Geometry/Topology Seminar

from Thursday
June 01, 2017 to Sunday
December 31, 2017
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Tuesday
September 12, 2017

4:00 PM - 5:30 PM
Math Tower P-131
Christina Sormani, CUNY
Rectifiablility of Gromov-Hausdorff Limits

The Gromov-Hausdorff 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 Burago-Gromov-Perelman, and if one one has a uniform lower bound on Ricci curvature, Cheeger-Colding 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: Matveev-Portegies, Perales and Li-Perales. 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 P-131
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 P-131
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 P-131
Jiyuan Han, UW-Madison
On closedness of ALE SFK metrics on minimal ALE Kahler surfaces

For 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 Metrics

In 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 n-1. Interesting examples occur for hyperkaehler 4-manifolds, 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 6-dimensional space. This is work joint with Lorenzo Foscolo and Johannes Nordstrom.


Tuesday
October 31, 2017

4:00 PM - 5:30 PM
Math Tower P-131
Nishanth Gudapati, Yale University
TBA


Tuesday
November 07, 2017

4:00 PM - 5:30 PM
Math Tower P-131
Mehdi Lejmi, CUNY
TBA


Tuesday
November 14, 2017

4:00 PM - 5:30 PM
Math Tower P-131
Eveline Legendre, Universite de Toulouse
TBA

TBA


Tuesday
November 28, 2017

4:00 PM - 5:00 PM
Math Tower P-131
Antonio Ache, University of Notre Dame
TBA


Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars