When:
Friday, November 14, 2025
4:00 PM - 5:15 PM CT
Where: Lunt Hall, 105, 2033 Sheridan Road, Evanston, IL 60208 map it
Audience: Faculty/Staff - Student - Public - Post Docs/Docs - Graduate Students
Contact:
Daniel Mallory
DanielMallory2025@u.northwestern.edu
Group: Department of Mathematics: Graduate Student Seminar
Category: Lectures & Meetings
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