Title: Recent progress on existence of minimal surfaces

Date: 04/25/2019

Time: 3:10 PM - 4:00 PM

Place: C304 Wells Hall

A long standing problem in geometry, conjectured by Yau in 1982, is that any any $3$-manifold admits an infinite number of distinct minimal surfaces. The analogous problem for geodesics on surfaces led to the discovery of deep interactions between dynamics, topology, and analysis. The last couple of years brought dramatic developments to Yau’s conjecture, which has now been settled due to the work of Marques-Neves and Song. I will survey the history of the problem and the several contributions made.