November 2, 2011
University of Pennsylvania professor to present 44th William J. Spencer Lecture Thursday
Professor Ron Donagi of the University of Pennsylvania will deliver the 44th William J. Spencer Lecture at 2:30 p.m. Thursday in 1073 Durland Hall.
Donagi will discuss recent progress on defining and calculating this quantum sheaf cohomology for toric varieties and hypersurfaces in them, as well as many open problems in this young field.
Quantum cohomology of a variety X is a refinement of its ordinary cohomology, which captures very detailed information about numbers of curves in X. Combined with mirror symmetry; it has led to amazing advances in enumerative geometry. Now physicists tell us that there should exist a similar refinement, quantum sheaf cohomology, of the cohomology of a variety valued in a vector bundle E or in a more general coherent sheaf. This bundle needs to be "omalous'' (not anomalous), which means that its first two Chern classes should match those of X. The usual (quantum) cohomology is recovered as the case that E is the tangent bundle of X.