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William Minicozzi (MIT), PDE Minischool

Title Lecture 1: Geometric heat equations Abstract:  The classical heat equation describes how a temperature distribution changes in time.  Over time, the temperature spreads itself out more and more evenly and, as time goes to infinity, the temperature goes to a … Continued

William Minicozzi (MIT), PDE Mini-School

Title Lecture 2: Mean curvature flow Abstract:  I will give an introduction to mean curvature flow (MCF) of hypersurfaces. MCF is a nonlinear heat equation where the hypersurface evolves to minimize its surface area and the major problem is to … Continued

Jared Wunsch, Northwestern University – Wunsch/PDE Mini-school

View Full Schedule here Title: Trapping, diffraction, and decay of waves Abstract: The long-time behavior of solutions to wave and Schrödinger equations is connected to geometry and dynamics via the correspondence principle, which states that at high-frequency, solutions propagate along classical particle … Continued

Oran Gannot, Northwestern University – Wunsch/PDE Mini-school

View Full Schedule here Title: Scattering resonances generated by diffractive trapping Abstract: In potential scattering where classical particles with a certain energy escape to infinity, it is expected that quantum states with neighboring energies decay rapidly in time. We will discuss some known results where the decay rate depends on … Continued

Jeffrey Galkowski, Northeastern University – Wunsch/PDE Mini-school

View Full Schedule here Title: Optimal Resolvent Estimates in Non-trapping Geometries Abstract: In this talk we discuss how propagation estimates can be used to prove resolvent estimates in non-trapping geometries. We will introduce the notion of defect measures and prove propagation estimates … Continued

UNC PDE Mini-School

With funding provided by the PDE group’s NSF RTG grant, we are excited to announce the return of the UNC PDE Mini-schools and wanted to invite you to the first of these.  The mini-schools are structured around a series of … Continued