10 problems

Geometric-cycle conjecture. Because of the symmetry in the example, $\delta^{l_p}$ is the cycle around

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

In the situation of the Picard–Lefschetz formula, let $c_1=w_1c_0$ and $c_2=w_2c_0$ with $w_1,w_2\in W$, and let $W_\chi^0$ be the specified subgroup of $W$. Assume that the cosets…

Let $G=U(1)^\alpha$ be the total gauge group of the quiver with a decoupled overall $U(1)$, so that $\widetilde\alpha=\alpha-1$. Let $\Sigma^F$ be the fundamental domain of the mod…

Let $G$ be a quiver gauge group of rank $\text{rank}(G)=\alpha$, and let $\widetilde{F}_{\infty}$ and $\widetilde{F}_{0}$ be the real-part restrictions of the asymptotic moduli-spa…

The refined Witten index is a function of the fugacity $y$, and the moduli space of the quiver theory has singularities whose crossings determine intersection coefficients. Interse…

Let $f$ be the family under consideration, let $X=f^{-1}(s)$ be a fiber, let $H^n(X,\mathbb{Z})_{(1)}$ denote the relevant eigenspace, let $Q$ be its polarization, and let $\Gamma$…

Let $(B^{(r+1)}, AX)$ be the pair in the construction, and let $\Omega$ carry the involution $z_{n-r}\to -z_{n-r}$. The fibre over the fixed point of this involution is…

Let $f\colon N\to\mathbb{R}$ be the Morse function, let $D(T^*N)$ be its disk cotangent bundle equipped with the complexified function $f_\mathbb{C}$, and let…