5 problems

Let $X$ be a connected $p$-compact group with maximal torus $T_X$. Its maximal torus normalizer is represented by the loop space $NT_X$. Maximal torus normalizer conjecture. The gr…

Polynomiality conjecture. For each $d\geqslant 0$, the invariant $\mathbf{m}(\mathcal{F}(q),\alpha,d)$ is a rational polynomial in $p^l$.

Analogue of Robinson's ordinary weight conjecture. The number of characters of defect $d$ in $\operatorname{Irr}(\boldsymbol{X}(q))$ should be countable by local data from the fusi…

Let $p$ be a prime and let $B\Gamma$ be the classifying space of a $p$-compact group. A faithful linear representation means a map from $B\Gamma$ to $BSU(n)$, for some $n$, whose h…

Let $Y$ be a space such that $H^*(Y;\mathbb{Z})$ is a polynomial ring. The rings … are the cohomology rings of $\mathbb{C}P^\infty$, $B\!\operatorname{SU}(n)$, and…