CMX Lunch Seminar
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.