- The following speakers are confirmed:
- Kenji Fukaya (Stony Brook)
- Title: A Infinity Category in Symplectic Geometry and Gauge theory
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.
Let us consider non-collapsing sequence of Riemannian manifolds, $M_j^m$. If they have nonnegative sectional curvature then a subsequence converges in the Gromov-Hausdorff sense to an ALexandrov space of nonnegative Alexandrov curvature which is $H^m$ rectifiable ( by work of Burago- Gromov-Pereliman).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 Cheeger-Colding) and has various notions of nonnegative Ricci curvature in the sense of Sturm and Lott- Villiani and Ambrosio-Gigli-Savare. 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 Matveev-Portegies and Perales. I will present joint work with Basilio and Dodziuk refining the statement of Gromov’ conjecture and joint work with Lee, Huang-Lee, 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.
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.