Higgs bundles, spectral data, and applications
Event details
| Date | 23.06.2015 |
| Hour | 14:15 › 16:00 |
| Speaker | Laura Schaposnik |
| Location | |
| Category | Conferences - Seminars |
Higgs bundles (introduced by N. Hitchin in 1987) are pairs of holomorphic vector bundles and holomorphic 1-forms taking values in the endomorphisms of the bundle. The moduli space of Higgs bundles carries a natural Hyperkahler structure, through which we can study Lagrangian subspaces (A-branes) or holomorphic subspaces (B-branes) with respect to each structure. Notably, these A and B-branes have gained significant attention in string theory.
We shall begin the talk by first introducing Higgs bundles for complex Lie groups and the associated Hitchin fibration, and recalling how to realize Langlands duality through spectral data. We will then look at a natural construction of families of subspaces which give different types of branes. Finally, we shall explain how the topology of some of these branes can be completely determined via the monodromy action of the Hitchin system. Time permitting, we shall give some applications of the above approaches in relation to Langlands duality and the study of character varieties. Some of the work presented during the talk is in collaboration with David Baraglia (Adelaide).
We shall begin the talk by first introducing Higgs bundles for complex Lie groups and the associated Hitchin fibration, and recalling how to realize Langlands duality through spectral data. We will then look at a natural construction of families of subspaces which give different types of branes. Finally, we shall explain how the topology of some of these branes can be completely determined via the monodromy action of the Hitchin system. Time permitting, we shall give some applications of the above approaches in relation to Langlands duality and the study of character varieties. Some of the work presented during the talk is in collaboration with David Baraglia (Adelaide).
Practical information
- General public
- Free