### About Zhiyuan Zhang

I obtained my PhD at Brown University in 2020 under the advisement of Walter A. Strauss. After that, in 2020 – 2023, I was a Courant Instructor at the Courant Institute of Mathematical Sciences at New York University. My main research interest is in kinetic models in plasma theory, including the relativistic Vlasov-Maxwell system, the Vlasov Poisson equation, etc. In particular, I have been working on the construction and the stability properties of special solutions of these equations, such as equilibria and solitary waves, as well as blow-up-like behavior of the solutions. I am also interested in related models in fluid dynamics and some dispersive equations.

Analysis and Geometry falls under the field of mathematical analysis, which is a broad branch of mathematics that encompasses many fields, generally sharing a basis in calculus. Historically, analysis has played a crucial role in solving problems in physics and engineering; recent years have seen surprising applications to solve problems in other mathematical fields like the Poincaré Conjecture in topology.