CERAMATHS - DMATHS seminar: presentation by Matthias Täufer

The CERAMATHS Mathematics Department seminar will welcome Matthias Täufer (FernUniversität in Hagen, Germany) at 2pm Monday July 1, 2024, for the following talk:

Quantitative unique continuation and applications

Unique continuation is a rigidity property which many solutions of PDEs have: If they vanish on a subdomain they cannot vanish identically. Quantitative variants of unique continuation establish a relation between the norm of functions and the norm of their restriction to a subdomain and are an exciting field connecting harmonic analysis with spectral theory and applications to engineering and Mathematical Physics.

In this talk, I will present several quantitative unique continuation estimates for functions in spectral subspaces of Schrödinger operators and two applications thereof: (1) Control cost estimates for the heat equation with explicit estimates on the cost of controllability which allow to study controllability in the so-called homogenization regime, and (2) Anderson localization for random Schrödinger operators.