8 problems

Let $A$ be a chainlet of class $N^r$, and let $Ch$ map differential forms of class $B^r$ to chainlets. A form is harmonic when it satisfies the relevant harmonic equation, and a ch…

Let ${\cal M}$ be Hitchin's moduli space of rank-$2$ Higgs bundles with fixed determinant of degree $1$ over a Riemann surface $\Sigma$ of genus $g>1$. It is a simply connected, no…

Nonexistence conjecture. There exist no $\mathbb Z_2$-harmonic $1$-forms on $Y$ with $\mathcal Z\neq\emptyset$ with respect to any metric. In particular, there exist no…

Harmonic intersection-cohomology conjecture. The vector space of $\mathbb{V}$-valued $i$-forms that are harmonic and $L^2$ with respect to the Kähler metric is isomorphic to

Let $G$ be a pseudo-reflection group. Write $\mathcal{SH}_G^{i,k}$ for the component of $x$-degree $i$ and $\theta$-degree $k$, let $\Delta_G$ be the discriminant, and let…

Differential operator conjecture. If $G=G(m,1,n)$, then this identity holds. The conjecture extends the proved cases for rank at most two and the real pseudo-reflection groups; com…

Near-extremal intrinsic functional conjecture. There exists an $\epsilon>0$ such that

Sen's conjecture. If $k$ and $\ell$ are coprime, then