13 problems

Determinantal formula. There is a function $C(x)$ such that

Let $\mathcal P$ be a regular rational polypol, and let $F_{\mathcal P}(u,v)$ denote its associated dual period. Consider the holonomic system annihilating $F_{\mathcal P}$, and th…

Let a scattering amplitude be viewed as a function of kinematic variables, and let $\Delta=0$ be a Landau singularity. A function is holonomic if it satisfies a holonomic system of…

Let $C$ be a conical hypersurface and let $g(u_0,\ldots,u_n)$ be an admissible function on it. Assume that the rank $rk(C)$ is finite. Rational-form conjecture. Any admissible $g$…

Piece-wise holonomic systems and smooth non-holonomic systems are considered as models of motion generated by manipulating system components. Ruina's convergence conjecture. The mo…

Let $V$ be a nice symmetric space for a connected reductive group $G$, let $V_{\operatorname{reg}}$ be its regular locus, and let ${\widetilde{{\mathcal{G}}}}_{\lambda}$ denote the…

Let $A$ be a commutative associative algebra over a field $k$ of characteristic zero, let $V\subset A$ satisfy that multiplication identifies $\operatorname{Sym}^g V$ with $A$, and…

Let $C$ be the underlying curve, let $g$ be a positive integer, and define the generating-series kernel … Let $X=\overline{C}^{2g+1}$, let $p=(v_{i_0},\ldots,v_{i_0})$, let…

Hashiguchi et al.'s conjecture. The operators

Let $X$ be a complex analytic manifold and let $\boldsymbol{P}$ denote the complex projective line. Consider the contravariant functors … obtained from tempered holomorphic solutio…

Holonomicity conjecture. The ideal $I$ is holonomic. This conjecture would establish holonomicity for the differential system used in the restriction algorithm for diagonal regions…

Let $F(x,y,r)$ be the Fisher–Bingham integral, and let … generate a holonomic ideal for every $n$. The claim is known by computer calculation for $n=1$ and $n=2$; the paper proves…

Let $D$ be the ring of differential operators with polynomial coefficients, and let the system of operators given in Theorem 1 generate an ideal in $D$. Holonomicity conjecture. Th…