5 problems

Gorsky–Hogancamp–Simental–Rasmussen conjecture. The knots $\hat\beta(\mathbf{a}(f))$ and $\hat\beta_f$ are isotopic. Up to a monomial in $q$ and $t$,

The local chain conjecture. There is a set $mathcal{L}$ of local chains of deficit $k$ and an involution mathcal{S}to mathcal{S}^ on $mathcal{L}$ such that: every…

Syzygy Hilbert-series conjecture. This Hilbert series equals

Let $n\ge2$, $m\ge2$, and let $d_1,d_2,k$ be positive integers satisfying … Set $\delta=\min(d_1,d_2)$, and let $M^{(m)}_{d_1,d_2}$ denote the bidegree-$(d_1,d_2)$ component of…

The higher $q,t$-Catalan numbers admit several definitions. In particular, the combinatorial, algebraic, geometric, symmetric-function, and representation-theoretic constructions d…