6 problems

Let $d$ be prime, let $\boldsymbol{1}_{2t}d0 (1,1,\dots,1)^\top$ be the all-ones vector in $\mathbb{F}_d^{2t}$, and let $\Sigma_{t,t}(d)$ denote the set of stochastic Lagrangian su…

Canonical embedding conjecture. The embedding $gl(m|n)\subset gl(m|n+1)$ is canonical: the double commutant of $L=gl(m|n)$ in

Mirror extension conjecture. Under these hypotheses, rationality of the extension $U^e$ implies rationality of the mirror extension $(U^c)^e$.

Let ${\mathcal W}^{{\mathfrak s}{\mathfrak l}_2[t]}$ be the commutant under consideration, and let ${\mathcal A}$ be the subalgebra generated by $v^x,v^y,v^h,F,C^{bbb},C^{ccc}$, to…

Let $V_{-n}({\mathfrak{sl}}_n)\otimes V_{-n}({\mathfrak{sl}}_n)$ act inside the rank-$n^2$ $\beta\gamma$ system, and let $\mathcal C=\operatorname{Com}(\mathcal A,\mathcal W)$ be t…

Let $T$ be an operator of class $C_{0}$ with finite multiplicity, and let $X$ be a closed, densely defined linear transformation commuting with every operator in the commutant…