The moduli space M(G) of G-Higgs bundles, for a complex reductive group G, carries a natural hyperkahler structure, through which we can study branes (of type A or B) with respect to each structure. Notably, these branes have gained significant attention in string theory and, according to homological mirror symmetry, there should be a correspondence between BAA-branes on M(G) and BBB-branes on M(L^G), where L^G is the Langlands dual group of G.
After introducing the basics about Higgs bundles and mirror symmetry, we will look at a particular BAA-brane which appears when considering the real form SU^*(2m) of SL(2m, C) and discuss its mirror. We do this by describing the whole fibre of the Hitchin fibration for the special linear group containing SU^*(2m)-Higgs bundles, which is a singular fibre.
If time permits we shall also discuss the duality for other real forms (SO^*(4m) and Sp(m,m)) and explain how one can describe the fibres in terms of semistable rank 1 torsion-free sheaves on a ribbon.
Donnerstag, den 19. November 2015 um 12:00 Uhr, in INF288, HS5 Donnerstag, den 19. November 2015 at 12:00, in INF288, HS5
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Professor Anna Wienhard