8 problems

Let $H_N$ be a mixed $p$-spin Hamiltonian on the sphere, let $\mathcal{N}(D)$ denote the number of its local maxima on $S_{N-1}$ whose normalized radial derivative lies in $D$, and…

Periodicity conjecture. For every $k\geq 3$, the function $b_{\mathbf{t}_{m},k}(n)$ is ultimately periodic with period $m^{k}$.

Let $M=\left\{b;\left(\epsilon,g,(t,k)\right);\left(\ \mid \ \right); \left((p_1,q_1),\ldots,(p_r,q_r)\right)\right\}$ be a non-orientable closed irreducible and $\mathbb P^2$-irre…

Lens-space complexity equality conjecture. For every $p\ge 3$,

Lens-space gem-complexity conjecture. For every $p\ge 2$,

Gem-complexity bound. One has

A cograph is a graph obtained from a single vertex by repeatedly applying disjoint union and complementation. For a graph $G$, the edge-clique cover problem asks whether the edges…

Let $c$ be a natural number, and let a complexity-$c$ irreducible 4-manifold mean an irreducible 4-manifold having complexity $c$. Finiteness conjecture. For every natural number…