Abstract Dima Arinkin

Dima Arinkin will speak on

Three types of Higgs bundles: additive, multiplicative, and elliptic

Abstract: Higgs bundles are natural geometric objects that have been studied from many different directions. One of the key tools is the Hitchin fibration, which is the geometric version of the fundamental idea from linear algebra: the data (Higgs bundle) is split into spectral data ('eigenvalues') and spacial data (`eigenspaces'). A further development of this idea is the theory of cameral covers developed by R.Donagi and D.Gaitsgory.

In my talk, I will extend the theory of cameral covers in two directions: to Higgs fields that need not be regular, and to different kinds of Higgs bundles, namely, 'group-valued' Higgs bundles. This extension allows to apply the theory to the space of semistable bundles on an elliptic curve, and to the space of regular connections on a punctured disk.