11 problems

Let ${\mathcal{F}}l(\mathbb C^n)$ be the complete flag variety, and let $\operatorname{reg}(\iota_*{\mathcal{O}}_{{\mathcal{F}}l(\mathbb C^n)})$ denote the multigraded regularity r…

Let $n_g$ denote the number of numerical semigroups of genus $g$. The Fibonacci conjecture. The sequence $(n_g)_{g\geq 0}$ is increasing, each term is at least the sum of the two p…

Let ${\mathcal{F}}l(\mathbb C^n)$ be the complete flag variety, and let $\operatorname{reg}(\iota_*{\mathcal{O}}_{{\mathcal{F}}l(\mathbb C^n)})$ be its multigraded regularity regio…

Regev's conjecture. For every PI-algebra $A$, there exist $g\in \frac{1}{2}{\mathbb Z}$, $p\in {\mathbb N}$, and $\lambda\in {\mathbb R}_{>0}$ such that

Growth conjecture for $bmu_d$. It has been conjectured that

Let $P_{m,n}$ be the quadratic multiplier polynomial and let $\Phi_\ell$ be the $\ell$-th cyclotomic polynomial. Write $a\asymp b$ when there are constants $c,C>0$ such that…

Lower-bound conjecture. There is a positive constant independent of $n$ such that

Partial-order growth conjecture. There is a constant independent of $n$ such that

Let $d$, $l$, $i$, $D^l_i(p,A,\eta)$, $h(p)$, $\vec{w}_i$, $\phi^{-l\vec{w}_i}$, and $\nu_G$ be as defined in the paper. Linear growth conjecture. The quantity … grows linearly wit…

Suppose a theory has a BPS spectrum partially controlled by the $m$-Kronecker quiver with $m\geq 3$. Let $D=D_{+}\cup D_{-}$ be the dense set of central-charge phases described in…

Filling-surface growth-rate finiteness conjecture. The number of topological types of filling surfaces with the same growth rate is finite.