9 problems

Let $W(E_8)$ be the Weyl group of $E_8$, and consider all $W(E_8)$-invariant weak Jacobi forms of integral weight and integral index. Let $M_*(\operatorname{SL}_2(\mathbb Z))$ deno…

Let $L$ be an even positive definite lattice, meaning $(v,v)\in2\mathbb Z$ for $v\in L$, and assume that $L$ is irreducible and not unimodular. Consider the free module of weak Jac…

For each index $t$, let $d_{k,t}$ be the number of weight-$k$ generators of the free module $J_{*,E_8,t}^{\operatorname{w},W(E_8)}$ of $W(E_8)$-invariant weak Jacobi forms. Stabili…

Let $t$ be an index, and let $W(E_8)$ denote the Weyl group of the $E_8$ root system. A weak Jacobi form is allowed to have Fourier terms with negative discriminant, and its weight…

Folklore finite-generation conjecture. The graded ring $J_{*,L,*}^w$ is finitely generated over $\mathbb{C}$ for every positive-definite integral lattice $L$.

Let the $A_{k+1}$ Kazama–Suzuki models with $M=2$ be given, and let the associated elliptic genera define weak Jacobi forms. Kazama–Suzuki slow-growth conjecture. The weak Jacobi f…

For each positive integer $m$, let $J_{0,m}$ denote the space of weak Jacobi forms of weight $0$ and index $m$, and define … Let $P(m)$ be the integer such that $J^{P(m)}_{0,m}=0$…

Let $m\in\operatorname{\mathbb{N}}$. For a weak Jacobi form $\varphi$ of weight $0$ and index $m$, and for $a,b\in\operatorname{\mathbb{N}}_0$ with $b^2-4ma>0$, let…

Let $X_{18}$ be the degree-$18$ hypersurface in the weighted projective space $\mathbb{P}(1,1,1,6,9)$, an elliptically fibered Calabi–Yau threefold, and let its topological string…