


== Past Colloquia ==


[[Colloquia/Blank|Blank Colloquia]]


===March 13:  Cameron Gordon===
[[Colloquia/Spring2017|Spring 2017]]


====Left-orderability and 3-manifold groups====
[[Archived Fall 2016 Colloquia|Fall 2016]]


[[Colloquia/Spring2016|Spring 2016]]


The fundamental group is a more or less complete invariant of a 3-dimensional manifold. We will discuss how the purely algebraic property of this group being left-orderable is related to two other aspects of 3-dimensional topology, one geometric-topological and the other essentially analytic.
[[Colloquia/Fall2015|Fall 2015]]


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


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

Revision as of 19:56, 7 December 2017


Mathematics Colloquium

All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.


Fall 2017

Date Speaker Title Host(s)
September 8 Tess Anderson (Madison) A Spherical Maximal Function along the Primes Tonghai Yang
September 15
September 22, 9th floor Jaeyoung Byeon (KAIST) Patterns formation for elliptic systems with large interaction forces Paul Rabinowitz & Chanwoo Kim
October 6, 9th floor Jonathan Hauenstein (Notre Dame) Real solutions of polynomial equations Nigel Boston
October 13, 9th floor Tomoko L. Kitagawa (Berkeley) A Global History of Mathematics from 1650 to 2017 Laurentiu Maxim
October 20 Pierre Germain (Courant, NYU) Stability of the Couette flow in the Euler and Navier-Stokes equations Minh-Binh Tran
October 27 Stefanie Petermichl (Toulouse) Higher order Journé commutators Betsy Stovall, Andreas Seeger
November 1 (Wednesday) Shaoming Guo (Indiana) Parsell-Vinogradov systems in higher dimensions Andreas Seeger
November 17 Yevgeny Liokumovich (MIT) Recent progress in Min-Max Theory Sean Paul
November 21, 9th floor Michael Kemeny (Stanford) The equations defining curves and moduli spaces Jordan Ellenberg
November 24 Thanksgiving break
November 27, Tristan Collins (Harvard) The J-equation and stability Sean Paul
December 5 (Tuesday) Ryan Hynd (U Penn) Adhesion dynamics and the sticky particle system Sigurd Angenent
December 8 (Friday) Nan Chen (Courant, NYU) A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems Leslie Smith
December 11 (Monday) Connor Mooney (ETH Zurich) Regularity vs. Singularity for Elliptic and Parabolic Systems Sigurd Angenent
December 13 (Wednesday) Bobby Wilson (MIT) Projections in Banach Spaces and Harmonic Analysis Andreas Seeger
December 15 (Friday) 9th floor Roy Lederman (Princeton) Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM) Leslie Smith
December 18 (Monday) B115 Jenny Wilson (Stanford) Stability in the homology of configuration spaces Jordan Ellenberg
December 19 (Tuesday) 9th floor Alex Wright (Stanford) Dynamics, geometry, and the moduli space of Riemann surfaces Jordan Ellenberg

Fall Abstracts

September 8: Tess Anderson (Madison)

Title: A Spherical Maximal Function along the Primes

Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.


September 22: Jaeyoung Byeon (KAIST)

Title: Patterns formation for elliptic systems with large interaction forces

Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.

October 6: Jonathan Hauenstein (Notre Dame)

Title: Real solutions of polynomial equations

Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.

October 13: Tomoko Kitagawa (Berkeley)

Title: A Global History of Mathematics from 1650 to 2017

Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?


October 20: Pierre Germain (Courant, NYU)

Title: Stability of the Couette flow in the Euler and Navier-Stokes equations

Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).

October 27: Stefanie Petermichl (Toulouse)

Title: Higher order Journé commutators

Abstract: We consider questions that stem from operator theory via Hankel and Toeplitz forms and target (weak) factorisation of Hardy spaces. In more basic terms, let us consider a function on the unit circle in its Fourier representation. Let P_+ denote the projection onto non-negative and P_- onto negative frequencies. Let b denote multiplication by the symbol function b. It is a classical theorem by Nehari that the composed operator P_+ b P_- is bounded on L^2 if and only if b is in an appropriate space of functions of bounded mean oscillation. The necessity makes use of a classical factorisation theorem of complex function theory on the disk. This type of question can be reformulated in terms of commutators [b,H]=bH-Hb with the Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such as in the real variable setting, in the multi-parameter setting or other, these classifications can be very difficult.

Such lines were begun by Coifman, Rochberg, Weiss (real variables) and by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of spaces of bounded mean oscillation via L^p boundedness of commutators. We present here an endpoint to this theory, bringing all such characterisation results under one roof.

The tools used go deep into modern advances in dyadic harmonic analysis, while preserving the Ansatz from classical operator theory.

November 1: Shaoming Guo (Indiana)

Title: Parsell-Vinogradov systems in higher dimensions

Abstract: I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions. Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed. Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.

November 17:Yevgeny Liokumovich (MIT)

Title: Recent progress in Min-Max Theory

Abstract: Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?

November 21:Michael Kemeny (Stanford)

Title: The equations defining curves and moduli spaces

Abstract: A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in algebraic geometry is to give a qualitative description of the equations defining a variety, together with the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures, which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.


November 27:Tristan Collins (Harvard)

Title: The J-equation and stability

Abstract: Donaldson and Chen introduced the J-functional in '99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point. The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equation. I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation.

December 5: Ryan Hynd (U Penn)

Title: Adhesion dynamics and the sticky particle system.

Abstract: The sticky particle system expresses the conservation of mass and momentum for a collection of particles that only interact via perfectly inelastic collisions. The equations were first considered in astronomy in a model for the expansion of matter without pressure. These equations also play a central role in the theory of optimal transport. Namely, the geodesics in an appropriately metrized space of probability measures correspond to solutions of the sticky particle system. We will survey what is known about solutions and discuss connections with Hamilton-Jacobi equations.

December 8: Nan Chen (Courant, NYU)

Title: A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems

Abstract: A conditional Gaussian framework for uncertainty quantification, data assimilation and prediction of nonlinear turbulent dynamical systems will be introduced in this talk. Despite the conditional Gaussianity, the dynamics remain highly nonlinear and are able to capture strongly non-Gaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the real-time data assimilation and prediction.

The talk will include three applications of such conditional Gaussian framework. In the first part, a physics-constrained nonlinear stochastic model is developed, and is applied to predicting the Madden-Julian oscillation indices with strongly non-Gaussian intermittent features. The second part regards the state estimation and data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers. Rigorous analysis shows that an exponential increase in the number of tracers is required for reducing the uncertainty by a fixed amount. This indicates a practical information barrier. In the last part of the talk, an efficient statistically accurate algorithm is developed that is able to solve a rich class of high dimensional Fokker-Planck equation with strong non-Gaussian features and beat the curse of dimensions.

December 11: Connor Mooney (ETH Zurich)

Title: Regularity vs. Singularity for Elliptic and Parabolic Systems

Abstract: Hilbert's 19th problem asks if minimizers of “natural” variational integrals are smooth. For the past century, this problem inspired fundamental regularity results for elliptic and parabolic PDEs. It also led to the construction of several beautiful counterexamples to regularity. The dichotomy of regularity vs. singularity is related to that of single PDE (the scalar case) vs. system of PDEs (the vectorial case), and low dimension vs. high dimension. I will discuss some interesting recent counterexamples to regularity in low-dimensional vectorial cases, as well as outstanding open problems. Some of this is joint work with O. Savin.

December 13: Bobby Wilson (MIT)

Title: Projections in Banach Spaces and Harmonic Analysis

Abstract: In this talk, we will discuss the measure theoretic principles of orthogonal projections that follow from the classical Besicovitch-Federer projection theorem. The Besicovitch-Federer projection theorem offers a characterization of rectifiability of one-dimensional sets in R^d by the size of their projections to lines. We will focus on the validity of analogues to the Besicovitch-Federer projection theorem with respect to such sets in general Banach spaces. In particular, we will show that the projection theorem is false when the Banach space is infinite-dimensional and discuss related applications to questions in Harmonic Analysis. This is joint work with Marianna Csornyei and David Bate.

December 15: Roy Lederman (Princeton)

Title: Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM)

Abstract: Cryo-EM is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson “for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution".

Cryo-electron microscopes produce a large number of very noisy two-dimensional projection images of individual frozen molecules. Unlike related methods, such as computed tomography (CT), the viewing direction of each image is unknown. The unknown directions, together with extreme levels of noise and additional technical factors, make the determination of the structure of molecules challenging.

While other methods for structure determination, such as x-ray crystallography and nuclear magnetic resonance (NMR), measure ensembles of molecules together, cryo-EM produces measurements of individual molecules. Therefore, cryo-EM could potentially be used to study mixtures of different conformations of molecules. Indeed, current algorithms have been very successful at analyzing homogeneous samples, and can recover some distinct conformations mixed in solutions, but, the determination of multiple conformations, and in particular, continuums of similar conformations (continuous heterogeneity), remains one of the open problems in cryo-EM.

I will discuss a one-dimensional discrete model problem, Heterogeneous Multireference Alignment, which captures many of the group properties and other mathematical properties of the cryo-EM problem. I will then discuss different components which we are introducing in order to address the problem of continuous heterogeneity in cryo-EM: 1. “hyper-molecules,” the mathematical formulation of truly continuously heterogeneous molecules, 2. computational and numerical tools for formulating associated priors, and 3. Bayesian algorithms for inverse problems with an unsupervised-learning component for recovering such hyper-molecules in cryo-EM.

December 18: Jenny Wilson (Stanford)

Title: Stability in the homology of configuration spaces

Abstract: This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.

December 19: Alex Wright (Stanford)

Title: Dynamics, geometry, and the moduli space of Riemann surfaces

Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel.

Spring 2018

date speaker title host(s)
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 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

<DATE>: <PERSON> (INSTITUTION)

Title: <TITLE>

Abstract: <ABSTRACT>


Past Colloquia

Blank Colloquia

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Spring 2015

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012