UW-PIMS Mathematics Colloquium: Jun-Cheng Wei

I will discuss recent new developments in De Giorgi Conjecture for Allen-Cahn equation. In dimensions up to 10, we shall establish the C2,α estimates of level sets for stable solutions of Allen-Cahn. By applying reverse gluing method we show that the obstruction to C2,α estimates is the existence of Toda System in one dimension less. Applications to classifications of finite Morse index solutions and some open problems will be discussed.