Sasakian manifolds were first introduced in 1962. This book's main focus is on the intricate
relationship between Sasakian and Kähler geometries, especially when the Kähler structure …

We calculate the E-polynomials of certain twisted GL (n, ℂ)-character varieties M_n of
Riemann surfaces by counting points over finite fields using the character table of the finite …

For G= GL 2, PGL 2, SL 2 we prove that the perverse filtration associated with the Hitchin
map on the rational cohomology of the moduli space of twisted G-Higgs bundles on a …

We take another approach to Hitchin's strategy of computing the cohomology of moduli
spaces of Higgs bundles by localization with respect to the circle action. Our computation is …

We propose a general conjecture for the mixed Hodge polynomial of the generic character
varieties of representations of the fundamental group of a Riemann surface of genus g to GL …

We prove that the number of geometrically indecomposable vector bundles of fixed rank r
and degree d over a smooth projective curve X defined over a finite field is given by a …

Using our earlier results on polynomiality properties of plethystic logarithms of generating
series of certain type, we show that Schiffmann's formulas for various counts of Higgs …

Parabolic Higgs bundles on a Riemann surface are of interest for many reasons, one of
them being their importance in the study of representations of the fundamental group of the …

We compute the E-polynomials of the moduli spaces of representations of the fundamental
group of a complex curve into SL (2, C), for the case of small genus g, and allowing the …

Building on our previous joint work with A. Schmitt, we explain a recursive algorithm to
determine the cohomology of moduli spaces of Higgs bundles on any given curve (in the …