Room 440, Astronomy-Mathematics Building, NTU

(台灣大學天文數學館 440室)

The Category of B-branes and Bridgeland Stability

Hung-Yu Yeh (Academia Sinica)

Abstract:

In physics, string theory contains open strings whose world sheet has non-trivial boundaries, and the ends of open strings with Dirichlet boundary conditions called D-branes can be embedded into submanifolds of the target space. In topological string theories, D-branes can naturally be considered as objects in a category and the morphisms are graded cohomological class. Precisely, the category of A-branes looks like the Fukaya category and the category of B-branes like the derived category of coherent sheaves.

Thus for the D-branes, considered as particles, we need suitable definition of the binding process, the formation or decay, called

-stability proposed by Douglas. Motivated by Douglas's work Bridgeland made a precise definition of stability on triangulated categories. So in this talk I would introduce the category of B-branes and the relevant Bridgeland stability, and, if time permitted, I would discuss some of my recent work in Bridgeland stability (In progress).