12 problems

Let ${\cal Q}_5={\cal W}_5/{\cal U}_5$ and ${\cal U}_5\subset{}\cal W_5$ be the homological quotient and sub-TQFT over $\mathbb Z/5$, and let $Q$ and $U$ be the linear polynomials…

The homological invariants $\widehat Z$ are invariants associated with three-manifolds, and a quantum modular form is a function on the rationals whose failure to be modular is sui…

Equality of y-fied and dualizable homology conjecture. For any link $L$,

Let $L$ be a link, let $\mathrm{HY}(L)$ denote the y-fied homology of $L$, and let $\mathfrak{F}$ be the involution induced by switching the variables $x_i$ and $y_i$. Gorsky–Hogan…

Asymptotic strict mixed Hodge inequality conjecture. There exists a positive integer $n_0$ such that, for every $n\geqq n_0$,

Let $\Gamma\curvearrowright (X,\mu)$ be a strongly ergodic distal action, and let its $0$-dimensional sofic homology be the degree-zero sofic homology associated to the action. The…

Let $\mathbb{K}$ be a compact abelian group, let $\Gamma$ be a countable group, and let $\Gamma$ act on the compact abelian group $\mathbb{K}^\Gamma/\mathbb{K}$ by the shift action…

A smooth projective variety has a homological unit, namely the graded algebra associated with the endomorphisms of its structure sheaf in the derived category. Abuaf's conjecture.…

Let $\overline{\mathrm{KhR}}(\mathcal{K})$ denote the reduced uncolored HOMFLY-PT homology of a knot or link $\mathcal{K}$, equipped with its $q$-grading. The q-symmetry conjecture…

The paper considers refined Chern–Simons invariants of $(n,m)$-torus knots and the Poincaré polynomials of their HOMFLY-PT homology. The refined Chern–Simons conjecture. These inva…

Triply graded tail-homology conjecture. B-adequate links have such a triply graded homology with the stated degree-zero identification.

Let $P_n(q,t)$ be the $n$-colored homological invariant, and take the limit $q=e^{\hbar}\to1$ with $t$ and $x=e^u=q^n$ fixed. Let $S_0(u,t)$ be the leading classical action in the…