10 problems

Torsion-polynomial conjecture. For every prime $p\ge3$, the map $q\mapsto \tau(p,q)$ is constant precisely on the orbits $\{\pm q^{\pm1}\}$. Equivalently, $\tau(p,q)$ distinguishes…

A zigzag multiplicity is the multiplicity of a zigzag summand in the bicomplex of differential forms of a compact complex manifold, and a Chern number is a characteristic number ob…

Let $Y$ be a negative-definite plumbed manifold, let $\spc{Y}$ denote its set of $spin^c$ structures, and let $\Delta_b$ be the corresponding invariant for $b\in \spc{Y}$. Let…

Yumoto–Misumi conjecture. Under these conditions, the maximal number of fermion species is

Let $M$ be a connected, non-compact, orientable 3-manifold with one toroidal end and a complete hyperbolic structure, and let $\rho:\pi_1(M)\to PSL(2,\mathbb{R})$ be an irreducible…

Atiyah's integrality conjecture.

Teissier's conjecture. If the germs have the same topological type, then

The Grassmann-algebraic Pachner-move invariant. The expression

Consider the $2\to4$ Pachner move replacing the 4-simplices $(12345)$ and $(12346)$ by $(12356)$, $(12456)$, $(13456)$, and $(23456)$. Let $\tilde{\mathcal W}_{ijklm}$ denote the c…

Let $\mathcal{D}^{H}$ be the category of modules under consideration, and let $\varpi\in\mathcal{U}^{H}$ be the central element defined by $\varpi=uS(u)^{-1}K_{2\rho}^{2(r-1)}$. Le…