10 problems

Let $X$) be a smooth projective complex variety. Let $\mathfrak I_n(X,\beta)$ be the moduli space of $1$-dimensional closed subschemes $Z$ of $X$ satisfying the paper's fixed numer…

Hecke-word Euler characteristic conjecture.

Let $M_{d,\chi}$ be the moduli space of one-dimensional sheaves on $\mathbb{P}^2$ with degree $d$ and Euler characteristic $\chi$, let $c_0(2)$ denote the normalized tautological c…

Let ${\mathcal M}_g$ denote the moduli space of smooth curves of genus $g$, and let $\chi_2({\mathcal M}_g)$ be its weight two compactly supported Euler characteristic. Eventual si…

Let $\mathcal{M}_g(2g-1)$ be the minimal stratum of differentials, let $\chi(\mathcal{M}_g(2g-1))^{\rm spin}$ denote its spin Euler characteristic, and let…

Let ${\mathcal{M}}_g(2g-1)$ denote the moduli space of minimal holomorphic strata of differentials in genus $g$, and let $\chi$ denote its orbifold Euler characteristic. Asymptotic…

Let $E$ be an elliptic curve over $\mathbb{Q}$ and let $p$ range over primes of good ordinary reduction. Let $\Gamma_{\mathbb{Q}}$ denote the cyclotomic Galois group and let…

Let $X^{\lambda}_\circ(F)$, $X^{\mu}_\circ(G)$, and $X^{\nu}_\circ(H)$ be Bruhat cells in the relevant Grassmannian, defined using generic flags $F^\bullet$, $G^\bullet$, and…

Let $G$ be a finite group and $p$ a prime. Let $\mathcal{S}_{G}^{p+*}$ be the poset of nontrivial $p$-subgroups of $G$, let $\chi_2(\mathcal{S}_{G}^{p+*},G)$ denote its second equi…

Let $G$ be a group of type FP over $\mathbb C$, and suppose that the centralizer of every finite-order element of $G$ has finite $L^2$-Betti numbers. Let $E(G)(s)$ denote the $s$-c…