3 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 $p^l$.

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…