- The following speakers are confirmed:
- Luis Caffarelli (UT Austin)
- Title: Some connections between Minimal surfaces and Free Boundary problems
will describe connections between the minimal surface theory, as develop from the point of view of sets with minimal perimeter and different approaches to free boundary regularity. I will also describe some problems in phase transition that combine both.
- Otis Chodosh (Stanford University)
- Title: Relating the index and topology of a minimal surface in R^3
The Morse index for the area functional at a minimal surface is a fundamental invariant of the surface. I will discuss some connections between the Morse index and the topology of the underlying surface which, as a consequence, show that there are no embedded minimal surfaces of index 2. This is based on joint work with Davi Maximo.
- Jim Isenberg (University of Oregon)
- Title: Asymptotic Behavior of Non Round Neckpinches in Ricci Flow
Neckpinch singularities are a prevalent feature of Ricci flow, and recent work has given us a
good picture of their asymptotic behavior, so long as the geometries are rotationally
symmetric. We discuss this asymptotic behavior, both for degenerate and non-degenerate
neckpinches. It has been conjectured that neckpinch singularities which develop in
non-rotationally symmetric Ricci flows do asymptotically approach roundness, and consequently
have very similar asymptotic behavior to those which are rotationally symmetric. We discuss very
recent work which supports this conjecture.
- Valentino Tosatti (Northwestern University)
- Title: Title: Long-time behavior of the Kahler-Ricci flow
Abstract: I will discuss the problem of understanding the long-time
behavior of the Kahler-Ricci flow on a compact Kahler manifold, assuming
that a solution exists for all positive time. Inspired by results from the
minimal model program in algebraic geometry, Song and Tian posed several
conjectures which describe this behavior. I will report on recent work
(joint with B.Weinkove, X.Yang and Y.Zhang) which confirms some of these