Tuesday September 12, 2017 4:00 PM  5:30 PM Math Tower P131
 Christina Sormani, CUNY
Rectifiablility of GromovHausdorff LimitsThe GromovHausdorff limits of sequences of Riemannian manifolds do not in general have any regularity. Ranaan Schul and Stefan Wenger produced a sequence of such manifolds which are noncollapsing (and even have a uniform contractibility function) whose limit space is not even countably $H^m$ rectifiable. If one has a uniform lower bound on sectional curvature then the limit is an Alexandrov space which is rectifiable by a theorem of BuragoGromovPerelman, and if one one has a uniform lower bound on Ricci curvature, CheegerColding proved rectifiability and more. By definition the intrinsic flat limits of Riemannian manifolds are always countably $H^m$ rectifiable, and so one may prove a GH limit is rectifiable by proving the GH and intrinsic flat limits agree. This was first done in a joint paper with Wenger applying the Gromov filling volume, and more recently in joint work with Portegies applying a new notion we call the sliced filling volume. I will also present work of postdocs in this area including: MatveevPortegies, Perales and LiPerales. This work is completely disjoint from my work on the convergence of manifolds with nonnegative scalar curvature as the GH and intrinsic flat limits do not agree and GH limits need not exist in that setting.

Tuesday September 26, 2017 4:00 PM  5:30 PM Math Tower P131
 Mark Lawrence, Nazarbeyev University
Totally real tori in $S^1 × C$ and their polynomial hulls.If $K ⊂ C^n$ is a compact subset, there is in general no hope of finding analytic structure in the polynomial hull $\hat{K}$ \K. Even for sets which are quite smooth, there are difficulties. In this talk, some theorems about analytic structure in the polynomial hull of a totally real torus in $S^1 × C$ will be discussed. Connections with knot theory (torus knots, quasipositivity) and holomorphic motions a la Slodkowski will be explained.

Tuesday October 10, 2017 4:00 PM  5:30 PM Math Tower P131
 Luca di Cerbo, Stony Brook University
Minimal Volumes, Hyperbolic Geometry and Lattices in PU(2, 1)The study of (minimal) volumes in hyperbolic geometry has attracted quite a bit of attention in the mathematical community. In the first part of the talk, I will give an overview of this fascinating field and review some classical results. In the second part of the talk, I will describe new results concerning complex hyperbolic surfaces. This is based on a couple of joint papers with M. Stover.

Tuesday October 17, 2017 4:00 PM  5:00 PM Math Tower P131
 Jiyuan Han, UWMadison
On closedness of ALE SFK metrics on minimal ALE Kahler surfacesFor certain cases with some topological assumption that gives the boundedness of Sobolev constant, we construct the space of ALE SFK metrics on minimal ALE Kahler surfaces asymptotic to C^2/G, where G is a finite subgroup of U(2). This is a joint work with Jeff Viaclovsky.

Tuesday October 24, 2017 4:00 PM  5:30 PM SCGP 102
 Mark Haskins, University of Bath
Codimension One Collapse and Special Holonomy MetricsIn this talk we describe recent developments related to codimension one collapse of exceptional holonomy metrics. i.e. where a family of special holonomy metrics on a space of dimension n converges in some limit to a metric on a space of dimension n1. Interesting examples occur for hyperkaehler 4manifolds, G_2 holonomy manifolds and Spin_7 holonomy manifolds. The talk will focus on the G_2 holonomy case, but will also draw on the better understood hyperkaehler case for inspiration and for useful analogies. These mathematical developments are closely related to important limits in physics, e.g. in the context of G_2 holonomy metrics it is related to the identification of the weak coupling limit of M theory compactified on a G_2 holonomy space being Type IIA String Theory on a 6dimensional space. This is work joint with Lorenzo Foscolo and Johannes Nordstrom.

Tuesday October 31, 2017 4:00 PM  5:30 PM Math Tower P131
 Nishanth Gudapati, Yale University
An energy functional for axially symmetric Maxwell perturbations of Kerrde Sitter black holesThe Kerrde Sitter black hole family is a solution of Einstein's equations of general relativity with a positive cosmological constant. After reviewing some background on these spacetimes, we shall discuss the proof that there exists a phase space of canonical variables for the (unconstrained) axially symmetric Maxwell's equations propagating on Kerrde Sitter, such that their motion is restricted to the level sets of a positivedefinite Hamiltonian, despite the ergoregion. If time permits, we shall discuss the equivalent results for the corresponding fully coupled (and constrained) EinsteinMaxwell initial value problem.

Tuesday November 07, 2017 4:00 PM  5:30 PM Math Tower P131
 Mehdi Lejmi, CUNY
On the ChernYamabe problemOn an almostHermitian manifold, the Chern connection is the unique Hermitian connection with Jantiinvariant torsion. In this talk, we compare the Chern scalar curvature with the Riemannian one. Moreover, we study an analog of Yamabe problem by looking for an almost Hermitian metric with constant Chern scalar curvature in a conformal class, extending results of Angella, Calamai and Spotti to the nonintegrable case.
We also study the ChernYamabe flow and get existence of solutions when the Chern scalar curvature is small enough. This is joint work with Markus Upmeier and Ali Maalaoui.

Tuesday November 14, 2017 4:00 PM  5:30 PM Math Tower P131
 Eveline Legendre, Universite de Toulouse
Localization formula applied to Sasaki geometryWe apply an extension of the DuistermaatHeckman Theorem to study the volume, the total scalar curvature and the EinsteinHilbert functionals defined on the Sasaki cone, and prove that they are all proper. This implies that the (transversal) Futaki invariant always admits a zero in a Sasaki cone.

Tuesday November 21, 2017 4:00 PM  5:30 PM SCGP 102
 Misha Gromov, IHES & NYU
TBA

Tuesday November 28, 2017 4:00 PM  5:00 PM Math Tower P131
 Antonio Aché, University of Notre Dame
Sharp Sobolevtrace inequalities of order fourWe establish sharp Sobolev inequalities of order four on Euclidean dballs for d greater than or equal to four. When d=4, our inequality generalizes the classical second order LebedevMilin inequality on Euclidean 2balls. Our method relies on the use of scattering theory on hyperbolic dballs. As an application, we characterize the extremals of the main term in the logdeterminant formula corresponding to the conformal Laplacian coupled with the boundary Robin operator on Euclidean 4balls. This is joint work with Alice Chang.

Tuesday December 05, 2017 4:00 PM  5:30 PM Math Tower P131
 Boris Botvinnik, University of Oregon
Topology of the spaces of metrics of positive scalar or positive Ricci curvatureI will first review Hitchin's indexdifference map from the space of positvescalarcurvature metrics to real Ktheory, and discuss my joint result with J. Ebert and O. RandalWilliams, that shows that the indexdifference map induces nontrivial homomorphisms of appropriate homotopy groups.
I will then describe some recent related results on the space of metrics of positive Ricci curvature. In particular, I will discuss my joint work with J. Ebert and D. Wraith, which shows that the space of such metrics on connected sums of certain products of spheres has nontrivial rational homotopy groups in specific dimensions.

