3 problems

Anick's conjecture. Suppose $A$ is an augmented connected graded $K$-algebra with polynomial growth and with global dimension $d<\infty$. Then the Hilbert series of $A$ is given by…

Artin–Schelter Gorenstein–twisted Calabi–Yau conjecture. For all connected graded noetherian rings, the Artin–Schelter Gorenstein property is equivalent to the twisted Calabi–Yau p…

Left–right Artin–Schelter conjecture. The left $A_\infty$-Artin–Schelter condition is equivalent to the right $A_\infty$-Artin–Schelter condition.