7 problems

Let $G$ be a Lie group with maximal compact subgroup $K$, let $X=G/K$ with its proper left $G$-action, and for each highest weight $\mu$ of $K$ let $D_\mu$ be the Dirac operator as…

Let $T_t$ be the family of operators described above, let $S$ be the associated selfadjoint operator, and suppose that $0\in\operatorname{spec}S$. For small $t$, the selfadjoint ex…

Let $G$ be a compact group. The equivariant Kasparov theory $KK^G$ is said to be very special when it has the special properties defined in the surrounding discussion. Compact-grou…

Countable stratification conjecture. The category $\Cell{G}$ is countably stratified for every finite group $G$.

Let $n$ be an integer indexing the topological defects of the two-dimensional square lattice, with positive $n$ corresponding to removing quarters of the lattice and negative $n$ t…

Countability and continuity conjecture. For every finite groupoid $H$ and finite-dimensional commutative $H$-algebra $A$, $KK^H(A,B)$ is countable for all $B\in KK^H$ and commutes…

Quantisation-commutes-with-reduction conjecture. For every $\lambda\in\Lambda_++\rho_K$,