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 CheegerNaber, 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.
 Mark Haskins (Imperial College London)
 Title: New $G_2$ holonomy cones and exotic nearly Kahler structures on the 6sphere and on the product of two 3spheres.
 Abstract:
A longstanding problem in almost complex geometry has been the question of existence of (complete) inhomogeneous nearly Kahler 6manifolds. One of the main motivations for this question comes from geometry: the Riemannian cone over a nearly Kahler 6manifold is a singular space with holonomy $G_2$. Viewing Euclidean 7space as the cone over the round 6sphere, the induced nearly Kahler structure is the standard $G_2$invariant almost complex structure on the 6sphere induced by octonionic multiplication. We resolve this problem by proving the existence of exotic (inhomogeneous) nearly Kahler metrics on the 6sphere and also on the product of two 3spheres. 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).
