22nd Geometry Festival
Schedule of Talks
University of Maryland
College Park, MD
Friday April 27 - Sunday April 29, 2007
All talks in the Mathematics
Building, room 3206.
Registration will be in the Mathematics
Building, room 3201, Friday afternoon and Saturday morning.
(If you miss one of the standard registration times, please contact
an organizer.)
| Date |
Time |
Speaker |
Title |
Abstract |
| Friday, April 27 |
3:00 PM |
Dan Freed, Texas |
Secondary differential-geometric invariants,
generalized cohomology, and QCD (Mathematics Colloquium) |
Topological invariants, such as the degree of a map, often have
associated secondary geometric invariants. In differential
geometry they were introduced by Chern, Simons, Cheeger, and
others. In the early 1980s they appeared in physics in work of
Wess, Zumino, Novikov, and Witten. Such invariants exist in any
generalized cohomology theory, as developed by Hopkins and Singer.
One recent application of these ideas is to the physics of pions in
quantum chromodynamics. |
| Friday, April 27 |
4:00 PM | Tea and registration
in room 3201. |
|
| Saturday, April 28 |
8:30 AM | Coffee, breakfast, and registration
in room 3201. |
| Saturday, April 28 |
9:30 AM |
Xiaobo Liu, Notre Dame |
Mean curvature flow for isoparametric submanifolds |
The mean curvature flow
for submanifolds with codimension bigger
than one has not been well understood. We study the mean curvature flow
for a class of higher codimensional submanifolds called isoparametric
submanifolds. In Euclidean spaces and spheres, isoparametric submanifolds
are submanifolds with constant principal curvatures. We will show that if
such a submanifold is not minimal, then its mean curvature flow always
converges in finite time to a smooth submanifold of lower dimension. In
fact the mean curvature flow equation for such submanifolds can be
explicitly solved using invariant polynomials of Coxeter groups.
This is a joint work with Chuu-Lian Terng. |
| Saturday, April 28 |
10:30 AM | Coffee and registration
in room 3201. |
| Saturday, April 28 |
11:00 AM |
Vitali Kapovitch, Toronto
and Maryland |
Some open problems in comparison geometry |
I will discuss some recent advances in the geometry of manifolds with
different lower curvature bounds including various nilpotency
phenomena for almost nonnegatively curved manifolds.
I will also discuss some new ideas, pose several open problems
and possible methods of solving them. |
| Saturday, April 28 |
2:00 PM |
Maryam Mirzakhani, Princeton |
Lattice point asymptotics and conformal densities on Teichmüller
space |
In this talk we discuss basic questions regarding the geometry
of Teichmüller space (with respect to the Teichmüller metric)
in analogy with complete negatively curved manifolds. |
| Saturday, April 28 |
3:00 PM | Coffee
in room 3201. |
| Saturday, April 28 |
3:30 PM |
Charles Epstein, Penn |
Stein fillings and index theorems |
A problem of great current interest in symplectic
topology concerns the
ways in which a compact 3-dimensional contact manifold can be realized
as the boundary of a symplectic, or Stein manifold. In this talk we
consider the problem of Stein fillings from the perspective of
analysis. The space of such fillings has a natural stratification
defined by a natural spectral invariant, called the relative index, of
the CR-structure on the boundary induced from the complex structure of
the Stein filling. Using a sub-elliptic boundary condition for the
Spinc-Dirac operator, we give a formula expressing this
relative index
in terms of the fundamental analytic and topological invariants of the
filling manifold. This is a special case of a new, rather general,
index formula, which includes the Atiyah-Singer formula as another
special case. |
| Saturday, April 28 |
7:00 PM | Banquet at the
Garden Restaurant, Inn and Conference Center. |
|
| Sunday, April 29 |
8:00 AM | Coffee and breakfast
in room 3201. |
| Sunday, April 29 |
9:00 AM |
Guoliang Yu,
Vanderbilt |
Group actions and K-theory |
In this talk, I will discuss groups actions and
applications to K-theory. |
| Sunday, April 29 |
10:00 AM | Coffee
in room 3201. |
| Sunday, April 29 |
10:30 AM |
Simon
Brendle, Stanford |
Blow-up phenomena for the Yamabe PDE in
high dimensions |
We will address recent
compactness and non-compactness results
for the Yamabe PDE. We will also discuss the longtime behavior of a
parabolic flow associated with the Yamabe problem. |
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