7 problems

Let $G$ be a semisimple simply-laced complex group, let $\theta$ be a diagram automorphism of $G$, and let $C$ be a Calabi–Yau Riemann surface. For any…

de Cataldo–Hausel–Migliorini P=W conjecture. Under this identification, the perverse filtration associated with $\pi$ satisfies

Let $\mathfrak{g}_{\mathbb{R}}$ be a real form, let $\hat{\mathcal{T}}_{\mathfrak{g}_{\mathbb{R}}}$ be the moduli space of $\mathfrak{g}_{\mathbb{R}}$-complex structures, and let t…

Let $C$ be an irreducible nonsingular projective curve of genus $g\geq 2$, let ${\mathcal M}_{\mathrm{Dol}}$ be its twisted Dolbeault moduli space with Hitchin fibration $h$, and l…

Numerical $P=W$ conjecture. The perverse numbers of the Hitchin fibration and the Hodge numbers of the corresponding character variety should agree:

Let ${\rm M}_{Dol}(S,C_{\cdot})$ be the Dolbeault (Hitchin) moduli space and ${\rm M}_B(S,C_{\cdot})$ the Betti character variety. Let $N^{\ast}_{Dol}$ and $N^{\ast}_B$ be neighbor…

Let $\mathcal{R}_{g,\boldsymbol{\mu}}$ be the character variety, let $\overline{\mathcal{R}_{g,\boldsymbol{\mu}}}$ be the compactification constructed from the representation varie…