Tony Pantev

Geometric transitions and integrable systems

This is a report on a joint project in progress with E.Diaconescu, R.Donagi, B.Florea and A.Grassi. We study geometric transitions of Calabi-Yau manifolds from the point of view of the derived category of coherent sheaves and develop a non-linear version of the Dijkgraaf-Vafa quantization argument. This process algebraizes the Hodge theory of a family of Calabi-Yau spaces and allows us to compute the quantum superpotential asymptotically in a large variety of examples.