In Spring 2010, we will meet on Tuesdays at 11:00am in Room
3212, 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:
Fall
2009,
SpringSummer
2009,
Fall 2008,
Spring 2008,
Fall 2007,
SpringSummer 2007,
Fall 2006,
SpringSummer 2006,
Fall 2005,
Spring 2005,
Fall
2004, Spring
2004, Fall
2003, Spring
2003, Fall
2002, Spring
2002, Fall
2001,
Spring
2001.
Spring 2010:

Tuesday, 2/16: no seminar
2/15 is Presidents Day

Tuesday, 2/23: Jian Song (Rutgers University)
The KahlerRicci flow through singularities
Abstract: We will show the KahlerRicci flow on projective varieties can
be uniquely continued though divisorial contractions and flips if they
exist.
In particular, we prove the analytic minimal model program with Ricci flow
for complex projective surfaces.

Tuesday, 3/2: Micah Warren (Princeton University)
Calibrating Optimal Transportation
Abstract: On a manifold M, there is a naturally occurring
pseudoRiemannian metric and K\"ahler form on the product M x M, which is
determined by the distance function M. The graph of the solution to the
optimal transportation problem for given smooth densities on M is a
calibrated maximal Lagrangian rectifiable ncurrent in M x M, with respect
to a conformal metric on M x M. The graph of the optimal map is special
Lagrangian in the sense of Hitchin. This variational characterization of
optimal transportation is different from the traditional one. The
calibrations which detect these special Lagrangians are pseudoRiemannian
analogues of the special Lagrangian calibrations for CalabiYau manifolds.
Like in the CalabiYau case, the moduli space of such submanifolds is
itself a manifold of dimension b_1(M). This is joint work with Kim and
McCann.
 Tuesday, 3/9: no seminar

Friday and Saturday, 3/123/13:
CUNY Geometric Analysis Conference

Tuesday, 3/16: Zheng Huang (CUNY Staten Island)
Mean Curvature Flows in QuasiFuchsian Manifolds
Abstract: QuasiFuchsian three manifold is an important class of
hyperbolic three spaces. The space of such three manifolds is a complex
manifold of dimension 6g6, where g is the genus of any incompressible
closed surface in a quasiFuchsian three manifold. In a subclass of the
same dimension, we deform an rather arbitrary closed incompressible
surface, which is a graph over a fixed reference surface of small
principal curvatures, to a nearby embedded minimal surface. The
deformation is made transparent by the mean curvature flow.
 Tuesday, 3/23: Radek Wojciechowski (University of Lisbon)
Stochastically Incomplete Manifolds and Graphs
Abstract: We present specific conditions which imply the stochastic
incompleteness of the heat kernel on manifolds and graphs. In particular,
we will show that there exists a family of stochastically incomplete
graphs of polynomial volume growth. In contrast, any stochastically
incomplete Riemannian manifolds must have super exponential volume growth.
Time permitting, we would also like to present some connections with
spectral properties of the Laplacian.

Tuesday, 3/30: no seminar
spring break

Tuesday, 4/6: no seminar
spring break

Tuesday, 4/13: Yi Wang (Princeton University)
Quasiconformal mappings, isoperimetric inequality and finite total
Qcurvature
Abstract: In this talk, we are going to prove the isoperimetric inequality
on the noncompact conformally flat four manifold with totally finite
Qcurvature and $\frac{1}{4\pi2}\int_{M}Q(x) dv_M(x)<1$. To do this, we
will look at the construction of the quasiconformal mapping with suitable
quantity of Jacobian. The affirmative answer to the existence of such
mapping would imply the bilipschitz parametrization of the manifold as
well as the isoperimetric inequality. Moreover, if the Qcurvature is
nonnegative, the conformal factor relates to $A_1$ weight.

Tuesday,
4/20: Joel Spruck (Johns Hopkins University)
Hypersurfaces of constant curvature in hyperbolic space with prescribed
asymptotic boundary
Abstract: Given a boundary at infinity $\Gamma$ in hyperbolic space
and a general "elliptic" curvature function $f(\kappa)$ we discuss the
problem of finding a complete hypersurface $\Sigma$ satisfying
$f(\kappa)=\sigma \in (0,1)$ with $\partial \Sigma=\Gamma$.

Tuesday, 4/27: Bing Wang (Princeton University)
Space of Ricci flows
Abstract: This is a joint work with xiuxiong Chen. Under the
noncollapsing
condition, we show that Ricci flows with bounded scalar curvature,
bounded half dimensional curvature integral norm have weak compactness
property.
This weak compactness property has applications in the convergence of
K\"ahler Ricci flows on Fano manifolds and the moduli space of Ricci
solitons.

Tuesday, 5/4: ChiungJue Sung (National Tsing Hua University)
pharmonic forms and pharmonic maps
Abstract: Let M be an mdimensional complete noncompact Reimannian manifold.
We prove that any bounded set of pharmonic kforms in L^q(M), is
relatively
compact with respect to the uniform convergence topology if the curvature
operator of M is asymptotically nonnegative. We also generalize our
results to p
harmonic maps.

Tuesday, 5/11: Nam Le (Columbia University)
Optimal conditions for the extension of the Ricci flow and the mean
curvature flow equations
Abstract: In this talk, we will discuss optimal curvature conditions for
the
existence of smooth solutions to the Ricci flow and the mean curvature
flow equations. Our results can be seen as sharpening those of Hamilton,
that the norm of the Riemannian curvature under the Ricci flow blows up at
a finite singular time; and of Huisken, that the norm of the second
fundamental form of an evolving hypersurface under the mean curvature flow
blows up at a finite singular time. In particular, we show that if the
scalar curvature is uniformly bounded over a finite time interval [0,T),
then we can extend the Ricci flow smoothly past time T.

Tuesday, 6/1: Stefano Nardulli (University of Palermo)
The isoperimetric profile of a complete noncompact Riemannian manifold
with bounded geometry

Tuesday, 8/17: Frederico Girao (SUNY Stony Brook)
The isoperimetric profile of a complete noncompact Riemannian manifold
with bounded geometry
Abstract: In his investigation of the Dirichlet problem for conformally
compact
Einstein metrics, Anderson showed that there are (at most) three
possibilities for the behavior, under subsequences, of a sequence of
conformally compact Einstein metrics, with controlled conformal
infinities, on a fourmanifold: convergence, orbifold degeneration, or
cusp degeneration. Motivated by this result, we study the phenomenon of
orbifold degeneration of a curve of conformally compact Einstein metrics.
We start by presenting some background material. After this, we survey the
known results concerning the Dirichlet problem, and we address some open
questions regarding orbifold degeneration. We then analyze a concrete
example of orbifold degeneration, namely, the Taubbolt family of
conformally compact Einstein metrics on the tangent bundle of the
twosphere, and we show that the orbifold Taubbolt metric is
nondegenerate, that is, the kernel of the Bianchi gauged Einstein operator
is trivial for this metric. Finally, we obtain results related to a
conjecture of Anderson about the boundary of the completion, in the
pointed GromovHausdorff topology, of the space of conformally compact
Einstein metrics on a fourmanifold. These last results give necessary
conditions for orbifold degeneration to occur.