14 problems

Let $\Delta\subset\mathbb{R}^{2}$ be a measurable set of finite measure, let $A=|\Delta|$, let $\varphi=h_{0}$ be the Gaussian, and let $V_{\varphi}f$ denote the short-time Fourier…

HRT conjecture. The functions

HRT conjecture. The functions $g_k$, $1\le k\le N$, are linearly independent in $L^2(\mathbb R,\mathrm{d}x)$. This is a central open problem in time-frequency analysis, also called…

Fixed-point conjecture. If for any $m>0$ we have $B_mf=f$, then $f$ is harmonic.

Let $F^p_\alpha$ be the Fock space on ${\mathbb C}^n$, let $L^p({\mathbb C}^n,dv)$ be Lebesgue $L^p$ space, and let $d_\alpha(z,w)$ be the distance function associated with the Foc…

Let $\bm\lambda,\bm\mu\in\mathcal{P}^r$ lie in a block $B$ of $\mathcal{H}_{r,n}$, with $\bm\mu$ $e$-multiregular. Obtain $\bm\lambda^{+\varnothing}$ and $\bm\mu^{+\varnothing}$ fr…

The global derivative contraction conjecture. For every $f\in\mathcal{F}_\alpha^2$,

Let $\mathcal{F}_\alpha^2$ be the Fock space, let $f^{(n)}$ denote the $n$th derivative of $f$, let $\mu_{n,\alpha}$ be the measure used to define the weighted derivative norm, and…

Converse categorification conjecture. If $\bicat{F}_{{\cat V}}$ categorifies $F_{{\cat V}}$, then $\pi$ is an isomorphism.

Let $t>0$ and let $f$ be a symbol for which the Toeplitz operator $T_f^t$ and its Berezin transform $tilde{f}^{(t/2)}$ are defined on the $t$-Fock space. Berger–Coburn conjecture.…

Let $\mathcal{F}_{\mathcal{A}_n}\cong \mathcal{F}_{[\mathbb{C}^2/\mathbb{Z}_{n+1}]}$ be the common Fock space, and let $D_0,\ldots,D_n$ be a basis of divisors. For each divisor, le…

Let $l\geq 1$, let $\mathcal{P}^l_n$ denote the set of $l$-multipartitions of $n$, and let $\Delta(\boldsymbol{\lambda})$ and $L(\boldsymbol{\mu})$ denote respectively the standard…

Let $\mathcal{X}_\lambda$ be the nilpotent orbit associated with the parameter $\lambda$, let $\mathcal{O}(\mathcal{X}_\lambda)$ denote its holomorphic functions, and let…

Let $m$ be a positive integer, let ${\boldsymbol \lambda}=(\lambda^{(1)},\ldots,\lambda^{(m)})$ be an $m$-tuple of partitions, and let $\mathcal{F}_{\mathbf{u}}$ and…