Wednesday, October 16, 2019
12:00 PM - 1:00 PM
Annenberg 213

CMX Lunch Seminar

A `Liquid-Solid' Phase Transition in a Simple Model for Swarming
Rupert Frank, Professor, Mathematics, Caltech,
Speaker's Bio:
Areas of mathematical interest Analysis, Mathematical Physics and Spectral theory, in particular Functional inequalities Fractional Laplacian Superconductivity Eigenvalues of self-adjoint and non-selfadjoint Schrödinger operators Semi-classical spectral asymptotics Matrix inequalities and Quantum information

We consider a non-local shape optimization problem, which is motivated by a simple model for swarming and other self-assembly/aggregation models, and prove the existence of different phases. In particular, we show that in the large mass regime the ground state density profile is the characteristic function of a round ball. An essential ingredient in our proof is a strict rearrangement inequality with a quantitative error estimate.

The talk is based on joint work with E. Lieb.

For more information, please contact Jolene Brink by phone at (626)395-2813 or by email at jbrink@caltech.edu or visit CMX Website.