Spring 2002 UCSD Topology/Geometry Seminars
Tuesday, April 2, 10am, 7218
Examples of Cayley Manifolds
Weiqing Gu (Harvey Mudd College)
We present several families of so-called Cayley 4-dimensional
manifolds in the real Euclidean 8-space. Such manifolds are of interest
because Cayley 4-manifolds and Cayley 4-cycles in Calabi-Yau 4-folds and
Spin(7) holonomy manifolds are supersymmetric cycles that are candidates
for representations of fundamental particles in String Theory. Moreover,
some of the examples of Cayley manifolds discovered in this paper may be
modified to construct explicit examples in our current search for new
holomorphic invariants for Calabi-Yau 4-folds and for the further
development of mirror symmetry. We apply the classic results of Harvey and
Lawson to find Cayley manifolds which are graphs of functions from the set
of quaternions to itself and which are invariant under certain three
dimensional subgroups of Spin(7).
Tuesday, April 9, 10am, 7218
Quantum affine algebras and solvable lattice models
Antony Wassermann (CNRS Luminy)
Tuesday, April 16, 10am, 7218
Quivers
Hans Wenzl (UCSD)
Tuesday, April 30, 10am, 7218
On Khovanov's cohomology
Xiao-Song Lin (UC Riverside)
I will prove a long exact sequence for Khovanov's cohomology for the
triple K+, K- and K\infty, so that the usual crossing change formula
is the Euler characteristic formula of this long exact sequence.
Tuesday, May 14th, 10am, 7218
Variation of the Liouville geodesic current of a hyperbolic surface
Francis Bonahon (USC)
The "random geodesic" construction associates a geodesic current (=
diffused homotopy class of closed curves) to each hyperbolic metric on
a surface S. We show that this geodesic current depends differentiably
on the metric, in a suitable sense. This is joint work with Yasar
Sozen.
Tuesday, May 14th: geometric analysis seminar
Calabi-Yau, hyperkaehler, and G_2 manifolds
Conan Leung (Minnesota)
Tuesday, May 21st, 10am, 7218
Lengths of simple loops on hyperbolic surfaces
Feng Luo (Rutgers)
Given a compact surface with a hyperbolic metric and a loop on the
surface, there exists a unique geodesic homotopic to the loop. The
length of the geodesic is a function defined on the product of the
Teichmuller space of all hyperbolic metrics and the space of all
homotopy classes of loops. Our main result establishes a Lipschitz
estimate of the length function expressed in terms of the
Fenchel-Nielsen of the Teichmuller space and Dehn-Thurston coordinates
of the space of all homotopy classes of loops. As a consequence, we
obtain a new proof of a result of Thurston that the length function
can be extended to a continuous function defined on the product of the
Teichmuller space and the space of measured laminations.
Tuesday, June 4th, 10am, 7218
Homology Whitehead torsion, knots and disk links
Des Sheiham (Riverside)
We describe a version of Whitehead torsion which is a homotopy
invariant of a homology equivalence, and involves universal
localization. We recover Reidemeister torsion for knots and M.Farber's
trace invariant for F-links. We obtain also a new invariant for disk
links.