Datum:
Die, 2013-05-07 14:00 - 15:00
In String theory S-duality and T-duality each correspond to certain relation between two quantum field theories. The former corresponds to a duality between the two string theories with coupling constants which are inverse of each other and the latter describes a certain symmetry between two theories associated to different geometries. The talk is a brief report on algebro-geometric constructions of these dualities and exploiting them in proving modularity conjectures for certain BPS counting theories such as D4-D2-D0 and D6-D2-D0 supersymmetric BPS theories.
My talk is composed of two sections:
1. S-duality (Invariants of one dimensional subschemes of a system of divisors in CY3): I will discuss a strategy to compute the invariants of torsion sheaves given by ideal sheaves of curves sitting on surfaces inside a general Calabi-Yau threefold and relate them to D4-D2-D0 supersymmetric BPS numbers computed by string theorists. This is joint project with Amin Gholampour and Richard Thomas.
2. T-duality (An algebro geometric D4/D2 duality and modularity of stable pair invariants) Here I will shortly discuss a strategy to prove the modularity properties of certain PT stable pair invariants over threefolds given by smooth and Nodal surface fibrations over a curve. Here our strategy is to use combination of degeneration techniques, conifold transitions, and wall crossing of Bridgeland stability conditions. I will try to state some interesting results and conjectures related to this part. This is joint project with Gholampour and Yukinobu Toda.
