Counting Quotients of Vector Bundles (Aaron Bertram, University of Utah)

04.05.2017 16:15

The quotient spaces (of fixed dimension) of a complex vector space are parametrized by the Grasmmann manifold. On the other hand there are situations in which the set of quotients (with fixed invariants) of a fixed complex vector BUNDLE is a finite set. The cardinality of that set is computed by a "Verlinde formula" when the vector bundle lives on a Riemann surface, and a multiple point formula when the vector bundle lives on an algebraic suface. A topological quantum field theory results when the Riemann surface is allowed to degenerate. Something similar seems to happen in the algebraic surface case, but what is the "physics" behind that? This is based on joint work with Thomas Goller and Drew Johnson.


PS. The Colloquium will be followed by an aperitif

Lieu

Room 17, Acacias, Colloque

entrée libre