Title: Course of Undergraduate Young Talent Project (UYTP): 4-manifolds and Ricci flow

Speaker: Professor Bennett Chow (University of California San Diego)

Teaching Language: English

Teaching Object: Undergraduate seniors and graduate students

Prerequisites: Basic knowledge of topology and geometry

Schedule: 

From March 25 to June 13

8:00 am to 10:00 am, every Monday

15:00 pm to 17:00 pm, every Wednesday

Venue: Room 508, Teaching Building 3 (三教), Peking University

Introduction:

Ricci flow deforms Riemannian metrics on manifolds by a nonlinear heat equation. In dimension 3 this led to the proof of the Thurston-Hamilton-Perelman geometrization theorem. In dimension 4 it is unknown if Ricci flow can be used to derive topological conclusions. In this course we discuss some of what is currently known in this direction. Our focus will be to present the prerequisite knowledge to understand various conjectures on this topic.

Website for the course: http://www.math.ucsd.edu/~benchow/bicmr/