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 … Read more
Title: TBA Abstract:
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 … Read more
Title: TBA Abstract: TBA
Title: TBA Abstract: TBA
Title: Small scale creation in ideal fluids Abstract: The incompressible Euler equation of fluid mechanics is one of the central equations of applied analysis, yet due to its nonlinearity and non-locality many fundamental properties of the solutions remain poorly understood. In particular, … Read more
Title: Small scale creation in ideal fluids Abstract: The incompressible Euler equation of fluid mechanics is one of the central equations of applied analysis, yet due to its nonlinearity and non-locality many fundamental properties of the solutions remain poorly understood. In particular, … Read more
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 … Read more
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 … Read more
View Full Schedule here Title: Stabilization rates for the damped wave equation with Hölder regular damping Abstract: We study the decay rate of the energy of solutions to the damped wave equation in a setup where the geometric control condition is violated. … Read more
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 … Read more
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 … Read more
