Spring 2017

RITs ("Research Interaction Teams") are informal groups designed to foster interaction between faculty, students, and postdocs, and to get students interested in current research. Most of them meet as informal seminars with active student participation (and in many cases, student organization as well).  In addition to the RITs, there are several student seminars which are run by students for students.

  • RIT on Applied Partial Differential Equations
    • Organizers: Jacob Bedrossian, Maria Cameron, Sandra Cerrai, Manoussos Grillakis, Pierre-Emmanuel Jabin, Dave Levermore, Doron Levy, Matei Machedon, Dionisios Margetis, Antoine Mellet, Eitan Tadmor (lead organizers in bold)
    • Meeting Time: 3:00pm - 3:50pm Mondays
    • Location: MTH 1311.
    • Description: We will study mathematical aspects of applied partial differential equations. These might include well-posedness, long-time behavior, attractor dynamics, stability of coherent structures, asymptotic limits, and the relationship between chaos and stochasticity. However the best description is the list of talks given on the website.
  • RIT on Statistics
    • Organizers: Paul Smith, and Tingni Sun
    • Meeting Time: Tuesdays 3:30-4:30, MTH 1313
    • Prerequisites: a basic knowledge of statistics
  • RIT on Analysis of Complex Networks
  • RIT on Advanced Elementary Number Theory
    • Organizers: Manjit Bhatia, Adam Lizzi, and Larry Washington
    • Meeting Time: Fridays 3:00 PM in room MTH 1308, starting Jan. 27
    • Description: The idea is to cover the fun stuff that is not usually included in Math 406. In other words, this will essentially be Math 407. We expect to meet once per week, with participants volunteering to lecture on various topics. We hope to keep at a level where someone who has studied number theory through quadratic reciprocity will be able to follow the lectures.
  • RIT on Quantum Information
    • Organizers: Brad Lackey, Carl Miller
    • When: Mondays 4:15-5:15, with Organizational Meeting Sept. 12
    • Where: CSS 3100A (Joint Center for Quantum Information and Computer Science)
    • Topics: The RIT will focus on various mathematical aspects of quantum information, as it pertains to quantum foundations, quantum computing, and other topics in theoretical physics. No previous experience in quantum theory is required, however linear algebra and (discrete) probability is a must. To start the term we'll look at some basics in quantum foundations, primarily about generalized probability theories. After getting through the main constructions we'll decide if we want to study more advanced topic in quantum foundations or switch to a topic in quantum communication or information theory. Here are some papers to consider for the first part:
  • RIT on Geometry and Physics
    • Organizers: Jonathan Rosenberg (Math), Richard Wentworth (Math), Tristan Hubsch (Howard and UMD, Physics), and Chuck Doran (Alberta, Math, and UMD, Physics)
    • Meeting Time: Thursdays at 3:30, room PHY 1117, starting Jan. 26.
    • Description: This interdisciplinary RIT will aim to foster interactions between mathematicians and physicists on topics of mutual interest, such as supersymmetry, string theory, and gauge theory.  Please see the web page or contact one of the organizers for more details.  The topic for this semester is the big Clay/AMS book on D-branes and mirror symmetry.
  • RIT on Higgs Bundles
    • Organizer: Richard Wentworth
    • Meeting Time: Fridays at 2:00, room TBA, starting September 9.
    • Description: This year's RIT may focus on parahoric structures.
  • RIT on Weather, Chaos, and Data Assimilation
    • Organizers: Kayo Ide (AOSC) and Brian Hunt (MATH).
    • Meeting Time: Mondays at 2:00 in CSS 4301, starting Sept. 12.
    • Description: We study prediction and estimation problems for nonlinear dynamical systems with main applications in (but not limited to) the atmosphere and the ocean. Emphasis is put on uncertainty quantification and reduction.
  • RIT on Applied Harmonic Aanlysis
    • Organizer: Radu Balan
    • Time: Mondays 12:00 - 1:00 PM in room MATH 1311
  • RIT on Financial Mathematics
    • Organizer: Dilip Madan
    • Time: 5-6 PM Tuesdays in VMH, room 3332
  • RIT on Computational Linguistics (aka CLIP Colloquium)
    • Organizers: Doug Oard, Jimmy Lin, et al.
    • Meeting Time: Wednesdays 11AM in AVW 3258
  • Student Algebra-Number Theory Seminar
    • Organizer: Adam Lizzi
    • Meeting Time: Tuesdays 1:00-2:00 PM
    • Location: MTH 2300.
  • Student Dynamics Seminar
    • Organizer: Kasun Fernando
    • Meeting Time: Tuesdays 3:00-4:00 PM
    • Location: MTH 2400.
  • Informal Geometric Analysis Seminar
  • Cancer Modeling RIT
    • Organizers: Jim Greene and Doron Levy
    • Organizational Meeting: Wednesday September 10th, at 12:30 pm in the CSCAMM seminar room (CSIC 4122).  If you are interested and cannot attend the organizational meeting, please email Dana () and we will add you to the mailing list.  It would also be helpful to know when you are available so we can schedule the regular meeting time.
  • RIT on Optimization and Equilibrium Problems with Applications in Engineering
    • Organizer: Steven A. Gabriel, Dept. of Mechanical Engineering
    • Times: Twice a month meetings 9:30-11:00am, 0151 EGR Conference room.  In Fall 2016, meetings will be on Fridays, Sept. 9, 16, Oct. 7, 14, Nov. 4, 18, Dec. 2, 9.
    • Topics: We will discuss theory, applications, and algorithms for solving optimization and equilibrium problems with an emphasis on engineering applications.
  • RIT on Particle Systems
  • RIT on Air Traffic Management
    • Organizers: David Lovell and Michael Ball
    • Time: 10:00 am - 12:00 pm Wednesdays
    • Location: AV Williams 2168
    • Description: We will study problems related to the control and management of the national air traffic system.  System concerns include safety, efficiency, performance, and fair allocation of public resources to private participants.  We develop and employ tools from discrete and continuous optimization, stochastic and deterministic queuing, and multivariate statistics.
  • RIT on Deep Learning
    • Organizers: Wojtek Czaja and Matt Guay (NIBIB/NIH)
    • Meeting Time: Wednesdays 12:00 - 1:00, MTH 1311.

Archives: 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018

  • Math Department Welcome

    Speaker: () -

    When: Wed, September 13, 2017 - 3:15pm
    Where: Kirwan Hall 3206
  • Approximation Algorithms: Some ancient, some new - the good, the bad and the ugly

    Speaker: Samir Khuller (University of Maryland Computer Science ) - https://www.cs.umd.edu/users/samir/

    When: Wed, September 20, 2017 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: NP-complete problems abound in every aspect of our daily lives. One approach is to simply deploy heuristics, but for many of these we do not have any idea as to when the heuristic is effective and when it is not. Approximation algorithms have played a major role in the last three decades in developing a foundation for a better understanding of optimization techniques - greedy algorithms, algorithms based on LinearProgramming (LP) relaxations have paved the way for the design of (in some cases) optimal heuristics. Are these the best ones to use in “typical” instances? Maybe, maybe not.

    In this talk we will focus on two specific areas - one is in the use of greedy algorithms for a basic graph problem called connected dominating set, and the other is in the development of LP based algorithms for a basic scheduling problem in the context of data center scheduling.
  • Faculty Meeting with CMNS Interim Dean, Jerry Wilkinson

    Speaker: (CMNS Dean's Office) -

    When: Wed, September 27, 2017 - 3:15pm
    Where: Kirwan Hall 3206
  • Binet-Legendre metric and applications of Riemannian results in Finsler geometry

    Speaker: Vladimir Matveev (Friedrich-Schiller-Universität Jena ) - http://users.minet.uni-jena.de/~matveev/

    When: Wed, October 4, 2017 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: We introduce a construction that associates a Riemannian metric $g_F$ (called the
    Binet-Legendre metric) to a
    given Finsler metric $F$ on a smooth manifold $M$. The transformation
    $F \mapsto g_F$ is $C^0$-stable and has good
    smoothness properties, in contrast to previously considered
    constructions. The Riemannian metric $g_F$ also behaves nicely under
    conformal or isometric transformations of the Finsler metric $F$ that
    makes it a powerful tool in Finsler geometry. We illustrate that by
    solving a number of named problems in Finsler geometry. In particular
    we extend a classical result of Wang to all dimensions. We answer a
    question of Matsumoto about local conformal mapping between two
    Berwaldian spaces and use it to investigation of essentially conformally Berwaldian manifolds.
    We describe all possible conformal self maps and all self similarities
    on a Finsler manifold, generasing the famous result of Obata to Finslerian manifolds. We also classify all compact conformally flat
    Finsler manifolds. We solve a conjecture of Deng and Hou on locally
    symmetric Finsler spaces. We prove smoothness of isometries of Holder-continuous Finsler metrics. We construct new ``easy to calculate''
    conformal and metric invariants of finsler manifolds.
    The results are based on the papers arXiv:1104.1647, arXiv:1409.5611,
    arXiv:1408.6401, arXiv:1506.08935,
    partially joint with M. Troyanov (EPF Lausanne) and Yu. Nikolayevsky (Melbourne).
  • (No colloquium)

    Speaker: General Departmental Meeting () -

    When: Wed, October 11, 2017 - 3:15pm
    Where: Kirwan Hall 3206
  • No colloquium

    Speaker: Departmental Meeting () -

    When: Wed, October 18, 2017 - 3:15pm
    Where: Kirwan Hall 3206
  • No colloquium

    Speaker: Departmental Meeting () -

    When: Wed, October 25, 2017 - 3:15pm
    Where: Kirwan Hall 3206
  • Some results on affine Deligne-Lusztig varieties

    Speaker: Xuhua He (UMD) - http://www.math.umd.edu/~xuhuahe/

    When: Wed, November 1, 2017 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: In Linear Algebra 101, we encounter two important features of the group of invertible matrices: Gauss elimination method, or the LU decomposition of almost all matrices, which is an important special case of the Bruhat decomposition; the Jordan normal form, which gives a classification of the conjugacy classes of invertible matrices.

    The study of the interaction between the Bruhat decomposition and the conjugation action is an important and very active area. In this talk, we focus on the affine Deligne-Lusztig variety, which describes the interaction between the Bruhat decomposition and the Frobenius-twisted conjugation action of loop groups. The affine Deligne-Lusztig variety was introduced by Rapoport around 20 years ago and it has found many applications in arithmetic geometry and number theory.

    In this talk, we will discuss some recent progress on the study of affine Deligne-Lusztig varieties, and some applications to Shimura varieties.
  • Quantitative estimates of propagation of chaos for large systems of interacting particles

    Speaker: Pierre-Emmanuel Jabin (UMD) - http://www2.cscamm.umd.edu/~jabin/

    When: Wed, November 8, 2017 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: We present a new method to derive quantitative estimates proving the propagation of chaos for large stochastic or deterministic systems of interacting particles. Our approach requires to prove large deviations estimates for non-continuous potentials modified by the limiting law. But it leads to explicit bounds on the relative entropy between the joint law of the particles and the tensorized law at the limit; and it can be applied to very singular kernels that are only in negative Sobolev spaces and include the Biot-Savart law for 2d Navier-Stokes
  • Scale, pattern and biodiversity

    Speaker: Simon Levin (Princeton ) -

    When: Wed, November 15, 2017 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: One of the deepest problems in ecology is in understanding how so many species coexist, competing for a limited number of resources. This motivated much of Darwin’s thinking, and has remained a theme explored by such key thinkers as Hutchinson (“The paradox of the plankton”), MacArthur, May and others. A key to coexistence, is in the development of spatial and spatio-temporal patterns, and in the coevolution of life-history patterns that both generate and exploit spatio-temporal heterogeneity. Here, general theories of pattern formation, which have been prevalent not only in ecology but also throughout science, play a fundamental role in generating understanding. The interaction between diffusive instabilities, multiple stable basins of attraction, critical transitions, stochasticity and far-from-equilibrium phenomena creates a broad panoply of mechanisms that can contribute to coexistence, as well as a rich set of mathematical questions and phenomena. This lecture will cover as much of this as time allows.
  • Math Teaching Forum

    Speaker: () -

    When: Fri, November 17, 2017 - 3:00pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: Our lecturers Hilaf Hasson, Kendall Williams and Allan Yashinski will be hosting the panel on the realities of teaching. The target audience first includes Math TAs but we are hoping to attract many in the department. Light refreshments to follow in room 3201.
  • Ergodic properties of parabolic systems.

    Speaker: Adam Kanigowski

    When: Wed, November 29, 2017 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: Parabolic dynamical systems are systems of intermediate (polynomial) orbit growth. Most important classes of parabolic systems are: unipotent flows on homogeneous spaces and their smooth time changes, smooth flows on compact surfaces, translation flows and IET's (interval exchange transformations). Since the entropy of parabolic systems is zero, other properties describing chaoticity are crucial: mixing, higher order mixing, decay of correlations.
    One of the most important tools in parabolic dynamics is the Ratner property (on parabolic divergence), introduced by M. Ratner in the class of horocycle flows. This property was crucial in proving famous Ratner's rigidity theorems in the above class.

    We will introduce generalisations of Ratner's property for other parabolic systems and discuss it's consequences for chaotic properties. In particular this allows to approach the Rokhlin problem in the class of smooth flows on surfaces and in the class of smooth time changes of Heisenberg nilflows.
  • Mobius disjointness for some dynamical systems of controlled complexity

    Speaker: Zhiren Wang

    When: Wed, December 6, 2017 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: Sarnak's Mobius disjointness conjecture speculates that the Mobius sequence is disjoint to all topological dynamical systems of zero topological entropy. We will survey the recent developments in this area, and discuss several special classes of dynamical systems of controlled complexity that satisfy this conjecture. Part of the talk is based on joint works with Wen Huang, Xiangdong Ye, and Guohua Zhang. No background knowledge in either dynamical systems or number theory will be assumed.

  • Dimension gaps in self-affine sponges

    Speaker: David Simmons (University of York) -

    When: Thu, December 7, 2017 - 2:00pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: Abstract: In this talk, I will discuss a long-standing open problem in the dimension theory of dynamical systems, namely whether every expanding repeller has an ergodic invariant measure of full Hausdorff dimension, as well as my recent result showing that the answer is negative. The counterexample is a self-affine sponge in $\mathbb R^3$ coming from an affine iterated function system whose coordinate subspace projections satisfy the strong separation condition. Its dynamical dimension, i.e. the supremum of the Hausdorff dimensions of its invariant measures, is strictly less than its Hausdorff dimension. More generally we compute the Hausdorff and dynamical dimensions of a large class of self-affine sponges, a problem that previous techniques could only solve in two dimensions. The Hausdorff and dynamical dimensions depend continuously on the iterated function system defining the sponge, which implies that sponges with a dimension gap represent a nonempty open subset of the parameter space. This work is joint with Tushar Das (Wisconsin -- La Crosse).
  • TBA (Douglas Lecture)

    Speaker: Daniel Tataru (UC Berkeley) - https://math.berkeley.edu/~tataru/

    When: Fri, December 8, 2017 - 3:15pm
    Where: Kirwan Hall 3206
  • Taking Mathematics to Heart

    Speaker: Alfio Quarteroni (Politecnico di Milano, Milan, Italy and EPFL, Lausanne, Switzerland ) - https://cmcs.epfl.ch/people/quarteroni

    When: Fri, February 2, 2018 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: Abstract : In this presentation I will highlight the great potential offered by the interplay between data science and computational science to efficiently solve real life large scale problems . The leading application that I will address is the numerical simulation of the heart function.

    The motivation behind this interest is that cardiovascular diseases unfortunately represent one of the leading causes of death in Western Countries.

    Mathematical models based on first principles allow the description of the blood motion in the human circulatory system, as well as the interaction between electrical, mechanical and fluid-dynamical processes occurring in the heart. This is a classical environment where multi-physics processes have to be addressed.

    Appropriate numerical strategies can be devised to allow for an effective description of the fluid in large and medium size arteries, the analysis of physiological and pathological conditions, and the simulation, control and shape optimization of assisted devices or surgical prostheses.

    This presentation will address some of these issues and a few representative applications of clinical interest.
  • Defects in periodic homogenization problems : Toward a complete theory [Appl Math Colloquium]

    Speaker: Claude Le Bris (Ecole des Ponts and Inria) - https://cermics.enpc.fr/~lebris/

    When: Tue, February 6, 2018 - 3:30pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: We will present some recent mathematical contributions related to nonperiodic homogenization problems. The difficulty stems from the fact that the medium is not assumed periodic, but has a structure with a set of embedded localized defects, or more generally a structure that, although not periodic, enjoys nice geometrical features. The purpose is then to construct a theoretical setting providing an efficient and accurate approximation of the solution. The questions raised ranged from the theory of elliptic PDEs, homogenization theory to harmonic analysis and singular operators.
  • Aziz Lecture

    Speaker: Claude Le Bris () -

    When: Wed, February 7, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • Spectral analysis on singular spaces

    Speaker: Alexander Teplyaev (University of Connecticut) - http://teplyaev.math.uconn.edu

    When: Fri, February 9, 2018 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: The talk will outline recent achievements and challenges in spectral and stochastic analysis on non-smooth spaces that are very singular, but can be approximated by graphs or manifolds. In particular, the talk will present two of most interesting examples that are currently
    under investigation. One example deals with the spectral analysis of the Laplacian on the famous basilica Julia set, the Julia set of the polynomial z^2-1. This is a joint work with Luke Rogers and several students at UConn. The other example deals with spectral, stochastic, functional analysis for the canonical diffusion on the pattern spaces of an aperiodic Delone set. This is a joint work with Patricia Alonso-Ruiz, Michael Hinz and Rodrigo Trevino.
  • Stability for symmetric groups and Hecke algebras

    Speaker: Weiqiang Wang (University of Virginia)

    When: Wed, February 14, 2018 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: We will describe a certain stability for the centers of the group algebras of the symmetric groups S_n for varying n, and its geometric counterpart. (To experts: this is not about Schubert calculus). We shall then explain the generalization of this stability phenomenon for wreath products and for Hecke algebras. This talk should be accessible to graduate students.
  • Alpha invariants and birational geometry.

    Speaker: Ivan Cheltsov (University of Edinburgh, UK) - http://www.maths.ed.ac.uk/cheltsov/

    When: Wed, February 21, 2018 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: Tian introduced alpha invariants to study the existence of
    Kahler-Einstein metrics on Fano manifolds.
    In this talk we describe (explicit and implicit) appearance of alpha
    invariants in (global and local) birational geometry.
  • Nonlinear fluid-structure interaction with fiber-reinforced soft composites: a unified mathematical framework for mathematical analysis, computation and applications

    Speaker: Suncica Canic (University of Houston) - https://www.math.uh.edu/~canic/

    When: Fri, February 23, 2018 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: Fiber-reinforced structures arise in many engineering and biological applications. Examples include space inflatable habitats, vascular stents supporting compliant vascular walls, and aortic valve leaflets. In all these examples a metallic mesh, or a collection of fibers, is used to support an elastic structure, and the resulting composite structure has novel mechanical characteristics preferred over the characteristics of each individual component. These structures interact with the surrounding deformable medium, e.g., blood flow or air flow, or another elastic structure, constituting a fluid-structure interaction (FSI) problem. Modeling and computer simulation of this class of FSI problems is important for manufacturing and design of novel materials, space habitats, and novel medical constructs.
    Mathematically, these problems give rise to a class of highly nonlinear, moving- boundary problems for systems of partial differential equations of mixed type. To date, there is no general existence theory for solutions of this class of problems, and numerical methodology relies mostly on monolithic/implicit schemes, which suffer from bad condition numbers associated with the fluid and structure sub- problems. In this talk we present a unified mathematical framework to study existence of weak solutions to FSI problems involving incompressible, viscous fluids and elastic structures. The mathematical framework provides a constructive existence proof, and a partitioned, loosely coupled scheme for the numerical solution of this class of FSI problems. The constructive existence proof is based on time-discretization via operator splitting, and on our recent extension of the Aubin-Lions-Simon compactness lemma to problems on moving domains. The resulting numerical scheme has been applied to problems in cardiovascular medicine, showing excellent performance, and providing medically beneficial information. Examples of applications in coronary angioplasty and micro- swimmer biorobot design will be shown.
  • Recent Work in Mixture Models and Clustering

    Speaker: Paul McNicholasAbstract: The application of mixture models for clustering has burgeoned into an important subfield of multivariate statistics and, in particular, classification. The framework for mixture model-based clustering is established and some historical context is provided. Then, some previous work is reviewed before some recent advances are presented. Previous work is discussed with some focus on technical detail. However, recent advances are presented with more focus on illustration via real data problems. The recent work discussed will include an approach for clustering Airbnb reviews as well as applications of mixtures of matrix variate distributions.

    When: Tue, February 27, 2018 - 3:30pm

    View Abstract

    Abstract: The application of mixture models for clustering has burgeoned into an important subfield of multivariate statistics and, in particular, classification. The framework for mixture model-based clustering is established and some historical context is provided. Then, some previous work is reviewed before some recent advances are presented. Previous work is discussed with some focus on technical detail. However, recent advances are presented with more focus on illustration via real data problems. The recent work discussed will include an approach for clustering Airbnb reviews as well as applications of mixtures of matrix variate distributions.
  • Five points on the sphere

    Speaker: Richard Schwartz (Brown University) - http://www.math.brown.edu/~res/

    When: Wed, March 14, 2018 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: In my talk I will discuss the problem of putting 5
    points on the sphere in such a way as to minimize their total
    potential energy with respect to a power law. General questions
    about the energy of point configurations go under the heading of
    Thomson's problem and have been studied for about 100 years.
    I'll sketch my rigorous computer-assisted proof that the
    triangular bi-pyramid is the global minimizer with respect to
    a power law of exponent s if and only if s<s*, where s* is
    a "phase transition constant" discovered experimentally by
    Melnyk-Knop-Smity in 1977.
  • Distinguished Lecture in Geometry - Richard Schoen (Stanford, UC Irvine)

    Speaker: Richard Schoen (Stanford, UC Irvine)

    When: Thu, March 15, 2018 - 4:30pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: This talk will be a survey of some of the geometric problems and ideas which either arose from general relativity or have direct bearing on the Einstein equations.
    It is intended for a general mathematical audience with minimal physics background.
    Topics will include an introduction to the Cauchy problem for the Einstein equations, problems related to gravitational mass which are closely related to the Riemannian geometry of positive scalar curvature, and trapped surfaces which are related to the mean curvature and minimal surfaces.
  • Distinguished Lecture Geometry - Richard Schoen (Stanford, UC Irvine)

    Speaker: Richard Schoen (Stanford, UC Irvine)

    When: Fri, March 16, 2018 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: Positive Mass Theorem Revisited - We will introduce the positive mass theorem which is a problem originating in general relativity, and which turns out to be connected to important mathematical questions including the study of metrics of constant scalar curvature and the stability of minimal hypersurface singularities. We will then give a general description of our recent work with S. T. Yau on resolving the theorem on high dimensional non-spin manifolds.
  • Overview of the N-body Problem

    Speaker: Richard Montgomery (UCSC) - https://people.ucsc.edu/~rmont/

    When: Wed, March 28, 2018 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: How can a cat, falling from upside-down with zero angular momentum, right herself? Viewing the cat’s problem from the perspective of symplectic reduction and gauge theory led me into the N-bodyproblem. The cat suggested the primacy of shape space: configuration space modulo symmetries. Deletingcollisions from the planar three body problem yields a shape space homotopic to a pair of pants: a thrice-punctured sphere. Is every free homotopy class of loops on this punctured sphere realized by some periodicsolution to the planar three-body problem? I aim to describe four results inspired by this last question.1. The figure eight orbit -its rediscovery, and existence proof. 2. That every negative energy zero angularmomentum solution (with a single exception) suffers collinear instants . 3. If I ‘cheat’ by changing thepotential from 1/r to 1/r2, and take the masses equal. then modulo symmetries, the bounded zero angularmomentum flow is conjugate to geodesic flow for a complete noncompact negatively curved metric on thepair of pants. 4. The answer to the homotopy question is ‘yes’ provided we accept small but nonzero angularmomentum and the masses are equal or nearly equal. (Result 1 is joint with Alain Chenciner, and result 4with Rick Moeckel. )
  • A Structure Theorem for Stationary Group Actions

    Speaker: Hillel Furstenberg () -

    When: Wed, April 4, 2018 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: Structure theorems play an important role in dynamics with Veech's structure theorem as an outstanding example. We will describe a structure theorem in a measure-theoretic context: namely for "stationary" group actions. These are actions where a measure on a group space is invariant "on the average" relative to a probability measure on the group. One application is to "multiple recurrence" for non-amenable group actions, and associated Ramsey type theorems.
  • Spring Teaching forum

    Speaker: Teaching forum () -

    When: Wed, April 11, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • TBA

    Speaker: Shrawan Kumar (UNC at Chapel Hill) - http://www.unc.edu/math/Faculty/kumar/

    When: Wed, April 18, 2018 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: TBA
  • TBA

    Speaker: Alexander Vladimirsky (Cornell University) - http://www.math.cornell.edu/~vlad/

    When: Wed, April 25, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • Counting points, counting fields, and new heights

    Speaker: Jordan Ellenberg http://www.math.wisc.edu/~ellenber/

    When: Fri, April 27, 2018 - 11:00am
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: The basic objects of algebraic number theory are number fields, and the basic invariant of a number field is its discriminant, which in some sense measures its arithmetic complexity. A basic finiteness result, proved by Hermite at the end of the 19th century, is that there are only finitely many degree-d number fields of discriminant at most X. It thus makes sense to put all the number fields in order of their discriminant, and ask if we can say how many you’ve encountered by the time you get to discriminant X.

    This is an old problem, governed by a conjecture of Narkiewicz. Interest in this area was revitalized by the work of Bhargava; the first step in his program was to count number fields of degree 4 and 5. (Degree 6 remains completely out of reach!) I’ll talk about the long history of this problem and its variants, and discuss two recent results:

    1) (joint with TriThang Tran and Craig Westerland) We prove that the upper bound conjectured by Narkiewicz is true “up to epsilon" when Q is replaced by a rational function field F_q(t) — this is much more than is known in the number field case, and relies on a new upper bound for the cohomology of Hurwitz spaces coming from quantum shuffle algebras: https://arxiv.org/abs/1701.04541

    2) (joint with Matt Satriano and David Zureick-Brown) Another much-studied counting problem in number theory is the Batyrev-Manin conjecture, which asks about the number of rational points on a variety of bounded height, or, in more concrete terms, questions like:
    “How many solutions does an equation like x^3 + y^3 + z^3 + w^3 = 0 have in integers of absolute value at most X?”

    It turns out there’s a way to synthesize the Narkiewicz conjecture and the Batyrev-Manin conjecture into a unified heuristic which includes both of those conjectures as special cases, and which says much more in general. This involves defining “the height of a rational point on an algebraic stack” and I will say as much about what this means as there’s time to!
  • The Geometry of Redistricting - Jordan Ellenberg

    When: Fri, April 27, 2018 - 3:30pm
    Where: 3206 Kirwan Hall
  • TBA

    Speaker: Lillian Pierce (Duke University/IAS) - https://services.math.duke.edu/~pierce/

    When: Wed, May 2, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • TBA (Aziz)

    Speaker: Arnaud Debussche (ENS, Rennes, France) - http://w3.ens-rennes.fr/math/people/arnaud.debussche/

    When: Fri, May 4, 2018 - 3:15pm
    Where: Kirwan Hall 3206