Higgs bundles and Hermitian symmetric spaces- Roberto Rubio Nunez

Conference Title: GEAR Retreat 2012 Theme: Higgs Bundles (5 of 5) Title: Higgs bundles and Hermitian symmetric spaces Speaker: Roberto Rubio Nunez, Oxford University; Date and Time: Tuesday August 7, 15:20 Description: We study the moduli space of polystable G-Higgs bundles for noncompact real Lie groups G of Hermitian type. First, we define the Toledo character and use it to define the Toledo invariant, for which a Milnor-Wood type inequality is proved. Then, for the maximal value of the Toledo invariant, we state a Cayley correspondence for groups of so-called tube type and point out a rigidity theorem for groups of so-called non-tube type. The proofs of these results are based on the Jordan algebra structure related to the tangent space of the Hermitian symmetric space given by G and are independent of the classification theorem of Lie groups. (Joint work with O. Biquard and O. Garca-Prada.) Sponsor: GEAR Network Local host: UIUC Department of Mathematics Funding provided by: National Science Foundation Research Networks in Mathematical Sciences programAbstract: Roberto Rubio Nunez, in this GEAR Retreat 2012 session on Higgs Bundles, will discuss his group's study of the moduli space of polystable G-Higgs bundles for noncompact real Lie groups G of Hermitian type.