The APDE seminar on Monday, 10/4, will be given by Sanchit Chaturvedi (Stanford University) online via Zoom from **4:10pm to 5:00pm PST**. To participate, email Sung-Jin Oh (sjoh@math.berkeley.edu)

**Title**: Stability of vacuum for the non-cut-off Boltzmann equation with moderately soft potentials.

**Abstract: **The vector field method developed by Klainerman has been widely successful in the study of wave equations and general relativity. Recently, the vector field approach has been adapted to understand the dispersion due to the transport operator in both collisionless and collisional kinetic models. As a proof of concept, I will discuss the stability of vacuum for Boltzmann equation with moderately soft potentials. The nonlocality of the Boltzmann operator poses a lot of difficulty and forces us to use a purely energy based approach. This is in contrast to the paper by Luk (Stability of vacuum for the Landau equation with moderately soft potentials) on Landau equation in a similar setting where a maximum principle is both proved and needed.