17 problems

Let $q=e^{2\pi i\tau}$, and let $\Omega$ be the subset of the graded ring of integer-weight quasi-modular forms of full level consisting of forms … whose Fourier coefficients…

Let $\mathfrak{bm}_0$ be the space of all $\Phi\in\mathbb{Q}\langle\mathcal{B}\rangle$ satisfying $(\Phi\mid b_0)=0$, $(\Phi\mid b_k)=0$ for $k=2,4,6$, primitiveness for the balanc…

Let $X$ be a smooth projective complex surface, and let $X^{[n]}$ be the Hilbert scheme of $n$ points on $X$. For line bundles $L_1,\ldots,L_N$ on $X$, let ${\rm ch}_k(L_i^{[n]})$…

Let $E$ be an elliptic curve, let $\overline{M}_{g,n}$ be the moduli space of stable curves, and let $\mathcal C_g(\gamma_1,\ldots,\gamma_n)$ denote the class defined in the paper…

Let $S$ be a K3 surface and let $\beta\in H_2(S,\mathbb Z)$ be primitive. For cohomology classes $\gamma_0,\gamma_1,\ldots\in H^*(S)$, define the partition function…

Let $n\geq 1$, let $k_{[i,j]}\geq 1$ and $s_{[i,j]}\geq 0$ be integers for $1\leq i\leq j\leq n$, and let $\zeta_{\mathfrak{sl}(n+1),q}[\cdots]$ denote the associated type-A bi-bra…

Let $\mathfrak{g}=\mathfrak{sl}(n+1)$ with $n\geq 1$, let $k\geq 3$, and let $\mathcal{QM}=\mathbb{C}[E_2(\tau),E_4(\tau),E_6(\tau)]$ and…

Let $\Delta$ be a root system of ADE type, let $\Delta_+$ be its set of positive roots, and let $r=|\Delta_+|$. For integers $k_\alpha\geq 1$, write … for the associated generalize…

Let $f_{l,w}$ be the normalised extremal quasi-modular form of weight $w$ and depth at most $l$, and let … be the set of weights for which its Fourier coefficients are integral. In…

The modularity conjecture. The relative potential has the form

Let $E_1$ and $E_2$ be nonsingular elliptic curves, let $\mathsf{A}=E_1\times E_2$ be fibered over $E_1$, and let ${\mathcal A}_{g,n}(\gamma_1,\ldots,\gamma_n)$ denote the reduced…

Calabi–Yau 1-fold quasi-modularity conjecture. The ancestor Gromov–Witten correlation functions defined above are quasi-modular forms. This is the one-dimensional formulation of th…

Let $\operatorname{\mathsf{qMZV}}$ denote the algebra of $q$-multiple zeta values, containing the ring of quasi-modular forms $\widetilde{M}_{\mathbb{Q}}=\mathbb{Q}[G_2,G_4,G_6]$,…

Let $T$ be an affine variety carrying a universal full family of enhanced projective varieties. Let $f:Y\to S$ be a family of projective varieties with fixed prescribed topological…

Let $\mathbb{T}_{>0}$ be the algebra of power series with positive convergence radius, and let $g$, $h$, and $\boldsymbol{s}_2$ be the almost $A$-quasi-modular forms used in the so…

Let $q=p^e$ be a prime power, let $A=\mathbb{F}_q[\theta]$, and let $f$ be a non-zero Drinfeld quasi-modular form of weight $w$ and depth $l\geq 1$. Write $\nu_{\infty}(f)$ for its…

Let $f$ be a differentially extremal element of the algebra $\widetilde{M}$ of Drinfeld quasi-modular forms. A form is defined over a field $L\subset C$ if $f\in L[E,g,h]$, where…