15 problems

Let $Y$ be the complement of a normal crossing divisor in a smooth proper Deligne–Mumford stack. A flat bundle on $Y$ is quasi-geometric if it extends as an algebraic regular-singu…

Let $R\subset\mathbb{C}$ be a finitely generated $\mathbb{Z}$-algebra, let $f:X\to S$ be a smooth proper morphism of smooth $R$-schemes, fix $s\in S(R)$, and let $\widehat{S}$ and…

Let $X/\mathbb{C}$ be a smooth projective curve, let $D\subset X$ be a reduced effective divisor, and let $(\mathscr{E},\nabla:\mathscr{E}\to\mathscr{E}\otimes\Omega_X^1(\log D))$…

Let $R\subset\mathbb{C}$ be a finitely generated $\mathbb{Z}$-algebra, let $X$ be a smooth $R$-scheme, let $(\mathscr{E},\nabla)$ be a flat vector bundle on $X/R$, let…

Finite-set correspondence conjecture. The connected components of the anyonic $SL(N,\mathbb C)$ flat-connection space are in one-to-one correspondence with the points of

Let $\mathcal C$ be a braided fusion category over $\Bbb C$. For objects $X_1,\ldots,X_n,Y\in\mathcal C$, the space $\operatorname{Hom}(Y,X_1\otimes\cdots\otimes X_n)$ carries an a…

Let $X$ be a smooth algebraic variety over $\overline{\mathbb{Q}}$ and let $\mathscr{F}$ be a flat bundle on $X$. A $G$-connection is a flat bundle satisfying the arithmetic condit…

Let $\Sigma$ be a surface, and let $\mathcal{A}(\lambda)$ be a family of $\operatorname{PSL}_n(\mathbb{C})$-connections satisfying … with…

Let $U$ be a neighborhood of the zero-section in T^*\bm\hat{\mathcal{T}}^n, and let $[(\mu_k,t_k)]\in U$. A connection … is considered up to unitary gauge. Local existence and un…

Let $\mathcal{A}//\mathcal{P}$ denote the space of parabolic connections with its infinitesimal higher-diffeomorphism action, and let $\operatorname{Symp}_0$ denote the correspondi…

Analytic stability data correspondence conjecture. The data and axioms described in 1)-8) are in bijection with the set of continuous families of analytic stability data parametriz…

The residue formula.

Let $M_3$ be a 3-manifold, let $b_1$ denote its first Betti number, and let $a$ and $b$ label (almost) abelian flat connections on $M_3$. Write $\operatorname{CS}(a)$ for the Chern…

Let $Q$ be a quiver of type ADE, let $\operatorname{QStab}_s\operatorname{\mathcal{D}}_\mathbb{X}(Q)$ be its space of $q$-stability conditions, and assume…

Let $(L_j,\beta_j)$ be a weighted arrangement in $\mathbb{CP}^2$ satisfying all conditions of Theorem existence apart from one inequality, and suppose it has a multiple point $x$,…