10 problems

Williamson's conjecture. There exists $\alpha'$ with $2<\alpha'<3$ such that $\Psi_\alpha(x)$ remains nonnegative for all $x>0$ when $\alpha\geq\alpha'$, but changes sign for…

Letellier's conjecture. The Fourier transform should satisfy

The exactness conjecture. The functor $\mathrm F_{G,\underline{\lambda}}$ is exact.

Let $G$ be a reductive group over a local field $F_v$, let $\rho$ be a representation of the dual group satisfying the stated mild technical conditions, and let…

Let $G$ be a reductive group over $\mathbb F_q$, let $\rho$ be a representation as in the Braverman–Kazhdan construction, and let $\Phi_{G,\rho,\psi}$ be the corresponding $\rho$-B…

Braverman–Kazhdan's exactness conjecture. The functor $\mathrm F_{G,\underline\lambda}$ is exact. The preceding theorem in the source establishes that this functor commutes with in…

Braverman–Kazhdan's conjecture. The functor $\mathrm F_{G,\rho}$ is exact with respect to the perverse $t$-structure, and it commutes with induction functors. This conjecture conce…

The structured random mapping uses an expansion $u=Dx$, where $D\in\mathbb{R}^{m\times d}$ and $x$ is an input vector. An unbiased transform is one whose output does not exhibit th…

Fourier-transform conjecture. The function $F$ belongs to the Laguerre–Pólya class:

Let $G$ be a reductive Lie group, let $\mathfrak{g}$ be its Lie algebra, and let $\mathcal{O}\subset \mathfrak{g}^*$ be a nilpotent coadjoint orbit. Let $H\subset G$ be a Cartan su…