# Geometry, Groups and

Dynamics/GEAR Seminar

The Geometry, Groups and Dynamics/GEAR Seminar, held at the Illinois hub of GEAR, features speakers of interest to network members. The talks are live streamed on the Illinois Math Department Youtube channel (click for playlist). Seminars postings and can also be found on the Illinois Mathematics Department Events Calendar.

Archive of past lectures.

**Current Semester**

**12:00 pm, Tuesday, January 16, 2018, 243 Altgeld Hall
Georgios Kydonakis (Illinois)
A Higgs bundle construction for representations in exceptional components of Sp(4,R) -character varieties**

Abstract: For a compact Riemann surface of genus g

__>__2, the components of the moduli space of Sp(4,

**R**)-Higgs bundles, or equivalently the Sp(4,

**R**) character varieties, are partially labeled by an integer d known as the Toledo invariant. The subspace for which this integer attains a maximum has been shown to have 3

^{.}2

^{2g}+ 2g−4 many components. A gluing construction between parabolic Higgs bundles over a connected sum of Riemann surfaces provides model Higgs bundles in a subfamily of particular significance. This construction is formulated in terms of solutions to the Hitchin equations, using the linearization of a relevant elliptic operator.