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 …

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 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 …

For we compute the intersection E-polynomials and the intersection Poincaré polynomials of
the G-character variety of a compact Riemann surface C and of the moduli space of G-Higgs …

Let $ X $ be a complex abelian variety. We prove an analogue of both the (cohomological) $
P= W $ conjecture and the geometric $ P= W $ conjecture connecting the finer topological …

arXiv:2103.04274v1 [math.AG] 7 Mar 2021 Page 1 arXiv:2103.04274v1 [math.AG] 7 Mar 2021
Deformations of compact Prym fibrations to Hitchin systems∗ Justin Sawon and Chen Shen …

Abstract For various 2-Calabi–Yau categories C for which the classical stack of objects M
has a good moduli space p: M→ M, we establish purity of the mixed Hodge module complex …