We met on Tuesdays 34 pm (and sometimes 1112 am Friday)
at the CUNY Graduate Center in Room 4419.
The organizers were Józef
Dodziuk,
Adam Koranyi,
Laurentiu Maxim (Max)
and Christina Sormani. Please feel free to contact
Christina Sormani
regarding scheduling.
Past Seminar Schedules and Abstracts:
Schedule, Spring 2008

Tuesday February 5: Matthais Keller, Chemnitz University of Technology
The Laplacian on rapidly branching graphs.
Abstract: We discuss the unbounded Laplace Operator on graphs with
uniformly increasing vertex degree and give a characterization for
absence of essential spectra. In particular we present this
characterization for planar tessellations in terms of the
combinatorial curvature.

Friday February 15: Marten Fels, University of Bonn and CUNY Graduate
Center student,
A Large Compactification of Symmetric Spaces
Abstract: The main topic of this talk is the construction of a new
compactification of symmetric spaces, which is larger than the known ones,
especially larger as the Karpelevich compactification. I will first give an
overview of the compactifications of symmetric spaces that has been known so
far, then describe the construction of my new compactification and discuss
several of its properties. If time permits, will also explain  using an
axiomatic approach , in which sense this compactification can indeed be
considered to be the largest "geometric" compactification of symmetric
spaces.

SatSun Feb 2324: CUNY Geometric Analysis 2008
Celebrating Józef Dodziuk's 60th Birthday
See the webpage to register.

Tuesday March 4: Neil Katz, CUNY City Tech
"Length normalization of the total scalar curvature"
Abstract: The Yamabe constant of a compact Riemannian manifold is the minimal
total scalar curvature over a conformal class normalized by volume.
In this talk we give necessary and sufficient conditions for a metric
to have minimal total scalar curvature in its conformal class normalized
with a lower bound on the length of a family of curves. The problem
is closely related to a conformal isosytolic inequality where volume
is minimized instead of total curvature. Examples of conformal minima
with nonconstant scalar curvature will be given.

Tuesday March 11: Youngju Kim, CUNY Graduate Center student
"Quasiconformal stability in hyperbolic 4space"
Abstract: An ndimensional Mobius group is said to be
quasiconformally stable
if its sufficiently small deformations in Isom+(Hn) are all quasiconformally
conjugate to it. Marden has shown that any geometrically finite Kleinian
group in dimension 3 must be quasiconformally stable. Here we discuss
quasiconformal stability in hyperbolic 4space. Applying these
methods we provide an example demonstrating that Marden stability does
not extend to dimension 4.

Friday March 14: no meeting
AMS meeting at Courant this weekend

Tuesday March 18: no meeting
"Singularities in Geometry and Topology" at Courant Institute
March 1720 see webpage

Tuesday March 25 Two seminars:
33:50pm: Marcello Lucia, College of Staten Island, CUNY
Isoperimetric profile and uniqueness for Neumann problems
Abstract:
Consider on a twodimensional compact Riemannian manifold $(M,g)$
the nonlinear problem: &Delta _{g} u = f(u).
Under suitable assumptions on the nonlinearity, we prove an inequality which
involves the isoperimetric profile of the surface. We apply it to get
lower bounds on the first nonzero Neumann eigenvalue, and to derive
uniqueness results for mean field type equations of the type
where f(u) is a renormalized $e^u$. The precise formula requires tex.
Optimal results are obtained on the sphere and some flat torus.
45:50pm: Omri Sarig, Pennsylvania State University
Generalized laws of large numbers for horocycle flows
Probability Seminar in 5417 relevant to differential geometers.
He will discuss a generalized law of large numbers for a natural class
of dynamical systems arising from hyperbolic geometry. More precisely,
if T: X >X is a map and m is a T inveriant ergodic measure, one
has a generalized law of large numbers if there is a procedure which
accepts as the input the number n such that T^n(x) is in the set
E (but not x or E) and provides as output the measure of E.

Friday March 28: Jesenko Vukadinovic, College of Staten Island, CUNY
Inertial manifolds for a nonlinear FokkerPlanck equation
Abstract: Although intrinsically infinitedimensional, many
dissipative parabolic systems
exhibit longterm dynamics with properties typical of
finitedimensional
dynamical systems. The global attractor, often considered the central
object
in the study of longterm behavior of dynamical systems, appears to
be
inadequate in capturing this finitedimensionality. If a very
restrictive spectral gap condition is satisfied,
an exponentially attracting invariant finitedimensional manifold 
termed inertial manifold 
appears much more appropriate. On it, the PDE reduces to an ODE
termed inertial form.
However, most physically relevant systems fail to satisfy the
spectralgap condition.
A transformation is used to prove the existence of inertial manifolds
for a class of nonlinear nonlocal
FokkerPlanck equations.

Tuesday April 1: Haydee Herrera, Rutgers at Camden,
"Rigidity and Vanishing Theorems on Almost Quaternionic Manifolds"
Abstract: In this talk, I will consider manifolds whose structure
group can be reduced to $Sp(n)Sp(1)$, known as almost quaternionic
manifolds. On them we can
define twisted Dirac operators. I prove the rigidity under circle
actions of several these operators and the vanishing of the indices of
some of them.

Friday April 4: Luis Fernandez (BCC CUNY)
"The moduli space of minimal 2spheres in spheres"
Abstract: I will give a description of the twistor space construction
of harmonic (aka minimal) maps from the round 2sphere to
higherdimensional spheres. Using this approach, one can give a
complete algebraic description of the moduli space of harmonic
2spheres in 2ndimensional spheres. I will also sketch the proof of
the fact that the dimension of the space of harmonic 2spheres in the
2nsphere with twistor degree d is 2 d + n^2, as was conjectured in
the early 90's.

Tuesday April 8: no meeting
conflict

Friday April 11: Chris Croke (U Penn)
Zoll surfaces as counterexamples to a geodesic length conjecture.
Abstract: In this talk we discuss the construction of Zoll surfaces (surfaces
all of whose geodesics are closed of length $2\pi$) and how they can be used
to find interesting examples.
In particular we (discussing a joint work with Balacheff and Katz) construct
Riemannian metrics on the 2sphere with $L>2D$ relating the diameter~$D$ and
the least length~$L$ of a nontrivial closed geodesic. This gives a
counterexample to a conjecture of Nabutovsky and Rotman. The construction
relies on Guillemin's theorem concerning the existence of
Zoll surfaces integrating an arbitrary infinitesimal odd deformation of the
round metric. We conclude that the round metric is not even locally optimal
for the ratio~$L/D$.

Tuesday April 15: no meeting
conflict

MonFri April 215: Spring Recess
no meetings

Tuesday April 29: no meeting
administrative meeting conflict
Abstract: TBA

Tuesday May 6: Daniel Garbin, CUNY Graduate Center student
"Spectral convergence of elliptically degenerating Riemann surfaces"
Abstract:
In this note we study spectral theory of the Laplacian on a sequence of
hyperbolic Riemann surfaces which have elliptic
elements whose order of ramification is unbounded. By extending results
from JorgensonLundeliusHuntley, we establish an asymptotic expansion for
the regularized heat trace in terms of the degeneration parameters. We
then derive asymptotic expansions for various
spectral functions including wave kernels, resolvent kernels, spectral
counting functions, spectral zeta functions, and
Selberg zeta functions. As a specific example,
we consider the sequence of elliptically degenerating surfaces formed from
the Hecke triangle groups, thus quantifying an
example first considered by Selberg. Our methods extend to sequences of
metrics which are hyperbolic near the diverging
elliptic points. This is joint work with J. Jorgenson.

Friday May 9: Fengbo Hang, Courant Institute, NYU
"Some rigidity results on the half sphere"
We will discuss some rigidity theorems for compact manifolds with boundary
and positive Ricci curvature. In particular we will show if a n dimensional
manifold has Ricci curvature at least n1, the boundary is totally geodesic
and isometric to standard S^{n1}, then the manifold is isometric to
standard upper half sphere. This is the Ricci version of a conjecture by
MinOo on scalar curvature rigidity. Similar statements for nonpositive
curvature had been established earlier by many authors (joint work with
Xiaodong Wang).

Tuesday May 27: Prof. Noel Lohoue (Orsay)
"The Poisson equation for
forms on locally symmetric spaces"