Geometry & Geometric Analysis Seminar
Main Content
The Geometry and Geometric Analysis (GAGA) Seminar is an opportunity for geometers, topologists, and others from TCU and other campuses to learn about new topics of mutual interest. GAGA meets most weeks during the school year. You can find notes from past talks at the GAGA Note Repository, located in a secure off-campus location.
The Fall 2026 GaGA seminar is Fridays at 1 pm in TUC 352 on TCU campus, and also the seminar will be available on Zoom. Contact Ken Richardson with any questions or issues with the link.
Friday, October 2, 1 pm
Speaker: Ken Richardson (TCU)
Title: Hopf conjecture on S^2\times S^2, part 2
Abstract: A famous conjecture of Hopf is that there does not exist a positive sectional curvature
(PSC) metric on S^2\times S^2. Recently, Brendle-Hung produced an AI-aided proof of the the existence of a PSC metric
on S^2\times S^2. In this second talk, I will briefly review the introduction in the previous talk,
and I will continue to discuss the J-P Bourguignon and Bourguignon-Deschamps-Sentenac
results on the nonexistence of positive sectional curvature metrics "close" to the standard metric.