Serguei NovikovIn honor of Sergei Novikov, who will be retiring shortly, the Mathematics Department at the University of Maryland announces an afternoon of talks on topics in geometric analysis by some of Novikov's distinguished students: Gennadi Kasparov (Vanderbilt University), Igor Krichever (Columbia University), and Anton Zorich (Paris Jussieu).  The event will take place on Wednesday, April 26, 2017, in William E. Kirwan Hall, University of Maryland, room 3206, and will be followed by a dinner.  All are invited to participate.

Program

Abstracts of the talks may be found here.

  • 2:00-3:00. Gennadi Kasparov, On the Novikov higher signature conjecture: history and development
  • 3:00-3:15. Tea across the hall in room 3201
  • 3:15-4:15. Igor Krichever, A discrete analog of the Novikov-Veselov hierarchy and its applications
  • 4:15-4:30. Short break
  • 4:30-5:30. Anton Zorich, Equidistribution of square-tiled surfaces, meanders, and Masur-Veech volumes
  • 5:30-6:00. Presentation to Sergei in the Yorke Rotunda downstairs
  • 6:00-8:00. Buffet dinner in the Yorke Rotunda downstairs

An afternoon of geometric analysis in honor of Sergei Novikov

Titles and Abstracts

Gennadi Kasparov (Vanderbilt University), On the Novikov higher signature conjecture: history and development

(This talk is part of the Lie Groups and Representation Theory Seminar)

Abstract:  The Novikov higher signature conjecture played and continues to play an important role in the development of several areas of mathematics: topology, geometric group theory, K-theory of C*-algebras. I will give a brief exposition of the history and progress in research related with the Novikov conjecture up to the most recent results.

Igor Krichever (Columbia University), A discrete analog of the Novikov-Veselov hierarchy and its applications

(This talk is part of the Mathematics Colloquium)

Abstract:  The spectral theory of the 2D Schrödinger operator on one energy level, pioneered by Novikov and Veselov, has developed over the years is still full of open problems. In the talk I will present recent progress in this area and its application to a wide range of problems including characterization of Prym varieties in algebraic geometry and solution of a sigma SO(N) model in mathematical physics.

Anton Zorich (Institut de Mathématiques Paris-Jussieu), Equidistribution of square-tiled surfaces, meanders, and Masur-Veech volumes

(This talk is part of the Dynamics Seminar)

Abstract:  We   show  how  recent  equidistribution  results allow one to compute
approximate values of Masur-Veech volumes of the strata in the moduli spaces
of Abelian and quadratic differentials, by a Monte Carlo method.

We also show how a similar approach allows one to count the asymptotical number of
meanders  of  fixed combinatorial type in various settings in all
genera.   Our  formulae  are  particularly  efficient  for classical
meanders in genus zero.

This is joint work with V. Delecroix, E. Goujard, and P. Zograf.

 

The DelMar Numerics Day 2013 will take place Saturday May 4, 9:30am-5:30pm, in MTH 3206. The keynote speaker is Jan Hesthaven (Brown University). Registration is free. For more information, go to http://delmar.math.umd.edu.


GF-poster-red


Colloquium Lecture by Simon Donaldson: Kähler-Einstein metrics,  extremal metrics and stability
Abstract: In the first part of the talk we will give a general outline of the two topics in Kä hler geometry in the title, both growing out of work of Calabi. We will also discuss the parallels with affine differential geometry which arise when one studies toric manifolds. We will explain the standard conjectures in the field, relating the existence of these metrics to algebro-geometric notions of “stability”. In the last part of the talk we will say something about recent work with Chen and Sun which establishes this conjecture in the case of Kä hler-Einstein metrics on Fano manifolds (Yau’s conjecture).



Lecture by Brian White: Gap theorems for minimal submanifolds of spheres
Abstract: The totally geodesic k-sphere is the minimal hypersurface in the (k+1)-sphere of smallest k-dimensional area. What is the next smallest area? This is closely related to the question: what is the smallest density that a minimal variety can have at a singular point? I will discuss these questions and some sharp partial results.



Lecture by Bo Berndtsson: Variations of Bergman kernels and symmetrization of plurisubharmonic functions
Abstract: I will discuss some applications of a theorem on variation of Bergman kernels. I will concentrate on a problem concerning symmetrization of plurisubharmonic functions and generalizations of the Polya-Szegö theorem. These problems turn out to have some relations to Kähler geometry and the openness conjecture for plurisubharmonic functions. (This is mostly joint work with Robert Berman.)



Lecture by Hans-Joachim Hein: Singularities of Kähler-Einstein metrics and complete Calabi-Yau manifolds
Abstract: When Einstein metrics form singularities one expects to see a bubble tree structure in which the bubbles are complete Ricci-flat spaces. We still lack a detailed understanding of this process in general. I will discuss several examples - old, new, and speculative - of singularity formation in the Kähler-Einstein case. Topics will include gravitational instantons in real dimension 4, and isolated Einstein singularities whose tangent cones have nonisolated singularities. Partly joint with Ronan Conlon and Aaron Naber.



Lecture by Andrea Malchiodi: Uniformization of surfaces with conical singularities
Abstract: We consider a class of singular Liouville equations which arise from the problem of prescribing the Gaussian curvature of a surface imposing a given conical structure at a finite number of points (as well as from models in Chern-Simons theory). The problem is variational, and differently from the "regular" case the Euler-Lagrange functional might be unbounded from below. We will look for critical points of saddle type using a combination of improved geometric inequalities and topological methods. This is joint work with D. Bartolucci, A. Carlotto, F. De Marchis and D. Ruiz.




Special Lecture by Eugenio Calabi



Lecture by Yuval Peres: The geometry of fair allocation to random points
Abstract: Given a random scatter of points (obtained as a limit of uniform picks from a large cube, or as the zeros of a random analytic function) , our goal is to allocate to each point of the process a unit of volume, in a deterministic translation-invariant way, so that the diameter of the region allocated to each point is stochastically as small as possible. One approach to this problem, studied in joint work with C. Hoffman and A. Holroyd, uses the stable marriage algorithm of Gale and Shapley. In  dimensions 3 and higher, gravity without inertia yields a satisfying solution.  The fairness of the allocation is a consequence of the divergence theorem; The diameters of the allocated regions are analyzed using methods from percolation theory.  Finally, I will relate the properties of the allocation to rigidity properties of the underlying point process.
References:
Hoffman, Christopher; Holroyd, Alexander E.; Peres, Yuval A stable marriage of Poisson and Lebesgue.Ann. Probab. 34 (2006), no. 4, 1241–1272.
Nazarov, Fedor; Sodin, Mikhail; Volberg, Alexander Transportation to random zeroes by the gradient flow. Geom. Funct. Anal. 17 (2007), no. 3, 887–935.
Chatterjee, Sourav; Peled, Ron; Peres, Yuval; Romik, Dan Gravitational allocation to Poisson points. Ann. of Math. (2) 172 (2010), no. 1, 617–671.
Subhro Ghosh and Yuval Peres, Rigidity and Tolerance in point processes: Gaussian zeroes and Ginibre eigenvalues. Preprint (2013), arXiv:1211.2381



[no video]
Lecture by Aaron Naber: Characterizations of bounded Ricci curvature and applications
Abstract:  The purpose of this talk is two-fold. First we give new ways of characterizing bounded Ricci curvature on a smooth metric measure space (Mn,g,e-fdvg). In essence, we show that bounded Ricci curvature controls the infinite dimensional analysis on the path space P(M) of a manifold in a manner analogous to how lower Ricci curvature controls the analysis on M. In particular, we show that the Ornstein-Uhlenbeck operator L on the based path space Px,T(M)= {γ:[0,T] → M; γ(0)=x}, which is a form of infinite dimensional Laplacian, has a spectral gap of (ekT+1)/2 if and only if the Bakry-Emery-Ricci curvature Rc+∇2f is bounded by k. Similarly the Ornstein-Uhlenbeck operator has a log-Sobolev constant of ekT+1 iff the Ricci curvature is bounded by k. We have many other characterizations as well, including notions which relate the Wasserstein geometry of the space of probability measures on M to the metric-measure geometry of path space, and including notions analagous to dimensional Ricci curvature bounds which control |Rc+∇2f-(1/(N-n))∇ f⊗ ∇ f|. In the second part of the talk we build the necessary tools in order to use these new characterizations to define bounded Ricci curvature on an essentially arbitrary metric measure space (X,d,v). The primary technical difficulty is to describe the right notion of parallel translation invariant vector fields along continuous curves in such a setting.  Even on a smooth manifold this requires deep ideas from stochastic analysis, but we provide a new approach even in this context which generalizes to arbitrary metric spaces. We spend some time discussing the structure of metric measure spaces with generalized bounded Ricci curvature. In particular we show its possible to define the Ornstein-Uhlenbeck operator on their path spaces, and that these operators also have the desired analytic control proven on smooth spaces. We also show spaces with generalized Ricci curvature bounded by k in this new sense have lower Ricci curvature bounded from below by -k in the sense of Lott-Villani-Sturm.



Lecture by Peter Kronheimer: Instanton homology for knots and webs
Abstract: Andreas Floer introduced instanton homology for 3-manifolds in the mid 1980's. He also described a variant he called knot homology, for knots in 3-manifolds. There has now been a lot of progress in understanding the structure of instanton knot homology and its relationship with other, more recent invariants of knots, such as Khovanov homology. Applications have included a proof that Khovanov homology detects the unknot. Replacing the Lie group SU(2) in Floer's construction with SU(N) for larger N leads to an invariant of "webs" (labeled trivalent graphs), with a connection to Khovanov-Rozansky homology. This talk will review some of these developments.

Subcategories

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
  • 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
  • (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
  • 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
  • Scale, pattern and biodiversity

    Speaker: Simon Levin (Princeton ) -

    When: Wed, November 15, 2017 - 3:15pm
    Where: Kirwan Hall 3206
  • Math Teaching Forum

    Speaker: () -

    When: Fri, November 17, 2017 - 3:00pm
    Where: Kirwan Hall 3206
  • Ergodic properties of parabolic systems.

    Speaker: Adam Kanigowski

    When: Wed, November 29, 2017 - 3:15pm
    Where: Kirwan Hall 3206
  • Mobius disjointness for some dynamical systems of controlled complexity

    Speaker: Zhiren Wang

    When: Wed, December 6, 2017 - 3:15pm
    Where: Kirwan Hall 3206
  • Dimension gaps in self-affine sponges

    Speaker: David Simmons (University of York) -

    When: Thu, December 7, 2017 - 2:00pm
    Where: Kirwan Hall 3206
  • 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
  • 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
  • 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
  • Stability for symmetric groups and Hecke algebras

    Speaker: Weiqiang Wang (University of Virginia)

    When: Wed, February 14, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • 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
  • 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
  • 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
    Where:
  • 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
  • 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
  • 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
  • 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
  • A Structure Theorem for Stationary Group Actions

    Speaker: Hillel Furstenberg () -

    When: Wed, April 4, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • Spring Teaching forum

    Speaker: Teaching forum () -

    When: Wed, April 11, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • Eigenvalue problem for reductive groups

    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
  • Agreeing to Disagree in Anisotropic Crowds

    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
  • The Geometry of Redistricting - Jordan Ellenberg

    When: Fri, April 27, 2018 - 3:30pm
    Where: 3206 Kirwan Hall
  • On a conjecture for p-torsion in class groups of number fields

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

    When: Wed, May 2, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • Sumca: Simple, Unified, Monte-Carlo Assisted Approach to Second-order Unbiased MSPE Estimation

    When: Thu, May 3, 2018 - 2:00pm
    Where: Kirwan 3206
  • Mad Guys Conference

    When: Fri, May 4, 2018 - 9:00am
    Where:
  • Stochastic nonlinear Schroedinger equations [Aziz Lecture]

    Speaker: Arnaud Debussche (ENS Rennes) - http://w3.bretagne.ens-cachan.fr/math/people/arnaud.debussche/

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