We met this Spring on Tuesdays 24 pm (and sometimes 1112 am Friday)
at the CUNY Graduate Center in Room 3209.
The organizers were
Isaac Chavel
Dan Lee
and
Christina Sormani.
Past Seminar Schedules and Abstracts:
Schedule, SpringSummer 2009

Tuesday Feb 3 (24pm): Reading Seminar:
Introduction to the Theory of Perimeter
and Functions of Bounded Variation
Isaac Chavel presenting

Tuesday Feb 10 (24pm): Reading Seminar:
Ricci curvature and mass transport
Michael Munn presenting

Tuesday Mar 3 (34pm): Indira Chatterji
"A characterization of hyperbolicity"
Abstract:
We will show that a geodesic metric space is hyperbolic (in the sense of
Gromov) if and only if the intersection of any two balls is at a uniformly
bounded Hausdorff distance to a ball. As a corollary, we characterize Rtrees
by the property that the intersection of any two balls is exactly a ball.
This is joint work with Graham Niblo, and will be accessible to
nonspecialists.

Tuesday Mar 17 (24pm): Reading Seminar Chavel presents

Tuesday Mar 24 (24pm): Reading Seminar Chavel presents

Tuesday Mar 31 (23pm): Lewis Coburn
"The Berezin operator calculus and
the Bergman metric"

Tuesday Apr 7 (34pm): Ovidiu Munteanu
"The Poisson equation on complete manifolds"
Abstract:
In this talk I will discuss some general conditions such that the
Poisson equation can be solved on a complete manifold. Existence of
harmonic maps between complete manifolds and existence of
HermitianEinstein metrics on holomorphic vector bundles over
complete manifolds will be mentioned as applications. This is joint
work with Natasa Sesum.

Friday Apr 24 (11am12 in 4214:03): Lydia Bieri
"An Extension of the Stability Theorem of the Minkowski Space in General Relativity"
Abstract:
The talk addresses the global, nonlinear stability of solutions of the Einstein equations in
General Relativity.
In particular, it deals with the initial value problem for the Einstein vacuum equations,
generalizing the
results of D. Christodoulou and S. Klainerman in 'The global nonlinear stability of the
Minkowski space'.
Every strongly asymptotically flat, maximal, initial data which is globally close to the
trivial data gives rise to
a solution which is a complete spacetime tending to the Minkowski spacetime at infinity along
any geodesic.
We consider the Cauchy problem with more general, asymptotically flat initial data. This yields
a spacetime
curvature which is not bounded in $L^{\infty}$ any more. The main proof is based on a bootstrap
argument.
To close the argument, we have to show that the spacetime curvature and the
corresponding geometrical quantities have the required decay.
In order to do so, the Einstein equations are decomposed with respect to specific foliations
of the spacetime.

Tuesday Apr 28 (24pm):Bobo Hua
Analysis on Singular Spaces and Generalized Ricci
Curvature
Abstract:
Harmonic functions are well defined on
Alexandrov spaces which generalize Riemannian manifolds with
sectional curvature bounded from below. We prove the Poincare
inequality and develop classical geometric analysis on the singular
spaces with generalized Ricci curvature lower bound. The Liouville
theorem and finite dimensional properties of polynomial growth
harmonic functions follow in the spirit of Poincare inequality and
volume growth condition. We also use the generalized Ricci curvature
definition on Alexandrov spaces by KuwaeShioya and by
LottVillaniSturm.

Friday May 1 (11am12): Michael Pevzner, Univ. Reims
"RankinCohen brackets and
covariant quantization"
Abstract: Initially introduced in the framework of holomorphic modular
forms, the RankinCohen brackets
form a family of bidifferential operators endowed with a very reach
algebraic structure. We shall give
an interpretation of its properties through the branching laws for tensor
products of highest weight HarishChandra
modules and the covariant quantization of causal symmetric spaces of Cayley
type.

Tuesday May 5 Two Talks:
 2:003:00 pm in 3209: Cedric Villani
Title TBA
Abstract: TBA
 3:304:30 pm in 8404: Andres Neves
"Positive scalar curvature and minimal surfaces"
Abstract: A classical result in differential geometry states that if a
compact 3manifold M with an areaminimizing torus admits a
metric with nonnegative scalar curvature then M is isometric to
a flat torus. I will show similar results for 3manifolds with
positive scalar curvature that have areaminimizing spheres or
projective planes.

June 910 11am 5:30pm and June 2324 11am 5:30 pm
CUNY Differential Geometry Workshop

Tuesday 8/4: 11am1pm (6493)
GromovHausdorff Convergence
C. Sormani presents Gromov's work

Tuesday 8/18: 11am1pm (6493) The pharmonic boundary
Michael Puls