PDE and Applied Mathematics Seminar
October 24, (CAS 220D, 12:00-1:00pm). Yaniv Almog (Louisiana State University)
will speak on "A Rigorous Proof of the Maxwell-Claussius-Mossotti Formula."
We consider a large number of identical inclusions (say spherical), in a bounded domain, with conductivity different than that of the matrix. In the dilute limit, with some mild assumption on the first few marginal probability distribution (no periodicity or stationarity are assumed), we prove convergence in H1 norm of the expectation of the solution of the steady state heat equation, to the solution of an effective medium problem, which for spherical inclusions is obtained through the Maxwell-Clausius-Mossotti formula. Error estimates are provided as well.
November 12, (CAS 220D, 12:00-1:00pm). Artem Zvavitch (Kent State University)
will speak on "Mahler's conjecture for convex bodies."
Let P(K) be the product of the volume of an origin symmetric convex body K and its dual/polar body K^*;. Mahler conjectured that P(K) is
minimized by a cube and maximized by a ball. The second claim of this
conjecture was proved by Santalo; despite many important partial results, the first problem is still open in dimensions 3 and higher. In this talk we will discuss some recent progress and ideas concerning this conjecture.