Title: A generalization of a theorem of Elkies
Brendan Owens (Cornell University)
Tuesday, September 7 at 1:30pm in Malott 406
Abstract:
In 1995, Elkies provided a characterisation of the Z^n lattice
-- all other integral unimodular lattices in R^n have shorter
characteristic vectors. Kronheimer used this to give a Seiberg-Witten
proof of Donaldson's celebrated diagonalisation theorem for smooth
4-manifolds. I will describe a generalisation of Elkies' result to
lattices of arbitrary determinant. Combined with results of Ozsvath and
Szabo this gives a generalisation of Donaldson's theorem. If time permits
I will discuss an application to unknotting numbers of knots in S^3.
(Joint work with Saso Strle.)