Week of May11-15, 2009, SC 507 and 530
| Mo | May | 11, | 4PM | Ivan Cheltsov (Edinburgh) | Alpha-invariants of Fano orbifolds |
| Tu | May | 12, | 4PM | Paolo Aluffi (FSU) | Unexpected applications of characteristics classes for singular varieties |
| Th | May | 14, | 3PM | Eric Zaslow (Northwestern) | Constructible sheaves and the Fukaya category |
| Th | May | 14, | 9AM | S.T. Yau, Spyros Alexakis (MIT), PoNing Chen, Michael Eichmair (MIT), Marc Nardmann, Markus Schmuck (MIT), Lydia Bieri |
Two-body problem in General Relativity, tracking apparent horizons of black holes |
Abstracts
Melanie Becker (Texas A&M) Chiral supergravity and log supergravity.
Abstract: We give an overview of recent developments in the context of
3D gravity and construct the supersymmetric version of chiral gravity
and log gravity. More explicitly, we study the linearized approximation
of N=1 topologically, massive supergravity around AdS3. Linearized
gravitino fields are explicitly constructed. For appropriate boundary
conditions, the conserved charges demonstrate chiral behavior, so that
"chiral gravity" can be consistently extended to "chiral supergravity."
The existence of a logarithmic gravitino mode indicates that a consistent
supersymmetric extension of log gravity, alias "log supergravity" might
be constructed. We comment on the possible relation between these theories
and string theory.
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Lan-Hsuan Huang (Stanford) Center of mass and constant mean
curvature foliations for isolated systems.
Abstract: I will first
introduce the concept of initial data sets in general relativity. An
asymptotically flat (AF) initial data set is a model of an isolated
system. I will discuss the concept of center of mass of such manifolds
from both Hamiltonian and geometric points of view. Then the rest of
talk is devoted to the geometric aspect: the existence and uniqueness of
the constant mean curvature foliation at infinity. Whether a constant
mean curvature foliation uniquely exists in an AF manifold was a question
proposed by Yau in the 80's. For manifolds with special asymptotics, some
results have been obtained by Huisken-Yau, Ye, and Metzger. We generalize
their results to AF manifolds with the parity condition at infinity. It
is known that center of mass is defined for those manifolds. Moreover,
we show the geometric center of the foliation is indeed center of mass,
so the foliation provides a geometric description of center of mass.
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Michael Anderson (Stony Brook) Recent progress on the Bartnik
static extension conjecture.
Abstract: We will discuss recent work on
a conjecture of Bartnik on the existence of AF static vacuum Einstein
metrics with prescribed inner boundary data. The conjecture is motivated
by Bartnik's definition of quasi-local mass.
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Joel Smoller (Michigan)
A one parameter family of expanding wave solutions of the Einstein
equations that induces an anomalous acceleration into the Standard
Model of Cosmology.
Abstract: Following up on an idea of Blake Temple that the anomalous
acceleration of the universe might be due to a secondary expansion
wave reflected back from the shock wave in our shock wave cosmology
model (and numerical computations of his student, Zeke Vogler, using a
locally inertial numerical method that Temple and Groah derived),
Temple invited me to join him on this project when he held the Gehring
Chair at the University of Michigan. Together we discovered a
surprising new family of expansion waves which perturb the Standard
Model of Cosmology, and lead to a mathematically rigorous, non-ad-hoc
possible explanation of the accelerating universe based only on
Einstein's equations of General Relativity.
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Poster
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