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.)