Baltimore-Washington
Metro Area Differential Geometry Seminar

Speakers

The following speakers are confirmed:

Christine Breiner (Fordham University)

Title: Quantitative Stratification and Higher Regularity for Biharmonic Maps
Abstract:

We consider $u \in W^{2,2}(\Omega^m,N)$, $m\geq 4$, which are critical for the biharmonic energy $E(u):= \int_\Omega |\Delta u|^2$. Using the techniques of quantitative stratification developed by Cheeger-Naber, we prove quantitative regularity results for minimizers. As an application, we prove that every minimizing map is in $W^{4,p}$ for $1\leq p<5/4$. This work is joint with Tobias Lamm.

Title: New $G_2$ holonomy cones and exotic nearly Kahler structures on the 6-sphere and on the product of two 3-spheres.
Abstract:

A long-standing problem in almost complex geometry has been the question of existence of (complete) inhomogeneous nearly Kahler 6-manifolds. One of the main motivations for this question comes from geometry: the Riemannian cone over a nearly Kahler 6-manifold is a singular space with holonomy $G_2$. Viewing Euclidean 7-space as the cone over the round 6-sphere, the induced nearly Kahler structure is the standard $G_2$-invariant almost complex structure on the 6-sphere induced by octonionic multiplication. We resolve this problem by proving the existence of exotic (inhomogeneous) nearly Kahler metrics on the 6-sphere and also on the product of two 3-spheres. This is joint work with Lorenzo Foscolo, Stony Brook.

László Lempert (Purdue University)

Title: Analytic cohomology in infinite dimensional complex manifolds.
Abstract:

I will start by introducing the principal actors, holomorphic functions in infinite dimensional spaces and cohomology groups derived from them. After reviewing the basic finite dimensional results, I will discuss the problem of cohomology vanishing in the infinite dimensional setting.

Past Speakers

Fall 2014 (at UMD).