7 problems

Multiplicity-free holonomy conjecture. For every finite group $H$, there exists a Bieberbach group $\Gamma$ with $\mathbb{Q}$-multiplicity-free holonomy representation…

HyperCube regularizer minimizer conjecture. The unitary group representation $A_g=B_g=C_g^\intercal=\varrho(g)$ describes the unique minimizer of $\mathcal{H}$ up to unitary basis…

Let $G$ be a group and let $\sigma:G\to\operatorname{GL}_k(\mathbb{C})$ be a homomorphism. Define $\widetilde{\sigma}:\mathbb{C}[G]\to\operatorname{Mat}_k(\mathbb{C}[G])$ by sendin…

Let $G$ be a Hermitian locally compact group, let $\widehat{G}$ denote its irreducible representations, and for $\pi\in\widehat{G}$ and a unit vector $\xi\in\mathcal{H}_\pi$ define…

Let $G$ be a Hermitian locally compact group. For a representation $pi$ of $G$ and a unit vector $xi$ in its representation space $\mathcal{H}_pi$, define … and, for $f\in L^1(G)$,…

Let $\Gamma$ be a discrete group, let $1\leq p\leq 2$, and let $q$ be its conjugate exponent, so that … Let $B_p(\Gamma)$ denote the coefficient space associated with isometric rep…

Let $M$ be a closed hyperbolic 3-manifold with infinite first homology, and let $a\in H^2(M;\mathbb{R})$ be an integral class satisfying the parity condition and having dual norm e…