Mathematics

 The course is focused on Partial Differential Equations. It will start from classical theorems up to some nonlinear PDEs under active research.

1) Basic notions and definitions, Cauchy-Kowaleskaya Theorem 
2) Some fundamental examples of linear PDEs: transport, Laplace, heat, wave equations
3) Some examples of fundamental nonlinear PDEs: Hamilton-Jacobi, conservation laws
4) Linear PDEs (elliptic, parabolic, wave): existence of solutions, regularity (with or without boundary)
5) Nonlinear PDEs and Calculus of Variation, Hamilton-Jacobi equations, Conservation Laws If time permits, the course will cover recent results for some nonlinear PDEs listed above.