Abstract: In the pretalk, we will introduce Taubes’ work on the analytic compactification of the SL(2,C) character variety of 3- and 4-manifolds from a gauge theory perspective. We will discuss the construction of the compactification, and understanding the boundary of the compactified space.

Abstract: Z/2 harmonic 1-forms, introduced by Taubes, describe the boundary behavior of moduli spaces arising from gauge-theoretic equations. The Hitchin–Simpson equations on a Kähler manifold are first-order nonlinear equations for a pair consisting of a connection on a Hermitian vector bundle and a 1-form valued in the endomorphism bundle. We study the behavior of solutions to the Hitchin–Simpson equations as the norm of the 1-form becomes unbounded, and explore its relationship with Z/2 harmonic 1-forms. In addition, we will discuss the deformation problem of Z/2 harmonic 1-forms in the Kähler setting.