Differential Geometry and Analysis Seminar

This seminar was organized by Christina Sormani, who can be contacted at sormani@comet.lehman.cuny.edu.

Schedule, Spring 2003

• Feb 5: Jeff McGowan (Central Connecticut State University)
  "Accumulation estimates for eigenvalues of the Hodge Laplacian on manifolds with degenerating metrics"
  hosted by Jozef Dodziuk
  
  
• Feb 12: No meeting grad center closed
  
  
• Feb 19: Prof. Dolgopyat (IAS)
  "Brownian Motion"
  The problem in question is to describe the motion of a particle moving under the influence of collisions with molecules of the surrounding fluid. We present some models of this as well as some open problems.
  hosted by David Fisher
  
  
• Feb 26: Mikhael Kovalyov (Gorentein Visiting Professor at Queens College of CUNY)
  "Nonlinear Fourier Transform"
  The method of the Inverse Scattering Transform is used to obtain/generate solutions of the so-called integrable equations (KdV, KP, NLS, etc.). The method is often referred to as nonlinear Fourier transform due to certain formal similarity to Fourier transform. It will be shown that the similarity is much deeper than has been thought. There is a nonlinear analogue of the Fourier integral formula that allows one to construct exact solutions (nonsolitons) with certain properties. The analogue is provided by a formula that by any account should not work, but it does despite common sense. This formula will be derived, discussed and its modulating properties will be illustrated.
  
  
• March 5: Thalia Jeffres (University of Michoacan, Mexico)
  "Regularity of the Heat Operator on a Cone"
  In this joint work with Paul Loya, we study differentiability properties of solutions to heat equation on a cone manifold. The heat operator considered here is that which corresponds to the Friedrichs extension of the Laplacian. For initial data in appropriately defined Holder spaces, the estimates are good enough to prove existence of solutions of certain semilinear parabolic equations.
  hosted by Jozef Dodziuk
  
  
• March 12: David Trubatch (Westpoint)
  "Discrete and Continuous Vector Solitons"
  Hosted by Christina Sormani
  
  
• March 19: Bill Minicozzi (Johns Hopkins University)
  "Embedded Minimal Disks"
  hosted by John Velling and Christina Sormani
  
  
• March 26: Iosif Polterovich (Univ of Montreal)
  "Combinatorics of heat invariants and trace regularizations"
  Relations between the geometric properties of manifolds and the spectrum of the Laplacian have been actively studied for decades. Heat equation asymptotics is an important source of geometric invariants, such as dimension, volume or scalar curvature. However, the complexity of heat invariants grows extremely fast, and most of the information they contain remains unaccessible. In the lecture we present a new approach to computation of heat invariants and some of its applications, particularly to combinatorics and to long range scattering.
  hosted by Yiannis Petrides
  
  
• April 2: Norbert Peyerimhoff (Universitat Bochum)
  "Dynamics of Magnetic Flows"
  hosted by Leon Karp
  
  
• April 9: Craig Sutton, (U. Penn)
  "Constructing isospectral simply-connected manifolds via Sunada's method"
  hosted by Christina Sormani
  
  
• April 16: No meeting Spring break
  
  
• April 23: No meeting Spring break
  
• Friday May 2 (12:30-1:30 pm): Dmitry Jakobson (McGill University)
  "Some results on L^p norms and critical points of eigenfunctions."
  We construct a metric of revolution on the 2-torus and a sequence of eigenfunctions with growing eigenvalues and exactly 16 critical points. We also discuss relations between positive and negative parts of eigenfunctions on Riemannian manifolds.
  hosted by Yiannis Petrides
  
  
• Wednesday May 14 (3:30-4:30 pm): Yisong Yang (Brooklyn Poly)
  "Harmonic Representatives for Topological Classes"
  hosted by Robert Sibner