15 problems

Let $M$ be a matroid and let $I_{\Delta(M)}$ be its Stanley–Reisner ideal. Write $\widehat{\rho}(I_{\Delta(M)})$ for its asymptotic resurgence, $\omega(I_{\Delta(M)})$ for the larg…

Integral Stokes coefficient conjecture. Each $\gamma_i$ determines such a normalized formal heat solution, and there exists a coefficient $S_{ij}^{+}\in\mathbb Z$ such that

Picard–Lefschetz/Alien correspondence. The pointed Alien derivative of $\widetilde K_0$ at $\omega$ is

Let $Z(t,\nu,\hbar)$ be the perturbative partition function for the Painlevé I system, and let $\mathfrak S$ denote the Stokes automorphism associated with the $B$-periods. Write…

Let $G(\Lambda,a)$ be the formal series for the two-point function of an asymptotically free quantum field theory, where $\Lambda$ is the kinematical parameter. Suppose its $\beta$…

Let $p$ be an odd integer and let $J^{(A,p)}_j(t)$, $J^{(B,p)}_j(t)$, $J^{(C,p)}_j(t)$, and $J^{(D,p)}_j(t)$ denote the vectors of Mordell–Borel integrals defined in the source. Wr…

Let $f\colon\mathbb{Q}\to\mathbb{C}$ be a $q$-series with $q={\rm e}^{2\pi {\rm i}y}$. Suppose its asymptotic expansion $\tilde{f}(y)$ as $y\to0$ extends to $y\in\mathbb{C}$ and ha…

Let $f_\infty(y)$ be the generating function in Eq., and let $\tilde{f}_\infty(y)$ be its asymptotic expansion as $y\to0$ with $\Im(y)>0$. Strong-coupling median-resummation conjec…

Let $\alpha$ and $\beta$ be critical points, let $\tau(\alpha)$ and $\tau(\beta)$ denote their corresponding torsions, and let $\mathcal{S}_{\alpha}^{\beta}$ be the Stokes coeffici…

Let $K$ be a knot. Let $F_K(x)=\Phi_K(e^{-1/x})$ be the formal expansion of the Habiro element $\Phi_K$ around a root of unity, let $G_K(p)$ denote the Borel transform of $F_K(x)$,…

All-order resurgent asymptotics. The coefficients satisfy the asymptotic expansion

Resurgence conjecture. In the canonical formal trivialization, the Taylor series of $\chi_\gamma(s(t))$ is resurgent. The same is true for the Taylor series of…

Let $K$ be a knot, let $J_n(q)$ be its $n$-colored Jones polynomial, and let $F_K(x,q)$ be the two-variable invariant defined by Borel resummation of the colored Jones expansion. F…

Unbounded fiber-product resurgence conjecture. There exists a homogeneous polynomial ideal $I$ such that

Let $M$ be a manifold, let $f_i$ be functions on $M$, and let $L_i={\rm graph\ }df_i\subset T^*M$ for $i=1,2,3$. For intersection points $p_{ij}\in L_i\cap L_j$, let $\psi_{ij}$ be…