Recently there has been some progress on Ricci flow in higher dimensions, in the form of a new compactness and partial regularity theory. This theory relies on a new geometric perspective on Ricci flows and provides a better understanding of the singularity formation and long-time behavior of the flow. In dimension 4, in particular, this theory may eventually open up the possibility of a surgery construction or a construction of a "flow through singularities”.

In the first part of the talk, will describe this new theory, the new geometric intuition that lies behind it and its implications on the study of singularities in dimension 4. In the second part, I will present new work (joint with Eric Chen) that concerns the resolution of conical singularities.  

Bio-Sketch: Richard Bamler is currently an associate professor at UC Berkeley. He received his undergraduate education at the University of Munich in Germany, where he was mentored by Professor Bernhard Leeb. In 2011, he received his Ph.D under the supervision of Professor Gang Tian at Princeton. After a postdoc at Stanford University, he joined the faculty of UC Berkeley in 2014. His research interests include geometric analysis, differential geometry, and Ricci flow. He is particularly interested in Ricci flow. A lot of his work concerns Ricci flow in dimension 3 and 4, extending earlier work of Perelman.