10 problems

Let $X$ be a compact smooth spin manifold. Consider the elliptic operators obtained from the formal twisted Dirac operators … Here $D$ is the Dirac operator and $q$ is a parameter.…

Class S elliptic-genus VOA-character conjecture. The $(0,2)$ elliptic genus for $\mathcal{T}[C_{g,n}]$ should be a linear combination of the module characters of the associated VOA…

Circular-quiver elliptic-genus character conjecture. The elliptic genus is a module character of the chiral algebra of the four-dimensional $\mathcal{N}=2$ circular quiver theory.

Elliptic-genus character conjecture. The $(0,2)$ elliptic genus can be expressed as a linear combination of characters of the corresponding chiral algebra.

Let $X$ range over the 23 Niemeier root systems and let $G^X$ be the associated umbral moonshine groups; let $\operatorname{Co}_0$ be the automorphism group of the Leech lattice. C…

Mixed-charge m-string elliptic-genus conjecture. Suitable linear combinations of products of the functions $J_{k_1,\ldots,k_{N-1}}(\tau,m,\epsilon_1)$ capture the elliptic genus of…

Let $X$ be a K3 surface with holomorphic tangent bundle $T:=T^{1,0}X$, and let $\mathbb E_{q,-y}$ be the formal power series of holomorphic vector bundles used to define the geomet…

The K3 elliptic genus decomposes as … where … Here $g_n$ and $f_n$ are the multiplicities of irreducible unitary representations of the $N=4$ superconformal algebra in the Ramond-s…

The K3 elliptic genus has a character expansion … Here $N_n$ denotes the coefficient associated with the character $\operatorname{ch}^{Q=0}_{\Delta=n}$ in this expansion. Ooguri's…

Twisted elliptic-genus module conjecture. For $k\equiv0,3\pmod4$ and $k\geq-1$, one has