Analysis Seminar

Organizers: Dan-Andrei Geba and Allan Greenleaf.

The seminar will be held usually on Fridays, 2-3PM, in Hylan 1106A.

Fall 2009 Speakers:

  • October 2, Mihai Tohaneanu, Purdue University, "Local energy estimates on Schwarzschild and Kerr backgrounds".

    Abstract: Understanding the decay of linear waves is crucial in dealing with the problem of stability of the Kerr spacetime. I will talk about one way to measure this decay, namely local energy estimates, from which one can deduce many other useful estimates (uniform energy bounds, pointwise bounds, Strichartz estimates, etc). This is joint work with Jeremy Marzuola, Jason Metcalfe, and Daniel Tataru (for Schwarzschild), and Daniel Tataru (for Kerr).

  • October 30, Stephen Robinson, Wake Forest University, "Nonlinear eigenvalue problems and generalizations of the Fredholm alternative".

    Abstract: Compact symmetric linear operators have a beautiful and well-understood spectral theory with an associated Fredholm Alternative that completely describes the solvability of nonhomogeneous linear problems. The last forty years have witnessed a great deal of effort to generalize these ideas to select nonlinear problems. In this talk I will review some fundamental variational ideas associated with eigenvalue problems, and I will apply those ideas to derive some generalizations of the Fredholm Alternative to nonlinear problems.

  • November 6, Sarada Rajeev, University of Rochester, "Renormalization in the Kondo problem".

    Abstract: When electrons in a metal encounter an impurity of small size, the zero temperature resistance is predicted to be infinite by the usual methods of quantum theory. Experimentally, the resistance grows at low temperatures, but remains finite. This contradiction was resolved by Wilson using his celebrated Numerical Renormalization Group method. I will discuss another approach which has the potential of being mathematically rigorous. Some toy models of renormalization with a rigorous mathematical formulation will also be discussed.

  • November 13, Magdalena Czubak, University of Toronto, "Eventual regularization of the slightly supercritical fractional Burgers equation".

    Abstract: We prove that a weak solution of a slightly supercritical fractional Burgers equation becomes H\"older continuous for large time.

  • November 20, Nsoki Mavinga, University of Rochester, "Nonlinear elliptic equations at resonance".

    Abstract: We consider a generalized Steklov-Robin eigenproblem with (singular) weights and prove existence results for nonlinear elliptic equations when the nonlinear perturbations are at resonance with the spectrum, in some sense. The proofs are based on variational methods, a priori estimates, and topological degree techniques.

Previous semesters