Graduate Student Seminar | Dewan Chowdhury (Northwestern University)

Title: The continuity method

Abstract: Suppose you want to show that the equation $f(x)=y$ has a solution. The continuity method goes as follows: We start from a point $y_0$ where a solution is obvious, connect it to our target $y$ by a path $y_t$. Then seek to follow the solution along the family $f(x_t)=y_t$ from t=0 to 1.

I will use this method to prove a case of the uniformization theorem for Riemann surfaces. Time permitting, I will also discuss generalizations, including Yau’s resolution of the Calabi conjecture, whose proof follows the same continuity framework.

Note: The talk will start at 4:10 pm

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