Historically, the first systematic approaches to finding optimal geometric structures have made use of variational approaches and/or elliptic PDEs. Ever since the work of Eells–Sampson and Hamilton, however, geometers have also embraced flows or parabolic methods, which are more dynamic in nature. Over the last thirty years, the mean curvature flow and the Ricci flow have become tremendously active areas of research. Highlights include Perelman’s spectacular proof of the Poincare and geometrization conjecture, the proof of the differentiable sphere theorem, and the analytic minimal model program. The mini-school will feature accessible introductions to some of the most exciting recent results on Ricci flow and mean curvature flow. The format will be two 5 hour courses delivered by teams of leading researches in the field.

Speakers and titles

Lu Wang (Wisconsin) and Jacob Bernstein (JHU): Mean curvature flow and entropy

Dan Knopf (Austin Texas) and Richard Bamler (Berkeley): Ricci flow through singularities