This semester we intend to run an informal, random working mathematical physics/analysis/applied math seminar. The main idea will be to talk about problems that we can't yet solve, as well as background information.
The seminar will normally meet on Thursdays, 4pm at VV B139. Everybody is welcome!
Schedule
February 2, Sergey Denisov
will speak on scattering for Dirac operator with L^2 potential in one dimension.
The corresponding question for Schrodinger is known for L^p, p<2, but is open for the borderline case.
February 16, Roman Shterenberg
will speak on Jost functions for Jacobi matrices. The talk will be a review of some recent results by Damanik and Simon, which may provide some technology useful for extending the existence of
wave operators to L^2 in the Schrodinger case.
March 2, Andrej Zlatos
On the eigenvalues of elliptic non-symmetric operators
April 6, 5pm (note special time) Fedya Nazarov
Volumes of sublevel sets of harmonic functions and related
questions.
Abstract: I will talk of a simple (in formulation) but still
unsolved (in dimensions greater than 2)
problem about harmonic functions in the unit ball that
may have numerious applications to the study of nodal domains of
the eigenfunctions of the Laplacian on smooth compact manifolds.
April 13, Ahyoung Kim
Jacobi matrices with slowly oscillating entries
April 27, 5pm (note special time) Lenya Ryzhik
Kinetic equations for waves in random and non-random media.
Abstract. I will discuss some of the problems related to the derivation of the kinetic limits for waves in random
media. I will explain that some of the difficulties disappear when some additional dissipation is introduced -- then
kinetic limits may be obtained in a straightforward manner in a large class of non-random media.