Avviso di Seminario di Geometria

From the orbit of matrices to geometric Langlands and back

ABSTRACT: The orbit of  matrices under the conjugation of a reductive Lie group has

some beautiful classical geometry such as hyperkahler structure. These properties reappear in "quantum geometry" such as the moduli space of Higgs bundle, a hot topic in

geometry and physics. These moduli space are conjectured to satisfy  some

mirror symmetry phenomenon, referred as geometry Langlands in the literature .

One can generalize geometric Langlands to the case of marked points. It

leads to the possibility of mirror symmetry among these orbits, a fascinating 

and yet unknown problem in classical geometry.