UCSD Topology/Geometry Seminars, Winter 2003

Math 292A, Winter 2003, Fridays 4:00-5:30 in room 7218.

Organisers: Justin Roberts, Peter Teichner

January 7: Stephan Stolz (Notre Dame) String structures and loop spaces

January 16: Conan Leung (Minnesota) (Colloquium, 4pm 7421) Riemannian geometry over different normed division algebras

January 17: Conan Leung (Minnesota) Geometry of Lagrangian submanifolds in Calabi-Yau, Hyperkahler and G_2-manifolds

January 24: Alistair Craw (Utah) The McKay correspondence

January 31: Henning Hohnhold (UCSD) A uniqueness theorem for certain 6-dimensional manifolds

February 6: Vassily Gorbounov (Kentucky) Gerbes of chiral differential operators

February 7: Vassily Gorbounov (Kentucky) Sheaves of vertex algebras over a manifold

February 13: Ralph Kaufmann (MPI Bonn) (Colloquium, 3pm 6438) The homotopy BV nature of arc operads and their relation to moduli spaces and string topology

February 14: Ralph Kaufmann (MPI Bonn) The link between cacti, Connes/Kreimer's Hopf algebra, and Deligne's conjecture

February 20: Grisha Mikhalkhin (Utah) (Colloquium, 3pm 6438) Toric surfaces, Gromov-Witten invariants and tropical algebraic geometry.

The talk presents a new formula for the Gromov-Witten invariants of arbitrary genus in the projective plane as well as for the related enumerative invariants in other toric surfaces. The answer is given in terms of certain lattice paths in the relevant Newton polygon. The length of the paths turns out to be responsible for the genus of the holomorphic curves in the count. The formula is obtained by working in terms of the so-called tropical algebraic geometry. This version of algebraic geometry is simpler than its classical counterpart in many aspects. In particular, complex algebraic varieties themselves become piecewise-linear objects in the real space. The transition from the classical geometry is provided by consideration of the "large complex limit" (which is also known as "dequantization" or "patchworking" in some other areas of Mathematics).

Tuesday March 4: S.-T. Yau (Harvard) (9.30am, 6438)Geometric Applications to Computer Graphics and Imaging

March 14: Eckhard Meinrenken (Toronto) Chern-Weil constructions in Lie theory

Tues March 18: Greg Leibon (Dartmouth) (1.30pm, 7218)The Symmetries of Hyperbolic Volume

justin@math.ucsd.edu

Image of (-2,3,-5) pretzel knot from Rob Scharein's KnotPlot Site.