We prove the P=W conjecture for GL_n for all ranks n and curves of arbitrary genus g≥2.
The proof combines a strong perversity result on tautological classes with the curious Hard …

Let $ H_2 $ be the Lie algebra of polynomial Hamiltonian vector fields on the symplectic
plane. Let $ X $ be the moduli space of stable Higgs bundles of fixed relatively prime rank …

We prove that the intersection cohomology (together with the perverse and the Hodge
filtrations) for the moduli space of one-dimensional semistable sheaves supported in an …

We study the interaction between Fourier-Mukai transforms and perverse filtrations for a
certain class of dualizable abelian fibrations. Multiplicativity of the perverse filtration and the" …

For various 2-Calabi-Yau categories $\mathscr {C} $ for which the stack of objects
$\mathfrak {M} $ has a good moduli space $ p\colon\mathfrak {M}\rightarrow\mathcal {M} …

What follows is a broad-brush overview of the recent synergistic interactions between
mathematics and theoretical physics of quantum field theory and string theory. The …

We construct natural operators connecting the cohomology of the moduli spaces of stable
Higgs bundles with different ranks and genera which, after numerical specialisation, recover …

arXiv:2402.08385v1 [math-ph] 13 Feb 2024 Page 1 arXiv:2402.08385v1 [math-ph] 13 Feb
2024 HITCHIN SYSTEMS: SOME RECENT ADVANCES OKSHEINMAN AND BIN WANG …

We explore connections between three structures associated with the cohomology of the
moduli of 1-dimensional stable sheaves on P 2: perverse filtrations, tautological classes, and …

We establish a compact analogue of the P= W conjecture. For a projective irreducible
holomorphic symplectic variety with a Lagrangian fibration, we show that the perverse …