Speakers
 The following speakers are confirmed:
 Kenji Fukaya (Stony Brook)
 Title: A Infinity Category in Symplectic Geometry and Gauge theory
 Abstract:
Recently `categorification of invariants` are discussed from various points of view. In this talk I will explain `categorification of invariants` using A infinity category and the moduli spaces of solutions of partial differential equation and is applied to symplectic geometry and gauge theory.
 Christina Sormani (CUNY)
 Title: Gromov’s Conjecture on the Intrinsic Flat Limits of Manifolds with Nonnegative Scalar curvature.
 Abstract:
Let us consider noncollapsing sequence of Riemannian manifolds, $M_j^m$. If they have nonnegative sectional curvature then a subsequence converges in the GromovHausdorff sense to an ALexandrov space of nonnegative Alexandrov curvature which is $H^m$ rectifiable ( by work of Burago GromovPereliman).If they have nonnegative Ricci curvature then a subsequence converges again by the Gromov Compactness Theorem in GH sense to a limit space which is $H^m$ rectifiable ( by the work of CheegerColding) and has various notions of nonnegative Ricci curvature in the sense of Sturm and Lott Villiani and AmbrosioGigliSavare. If the sequence has nonnegative scalar curvature a subsequence need not converge in the GH sense, but with an imposed upper bound on volume and diameter, there is a subsequence converging in the intrinsic flat sense (by Wenger’ Compactness Theorem). Gromov has conjectured that the intrinsic flat limits have generalized nonnegative scalar curvature. This notion of convergence always has $H^m$ rectifiable limits. I will present the definition of intrinsic flat convergence (defined in joint work with Wenger), and properties of this convergence appearing in joint work with Portegies, with Lakzian, and by MatveevPortegies and Perales. I will present joint work with Basilio and Dodziuk refining the statement of Gromov’ conjecture and joint work with Lee, HuangLee, Stavrov, and Sakovich towards a related conjecture: the Almost Rigidity of the Positive Mass Theorem.
 Wolfgang Ziller (University of Pennsylvania)
 Title: The Initial Value Problem for Einstein Metrics on cohomogeneity one Manifolds.
 Abstract:
The Einstein equation reduces to an ODE if the metric is invariant under a cohomogeneity one action. In trying to produce examples, it is natural to start a solution at a singular orbit. This initial value problem is surprisingly complicated and we will discuss existence and uniqueness.
