11 problems

Let $\Gamma$ and $\Gamma'$ be lattices with quadratic forms $q$ and $q'$, let $g:(\Gamma\oplus\Gamma^*,q)\to(\Gamma'\oplus{\Gamma'}^*,q')$ be a lattice isomorphism, and let…

Let ${\cal V}$ be the strongly finitely generated vertex operator algebra associated with a four-dimensional ${\cal N}=2$ superconformal field theory, and let … be its refined char…

Let $a_n$ be the coefficients of a supersymmetric partition function for a three-dimensional $\mathcal{N}=2$ theory. Let $r\in\mathbb{Q}/\mathbb{Z}$ and let…

BPS Cardy conjecture. In every three-dimensional superconformal field theory with $\mathcal{N}=2$ supersymmetry, the spectrum of supersymmetric (BPS) states obeys this Cardy asympt…

Let $\SQFT^\bullet$ be the spectrum formed from spaces of compact unitary $\mathcal N=(0,1)$ SQFTs, with grading determined by the corresponding fermionic anomaly. SQFT spectrum co…

Let $\mathcal F$ be an $\mathcal N=(0,1)$ SQFT with cylindrical ends and boundary $\partial\mathcal F$, satisfying $Z_{RR}(\partial\mathcal F)=0$, and suppose $\partial\mathcal F$…

Let $\SQFT^\bullet$ denote the spectrum whose spaces classify compact unitary $\mathcal N=(0,1)$ superconformal field theories, graded by anomaly. Let $\mathrm{TMF}^\bullet$ denote…

Higgs-branch survival conjecture. The vector space of Higgs branch Schur operators is not affected by the KK reduction.

Let $V$ be a holomorphic $\mathcal N=1$ superconformal field theory of central charge $c=12k$, and let $Z_{RR}(V)$ be its supersymmetric index. Index divisibility conjecture. The i…

Let $V$ be a holomorphic vertex operator algebra of central charge $c$ equipped with $=1$ supersymmetry. Let $Z_{RR}(V)\in\mathbb Z$ denote its supersymmetric index, and let $\eta$…

Let $C$ be a self-dual ternary code of length $c$. Its index is the number of even maximal codewords minus the number of odd maximal codewords. Index divisibility conjecture. The i…