6 problems

Let $X_k=\mathcal O(k)\oplus\mathcal O(-2-k)\rightarrow\mathbb P^1$ be equipped with a diagonal $T^2$ action on the bundle with weights $(\lambda,\lambda)$, and let $I_k^T(q)$ deno…

Equivariant mirror conjecture. A full set of solutions to the $T$-equivariant quantum differential equations of $G/P$ is given by these integrals. This is the $T$-equivariant exten…

Let $X$ be a smooth projective variety equipped with an algebraic $T_\mathbb{C}$-action, and let $Y$ be a smooth GIT quotient of $X$ without orbifold singularities. Let…

Let $X$ be a Hamiltonian $T$-manifold with moment map $mu$, and let $X//_tT=mu^{-1}(t)/T$ be the smooth symplectic reduction. Let $Pi_X^{\rm eq}$ denote the equivariant quantum vol…

Let $T$ act on a Fano manifold $X$, and let $X//T$ be the GIT quotient with respect to the polarization $c_1^T(TX)$. Write $QH_T^*(X)$ for equivariant quantum cohomology and…

Let $M$ be a symplectic manifold with $chat{T}$-equivariant quantum cohomology $QH^*_{chat{T}}(M,chat{\rho})$, equipped with an equivariant quantum connection, and let the equivari…