The aim of this paper is two-fold. Firstly, we prove Toda's-independence conjecture for
Gopakumar–Vafa invariants of arbitrary local curves. Secondly, following Davison's work, we …

We establish P= W and PI= WI conjectures for character varieties with structural group GLn
and SLn which admit a symplectic resolution, ie, for genus 1 and arbitrary rank, and genus 2 …

We prove a general result on the existence of irreducible symplectic compactifications of non-
compact Lagrangian fibrations. As an application, we show that the relative Jacobian …

We give a lattice-theoretic characterization for a manifold of type associated to any smooth
cubic fourfold. Moreover, we determine when a birational transformation is induced by an …

We study the summands of the decomposition theorem for the Hitchin system for GLn, in
arbitrary degree, over the locus of reduced spectral curves. A key ingredient is a new …

We extend results of Looijenga-Lunts and Verbitsky and show that the total Lie algebra
$\mathfrak g $ for the intersection cohomology of a primitive symplectic variety $ X $ with …

We study the interplay between the Fourier-Mukai transform and the decomposition theorem
for an integrable system $\pi: M\rightarrow B $. Our main conjecture is that the Fourier-Mukai …

In view of the recent proofs of the P= W conjecture, the present paper reviews and relates
the latest results in the field, with a view on how P= W phenomena appear in multiple areas …

Perverse–Hodge complexes are objects in the derived category of coherent sheaves
obtained from Hodge modules associated with Saito's decomposition theorem. We study …

We investigate the Hodge structure of the singular O'Grady's six and ten dimensional
examples of irreducible symplectic varieties. In particular, we compute some of their Betti …