66 problems

Let $A_i$ and $B_j$ be Sakai's $W(E_8)$-invariant Jacobi forms, let $E_6$ be the classical modular form, and let $P_{16,5}$ be the exceptional polynomial … A Jacobi form expressed…

Let the pure theta block $\Theta_f$ be a holomorphic Jacobi form of weight $k$ and index $m$ with vanishing order $1$ in $q$, where $k,m\in\mathbb Z_{>0}$. Define the nearly holomo…

Let $\cone_k$ denote the modular cone associated with weight $k$. Polyhedrality conjecture. Suppose that $k\equiv 2$ modulo $4$ and $k>4$. The cone $\cone_k$ is polyhedral. The pap…

Let $p$ be a prime, and let a reflective lattice of prime level mean a reflective lattice whose level is $p$. Prime-level conjecture. There is no reflective lattice of prime level…

For each positive integer $K$, let $T^{(K)}(\tau,m)$ be the unique combination of the forms $\widehat{F}^{(\{k_i\})}$ summed over all positive-integer partitions of $K$: … Let…

Let $A$ be an abelian surface over $\mathbb{C}$, let $A^{[\ell]}$ be its Hilbert scheme of length-$\ell$ subschemes, and let $A^{\langle\ell-1\rangle}$ be the fiber over $0$ of the…

The chamber formula conjecture. In the fundamental chamber,

Mocanu's conjecture. For every $k \geq 2$, there are Hecke-equivalent isomorphisms

For a genus-one fibered Calabi–Yau threefold, let the topological string partition function be decomposed by base degree, and let the topological string coupling be denoted by the…

Let $\mathfrak Y$ be a compactification with higher supersymmetry, let $\gamma=(p^0,p^A,q_A,q_0)$ be an electromagnetic charge vector, and let … After restricting to the sublattice…

Let $\boldsymbol\gamma=(\gamma_1,\ldots,\gamma_n)$ be an ordered collection of charges, let $\hat{\boldsymbol\gamma}$ denote the corresponding hatted charge data, and let…

Let $n_0$ be an integer. For a set of charges ${\boldsymbol r}$ with $n$ charges, let $\phi^{({\boldsymbol r})}_{\boldsymbol\nu}(\tau,z)$ be the Jacobi-like forms entering the cons…

Kohnen–Skoruppa conjecture. It is conjectured that

Let $J^{cusp}_{k,1}(N)$ denote the space of Jacobi cusp forms of index $1$ and level $N$, and let $\phi\in J^{cusp}_{k,1}(N)$ be an $L^2$-normalized newform. Write…

Let $J^{cusp}_{k,1}(N)$ denote the space of Jacobi cusp forms of index $1$ and level $N$, and let $\sup(J^{cusp}_{k,1}(N))$ denote its associated supremum quantity. Jacobi index-on…

Let $\mathfrak{g}_I$ be an intermediate Lie algebra between $\mathfrak{g}_1$ and $\mathfrak{g}_2$, and let the associated theta block be constructed from the positive roots and wei…

For each intermediate Lie algebra in the intermediate exceptional series, form the theta block from its associated positive roots and weights, using the construction described in t…

Let $\vartheta_{E_{7+1/2}}(\tau,\mathfrak z)$ be the weak Jacobi form of weight $4$ and index $24$ for $E_7$ defined from the formal denominator of the conjectural generalized affi…

Let $n$ be positive, let $m$ be a positive scalar index, and let $J^{cusp}_{k,m;(n,1)}$ denote the space of Jacobi cusp forms of weight $k$ and index $m$. Let…

Let $g,n$ be positive integers, let $S\in\Lambda_g^+$ be a symmetric positive-definite half-integral matrix, and let $J^{cusp}_{k,S;(n,g)}$ be the space of Jacobi cusp forms of wei…

Let $k>4$ with $k\equiv 2$ modulo $4$. For every reduced matrix $T\in\halfint^+_2$ with bottom-right entry $m$, let $S_m(n,T)$ be the set of integers $r$ such that…

Let $m$ be an index and let $k$ be the weight of a $W(E_8)$-invariant weak Jacobi form. Sun and Wang's lower-bound conjecture. Every non-zero $W(E_8)$-invariant weak Jacobi form of…

Let $E_6,A_i,B_j$ denote the standard Eisenstein series and $W(E_8)$-invariant Jacobi forms, and let $P_{16,5}$ be the form … A polynomial in $E_6,A_i,B_j$ is understood as a polyn…

Let $P_{16,5}$ be the $W(E_8)$-invariant holomorphic Jacobi form of weight $16$ and index $5$ given by … Here $E_4$ and $E_6$ are the usual Eisenstein series, and $A_i,B_j$ are the…

Let $\Theta_f$ be a theta block of $q$-order one that is a holomorphic Jacobi form of integral weight $k$ and integral index $N$ for $A_1$. Let $\operatorname{Grit}(\Theta_f)$ deno…