In Fall 2010, we will meet on Tuesdays at 3:00pm in Room
3207, unless otherwise noted. The organizers of this seminar are Dan Lee and Marcello Lucia. Please
email Dan at Dan.Lee2(NoSpamPlease)qc.cuny.edu to schedule a guest
speaker.
The CUNY Graduate Center is located at 365 Fifth Avenue at 34th Street, diagonally across the street
from the Empire State Building, just two blocks from Penn Station (NYC).
Past Seminar Schedules and Abstracts:
Spring
2010,
Fall
2009,
Spring-Summer
2009,
Fall 2008,
Spring 2008,
Fall 2007,
Spring-Summer 2007,
Fall 2006,
Spring-Summer 2006,
Fall 2005,
Spring 2005,
Fall
2004, Spring
2004, Fall
2003, Spring
2003, Fall
2002, Spring
2002, Fall
2001,
Spring
2001.
Fall 2010:
-
Tuesday, 8/31: We will play a video of a lecture by Gerhard Huisken
(Max Planck Institute)
An Isoperimetric Concept for the Mass in General Relativity
This is sort of an experiment. If it is successful, we may try it again.
-
Tuesday, 9/7: no seminar
9/6 is Labor Day
- Tuesday, 9/14 at 1:00pm in Math Thesis Room (note special time
and room): Tom Koornwinder
(University of Amsterdam)
The Askey scheme as a four-manifold with corners
Abstract: Racah and Wilson polynomials with dilated and translated
argument are
reparametrized such that the polynomials are continuous in the parameters
as long as these are nonnegative, and such that restriction of one or more
of the new parameters to zero yields orthogonal polynomials lower in the
Askey scheme. Geometrically this will be described as a manifold with
corners.
Reference: Ramanujan J. 20 (2009), 409-439; arXiv:0909.2822
-
Tuesday, 9/21: Victor Alvarez (CUNY Graduate Center)
The Brendle-Marques-Neves counterexample to the Min-Oo Conjecture
-
Tuesday, 9/28: no seminar
-
Tuesday, 10/5: Chenxu He (Lehigh University)
Non-negatively curved cohomogeneity one manifolds
Abstract: Manifolds with positive or non-negative sectional curvature have
been of interest from the beginning of the global Riemannian geometry. It
is always a difficult problem to construct such examples. K. Grove and W.
Ziller discovered many new examples with non-negatively curved metrics in
cohomogeneity one manifolds, i.e., they support an isometric action with
one dimensional orbit.
However not every cohomogeneity one manifold admits an invariant metric
with non-negative curvature. The first examples of obstructions were
founded by K. Grove, B. Wilking, L. Verdiani and W. Ziller and then they
were generalized to a large family. In this talk I will also present
recent progress of finding new examples of cohomogeneity one manifolds
under various geometric and topological restrictions.
-
Tuesday, 10/12: no seminar
10/11 is Columbus Day
-
Tuesday, 10/19: Gabor Szekelyhidi (Columbia University)
On blowing up extremal Kahler manifolds
Abstract: I will talk about recent progress on constructing extremal
metrics on blowups building on the work of Arezzo-Pacard-Singer.
-
Tuesday, 10/26: Lu Wang (MIT)
Bernstein type theorem for self-similar shrinkers
Abstract: I will talk about the Bernstein type theorem for
self-shrinkers of mean curvature flow. Namely, the only smooth
self-shrinkers, that are entire graphs, are
hyperplanes in Euclidean space. Reference: http://arxiv.org/abs/0912.1809
-
Tuesday, 11/2: no seminar
-
Tuesday, 11/9: Longzhi Lin (Johns Hopkins University)
Modified Mean Curvature Flow of Star-shaped Hypersurfaces in Hyperbolic
Space
Abstract: Abstract: I will talk about my recent joint work with Ling
Xiao on the modified mean curvature flow (MMCF) of star-shaped
hypersurfaces in hyperbolic space with fixed prescribed asymptotic
boundary at infinity. As an application, this recovers the existence and
uniqueness of smooth complete hypersurfaces of constant mean curvature in
hyperbolic space with prescribed asymptotic boundary at infinity, which
was first shown by Guan and Spruck.
Reference: http://arxiv.org/abs/1010.2091
-
Tuesday, 11/16: William Wylie (University of Pennsylvania)
On warped product Einstein metrics
Abstract: We discuss questions about when a Riemannian manifold is the
base of a warped product Einstein metric. There is a complete
classification in dimensions one and two, but there are interesting
examples in higher dimensions. A special (and exceptional) case are
static metrics, which arise in considerations regarding general relativity
and the positive mass theorem. Recently these spaces have also been of
new interest because of their similarity to the Ricci soliton equation and
because of their connection to optimal transport theory on Riemannian
manifolds. In this talk I'll discuss these motivations and describe some
new results and examples which arise from this viewpoint. This is joint
work with Chenxu He of Lehigh and Peter Petersen of UCLA.