A bstract We consider the vacuum geometry of supersymmetric theories with 4
supercharges, on a flat toroidal geometry. The 2 dimensional vacuum geometry is known to …

We construct a lax monoidal Topological Quantum Field Theory that computes Deligne-
Hodge polynomials of representation varieties of the fundamental group of any closed …

We review the construction known as the Nahm transform in a generalised context, which
includes all the examples of this construction already described in the literature. The Nahm …

Abstract We study the Fourier-Mukai transform for holonomic D-modules on complex abelian
varieties. Among other things, we show that the cohomology support loci of a holonomic D …

This PhD Thesis is devoted to the study of Hodge structures on a special type of complex
algebraic varieties, the so-called character varieties. For this purpose, we propose to use a …

This paper establishes that the Nahm transform sending spatially periodic instantons
(instantons on the product of the real line and a three-torus) to singular monopoles on the …

The Dirac–Higgs bundle is a hyperholomorphic bundle over the moduli space of stable
Higgs bundles of coprime rank and degree. We provide an algebraic generalization to the …

The main result is a computation of the Nahm transform of a SU (2)-instanton over R x T³,
called spatially-periodic instanton. It is a singular monopole over T³, a solution to the …

We compute the Hodge polynomials for the moduli space of representations of an elliptic
curve with two marked points into SL (2, ℂ). When we fix the conjugacy classes of the …

We study the asymptotic behaviour of doubly periodic instantons with square-integrable
curvature. Then we establish an equivalence given by the Nahm transform between the …