Seminar by Mr. Tooryanand Seetohul on 5 March at 4pm

We are very happy to announce the following seminar by Mr. Tooryanand Seetohul. The details are as follows:

Speaker: Mr. Tooryanand Seetohul

Affiliation:Institut de recherche de mathématique de Rennes, Université de Rennes, France

Title:Landau damping around inhomogeneous steady states of the Vlasov-HMF model

Time & Date: 05 March 2026, 16:00 hrs
Venue: Harish-chandra Seminar hall (MSB 215)

Abstract: Plasma dynamics, often modeled by Vlasov equations, have interactions encoded by a potential kernel. A striking phenomenon in such systems is Landau damping whereby particles relax back to a natural equilibrium state when slightly perturbed. In this talk, we investigate Landau damping around inhomogeneous (spatially-dependent) steady states, focusing on the Vlasov-HMF (Hamiltonian Mean-Field) model, a simplified model of the known Vlasov-Poisson potential kernel. We first present the linearized analysis, showing how Landau damping emerges via an action-angle formulation. The talk addresses the passage from this linear picture to a nonlinear result for initial data with Sobolev regularity. This step is complicated by plasma echoes: nonlinear particle interactions that can destabilize the system. Using compact support hypotheses for symmetric perturbations, we close a bootstrap argument coupling high and low regularity norms, guaranteeing that Landau damping holds for long but finite time.