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Geometry

Organizers:  Otis ChodoshYi Lai, and Greg Parker

Past Events

May
15
Date3:15 PM
Location
383N
Speaker
Michele Caselli (Stanford & Scuola Normale Superiore)

In this talk, I will explain why fractional (or nonlocal) minimal surfaces are ideal objects to which min-max methods can be applied on Riemannian manifolds. After a short introduction about these objects and how they approximate minimal surfaces, I will present a vision for the future on how to…

Mar
20
Date3:15 PM
Location
383N
Speaker
Daniel Stern (Cornell)

I'll describe joint work with Karpukhin, Kusner, and McGrath, in which we produce many new families of closed minimal surfaces in S^3 and free boundary minimal surfaces in B^3 via constrained optimization problems for Laplace and Steklov eigenvalues on surfaces. Along the way, I'll highlight…

Mar
15
Date3:00 PM
Location
383N
Speaker
Ronan Conlon (UT Dallas)

Steady Kahler-Ricci solitons are eternal solutions of the Kahler-Ricci flow. I will present new examples of such solitons with strictly positive sectional curvature that live on C^n and provide an answer to an open question of H.-D. Cao in complex dimension n>2. This is joint work with Pak-…

Mar
04
Date3:15 PM
Location
380W
Speaker
Richard Bamler (UC Berkeley)

We prove the Multiplicity One Conjecture for mean curvature flows of surfaces in R^3. Specifically, we show that any blow-up limit of such mean curvature flows has multiplicity one. This has several applications. First, combining our work with results of Brendle and Choi-Haslhofer-Hershkovits-…

Feb
14
Date3:15 PM
Location
383N
Speaker
Tristan Ozuch (MIT)

Einstein metrics and Ricci solitons are the fixed points of Ricci flow and model the singularities forming. They are also critical points of natural functionals in physics. Their stability in both contexts is a crucial question, since one should be able to perturb away from unstable models.

Jan
31
Date3:15 PM
Location
ZOOM
Speaker
Zhenhua Liu (Princeton)

We will review some recent progress on the general geometric behavior of homologically area-minimizing subvarieties, namely, objects that minimize area with respect to homologous competitors. They are prevalent in geometry, for instance, as holomorphic subvarieties of a Kahler manifold, or as…

Jan
09
Date4:00 PM
Location
384H
Speaker
David Jerison (MIT)

Abstract

We introduce a new way to look at level sets of eigenfunctions by viewing the value of the eigenfunction as an independent time variable, with successive level surfaces evolving over time. The evolution obeys a variational principle analogous to mean curvature flow, and this…

Dec
06
Date3:15 PM
Location
383N
Speaker
Josh Daniels-Holgate (Hebrew University of Jerusalem)

We discuss some regularity results for mean curvature flows from smooth hypersurfaces with conical singularities. We then discuss how to use these results to tackle two conjectures of Ilmanen. 

Nov
15
Date3:15 PM
Location
383N
Speaker
Paul Minter (Princeton)

Recently there have been significant developments in how we can think about singularities in minimal submanifolds. I will discuss this circle of ideas, in particular how the new planar frequency function of B. Krummel & N. Wickramasekera allows for a more efficient and refined study of…

Nov
08
Date3:15 PM
Location
383N
Speaker
Antoine Song (Caltech)

A fundamental result about the dynamics and geometry of hyperbolic manifolds is Besson-Courtois-Gallot's entropy inequality. The volume entropy of a Riemannian metric measures the growth rate of geodesic balls in the universal cover. The result says that given a closed hyperbolic manifold (M,g_0…