Events for 11/17/2016 from all calendars

Mathematical Physics and Harmonic Analysis Seminar

Time: 3:00PM - 4:00PM

Location: Bloc 628

Speaker: Julia Meshkova, Chebyshev Laboratory, St.Petersburg State University

Title: Homogenization of elliptic and parabolic Dirichlet problems in a bounded domain

Abstract: Let U⊂ℝ^d be a bounded domain of class C^1,1. In L₂(U; ℂⁿ), we consider a self-adjoint second order elliptic differential operator B_D,ε with the Dirichlet boundary condition. The coefficients of B_D,ε are periodic and depend on x/ε; so, they oscillate rapidly as ε→0. We obtain approximations for the resolvent (B_D,ε-ζ I)^-1 and for the semigroup e^(-B_D,εt), t≥0, both in the L₂→ L₂- and L₂→H¹-norms. The results of such type are called operator error estimates in homogenization theory.

The talk is based on a joint work with T.A. Suslina.

Douglas Lectures

Time: 4:00PM - 5:00PM

Location: BLOCKER 117

Speaker: Hari Bercovici, Indiana University

Title: Eigenvalues of sums of matrices: Non-random Matrices

Abstract: Suppose that the eigenvalues of two selfadjoint matrices A and B of size N are known. As shown by Klyachko, the possible eigenvalues of A+B are described by a system of inequalities which were later shown by Knutson and Tao to be the same as a system first described by Horn. The Horn inequalities can now be proved in a completely elementary way which allows us to prove similar results in other contexts, for instance in an arbitrary factor. The argument involves an elementary solution to certain intersection problems in Grassmann manifolds.