11 problems

Let $R$ be the polynomial ring in the variables ${\bf x}$, and let $D_1,\ldots,D_d$ be the inversion factors associated to the basic representatives of a general linear…

Period-four conjecture. Every tame symmetric periodic algebra of non-polynomial growth has period $4$.

Let $\Lambda$ be a finite-dimensional algebra over a field $K$. A tame symmetric algebra of period four (TSP4) is a tame symmetric algebra whose period as a $\Lambda$-bimodule divi…

Let $A$ be a finite-dimensional symmetric algebra. The algebra $A$ is $\tau$-tilting finite if it has only finitely many isomorphism classes of support $\tau$-tilting modules, and…

Let $R=S/(f,g)$ and let $\rho$ be the map in the resolution of the symmetric algebra of the module of differentials associated with $R$, under the assumptions of the main result on…

Symmetrising-form conjecture. The form $t_{W,\mathbf u}$ takes values in $A$ and is a symmetrising form on $\mathcal H(W,\mathbf u)$. This is the Hecke-algebra conjecture attribute…

Representation-directed symmetric algebra conjecture. Theorem should hold for every symmetric algebra which is representation-directed.

Wolffhardt's conjecture. If $\operatorname{Sym}_R(M)$ is a $\operatorname{UFD}$, then

Let $W_+$ be the positive Witt algebra over a field of characteristic zero, and let ${\rm S}^m(W_+)$ denote its $m$th symmetric power, viewed as a $W_+$-module. For every nonnegati…

Let $\mathfrak{g}$ be a complex semisimple Lie algebra with fixed Borel subalgebra $\mathfrak{b}$, Cartan subalgebra $\mathfrak{h}\subset\mathfrak{b}$, and parabolic subalgebra…

Let $W$ be an irreducible complex reflection group, let $A$ be the coefficient ring, and write ${\mathcal{H}}(W,{\mathbf u})$ for its cyclotomic Hecke algebra. Let $B(W)$ be the br…