6 problems

Let $C$ be a smooth projective curve, let $E$ be a vector bundle on $C$ with $\operatorname{rk} E\ge 2$, and let $\operatorname{Quot}_d(E)$ be the punctual Quot scheme of length-…

Define … Let $\Phi_r(q)$ denote the cyclotomic polynomial of order $r$. The normalized cusp-polynomial irreducibility conjecture. The polynomial $P_d(t;q)$ lies in…

Let $A$ be a commutative ring with $1$, let $q\in A$, and let $\mathit{NH}_d(t)\in A[t]$. Let ${d\brack r}_q$ be the $q$-binomial coefficient, $(t;q)_m$ the finite $q$-Pochhammer s…

For each $d\geq 0$, let $\mathit{NH}_d(t)$ be the normalized cusp Hilbert series, let ${d\brack r}_q$ be the $q$-binomial coefficient, and let $(t;q)_m$ be the finite $q$-Pochhamme…

Let $(X,p)$ be the cusp singularity $x^2=y^3$, and let $\operatorname{Quot}_{d,n}(X,p)$ be its punctual quotient scheme. The motivic polynomiality conjecture. The motive of…

The exact motivic formula conjecture.