Department of Mathematics

Leonardo Abbrescia

Picture of Leonardo Abbrescia

Graduate Student

Research Interests

My advisor is Willie Wong and I am studying partial differential equations. More specifically, my goal is to give a sharp description of shock formation to two dimensional quasilinear waves modeled on a physically motivated class of background metrics.

I am also working on a side project with Professor Jun Kitagawa on regularity theory for the real Monge-Ampère equation with hopeful applications to generated Jacobian equations.

When I was an undergrad, I worked on contact and symplectic topology with Jo Nelson.

Selected Publications
  • Global Existence to Convolution-Type Vlasov Equations, in preparation.  
  • L. Abbrescia, I. Huq-Kuruvilla, J. Nelson, N. Sultani., Reeb Dynamics of the Link of the $A_n$ Singularity, Involve Vol. 10 (2017), No. 3, 417-442.  Open