February 1: Sean Paul (Columbia).
Title: Kahler Einstein Metrics and
K-Stability. abstract: The speaker will introduce the problem
of finding special Kahler metrics on Kahler Manifolds, in particular the
Kahler-Einstein metrics. This problem reduces to the question of finding a
solution to a nonlinear PDE: the complex Monge-Ampere equation, so is at
first sight an analytic problem. The is that this problem is deeply
connected to algebraic geometry. The speaker will give an account of these
connections. This is joint work with Gang Tian. Graduate students are
encouraged to attend.
February 8: Emmanuel Breuillard (IHES). Title: The asymptotic shape of metric balls in Lie groups of polynomial
growth, and pointwiseergodic theorems.
abstract: Let G be a connected Lie group of polynomial growth. We show
that G has strict polynomial growth and obtain a formula for the
asymptotics of the volume of large balls. This is done via the study of
the asymptotic shape of metric balls. We show that large balls, after a
suitable renormalization, converge to a limiting compact set, which can be
interpreted geometrically as the unit ball for some Carnot-Caratheodory
metric on the associated graded nilshadow. The results hold for a large
class of pseudometrics including left invariant Riemannian metrics or
``word metrics'' associated to a compact generated set. This generalizes
results of P. Pansu for discrete finitely generated nilpotent groups. As
an application, we also derive new pointwise ergodic theorems on nilpotent
Lie groups and Lie groups of polynomial growth.
February 15: Marc Burger
(ETH - Zurich)
and Alessandra Iozzi (Uni. Basel)Double Header.
Titles: Bounded Cohomology
in Hermitian Geometry (Iozzi)
and Maximal Representations of surface
Iozzi will talk at and Burger at 4, with a half hour for
tea in between. The talks will be in room 4419, and tea will be in the
math program lounge.
February 22: SlavaKruskhal (University
of Virginia). Title:Quantum representations of mapping class
groups and the Fourier transform.
abstract: A question about the the metaplectic representation of SL(2,Z) leads to a problem in Fourier analysis on the
real line. A variant of Kazhdan's property (T) - concerning the rigidity
of representations of a group - implies that this problem does not have a
solution. Quantum representations, given by the Jones-Witten theory,
provide a a generalization of this to mapping class groups of surfaces -
for which Kazhdan's property is not known to hold. (Joint work with
March 1: Anders Karlsson (KTH-Stockholm and YaleUniversity). Title: Metric geometry and group
actions: two examples.
abstract: Metrics and semicontractions/isometries arise in many places in
mathematics. I will focus on two such instances. First, concerning random
walks on infinite groups, I will discuss a conjectural and very general
noncommutative law of large numbers. Some partial progress on this will be
explained. Second, I will discuss a result on the radial variation of
harmonic functions on SL_n(Z) and mapping class groups. The talk will be
aimed at a general audience.
March 8: IndiraChatterji (Cornell, Columbia,andOhioState). Title: Property RD on connected
abstract:For a locally compact group, the property of Rapid Decay
(abbreviated by property RD) gives a control on the convolution norm of
any compactly supported measure in terms of the $L^2$-norm of its density
and the diameter of its support. We give a complete classification of
those connected Lie groups with property RD. This is joint work with Ch.
Pittet and L. Saloff-Coste.
March 15: Michelle Bucher (Yale). Title:Finiteness
properties of characteristic classes of flat bundles.
abstract: We will outline a new proof of Gromov's boundedness of primary
characteristic classes of flat bundles which, in contrast to Gromov's
orginal proof, does not rely on Hironaka's resolution of singularities.
Moreover, we point out that a representative for these classes can be
found which in fact only takes a finite set of values (as opposed to
merely being bounded) on singular simplices. This will be illustrated on
the Euler class with previous results of Milnor, Wood, and Sullivan.
April 5: Werner Muller (IAS and U. Bonn). Title: Analytic torsion of hyperbolic manifolds.
abstract: The talk will be concerned with a refinement of the Ray-Singer
analytic torsion, introduced by Braverman and Kappeler. The refined
torsion is a holomorphic function on the representation variety of the
fundamental group. In the talk we will study the refined torsion for
hyperbolic manifolds. For special representations of the fundamental group
we will show that it is given as the value at zero of a Ruelle zeta
function. Then we will discuss some applications for hyperbolic
April 12: Jose Rodrigo (YaleUniversity). Title: Evolution of sharp fronts
for the quasi-geostrophic equation.
abstract: The talk will consist of two parts. In the first part I will
describe the strong similarities between the quasi-geostrophic equation
and 3D-Euler. I will describe the evolution of sharp fronts (the analogue
of the evolution of a vortex line for 3-D Euler) and obtain a rigorous
derivation of an equation for a front ( the equation for the evolution of
a vortex line is an open problem). In the second part I will prove the
local well-posedness of the equation for a sharp front (for smooth initial
data) using a Nash-Moser argument.
April 19: Ben Schmidt (University
of Michigan). Title Weakly hyperbolic group
actions. abstract: A group action on a closed Riemannian
manifold is said to be weakly hyperbolic provided that a finite family of
group elements act by partially hyperbolic diffeomorphisms with stable
distributions jointly spanning the tangent bundle. Weakly hyperbolic
integer actions are generated by an Anosov diffeomorphism, providing
motivation for our two main results: 1) ergodicity of volume preserving
weakly hyperbolic actions, and 2)weak hyperbolicity is inherited by the
induced action on the fundamental group for volume preserving weakly
hyperbolic actions (with a fixed point) of Kazhdan property (T) groups on
tori. This work stems from Zimmer's program of classifying the volume
preserving ergodic actions of lattices in higher rank Lie groups.
April 26: Spring Recess no meeting
May 3: Cancelled
May 10: T. Szoke (Univ. of Budapest, Purdue University) Title: Complex Crowns of Projective Spaces
May 17: T. J. Hitchman (Rice University) Title: Vanishing Cohomology and Cocycle Superrigidity through Geometry
Two of the most important rigidity properties for lattices in
semisimple Lie groups of higher real rank are
1) vanishing of first cohomology with coefficients in a
suitable representation, and
2) Zimmer's measurable cocycle superrigidity theorem for
ergodic measure preserving actions.
We shall discuss geometric approaches to these results, and how
the two properties are related. The geometric approach gives a
uniform method for investigating all those groups for which
superrigidity is expected, including the rank one groups which
satisfy Kazhdan's property (T). For these rank one groups the
results are new.
The techniques build on work of Matsushima and Murakami,
Raghunathan, Mok, and Korevaar and Schoen, among others, and
involve Bochner formulae on locally symmetric spaces and harmonic
maps with metric space targets.
This is joint work with David Fisher.
Special Seminar on Wednesday July 6 at 2pm in 5212:
R. Rentschler, Institut de Mathematiques de Jussieu
"On Dixmier's Problem on Hearts of Prime Quotients of Enveloping
hosted by A. Rocha
Abstract: The answer to problem #8 of Dixmier's book "Enveloping
Algebras" is negative: the speaker will present a counter-example and also
speak on his recent work with W. Borhu.