10 problems

Let $\Gamma$ and $\Gamma'$ be lattices with quadratic forms $q$ and $q'$, let $g:(\Gamma\oplus\Gamma^*,q)\to(\Gamma'\oplus{\Gamma'}^*,q')$ be a lattice isomorphism, and let…

Let $X$ be a torus with a geometric $N=2$ structure $(I,J)$, and let $C^{\mathrm{B}}_{I,J}(X)$ denote the category of B-branes and $\mathcal{D}\operatorname{Coh}_{I,J}(X)$ the deri…

Let $X$ be a Calabi–Yau threefold containing a subspace $E$, let $i:E\hookrightarrow X$ be the inclusion, and let $q:E\to Z$ be the map contracting $E$ to a lower-dimensional subsp…

Let $X$ be a Calabi–Yau threefold, and let $\Delta$ be the discriminant locus in the moduli space of conformal field theories. Its primary component is the component corresponding t…

Let $X$ be a Calabi–Yau threefold, let $\Delta_0$ be the primary component of the discriminant, and let a 0-brane be an object $P\in\mathbf{D}(X)$ with Chern character equal to the…

Let $Y$ be a reduced quasi-projective variety over $\mathbb{C}$, and let $\rho:Y'\to Y$ be a resolution of the singularities of $Y$. Let $\mathfrak M^{0^{A\!z^f}_{p}}_r(Y)$ denote…

Let $Y$ be a reduced quasi-projective variety over $\mathbb{C}$. Let $\mathfrak M^{0^{A\!z^f}_{p}}_r(Y)$ be the moduli stack of punctual D0-branes of rank $r$ on $Y$. The abundance…

Let $Y$ be a scheme over $\mathbb{C}$, let $r\in\mathbb{N}$, and let $\mathfrak M^{{0^{A\!z}}^f}_r(Y)$ be the moduli stack of rank-$r$ D0-branes on $Y$. Write … for this Azumaya st…

Let $Y$ be a target space-time, and let $Z_{D2}(Y)$ and $Z_{M2}(Y)$ denote the path integrals of perturbative D2-brane and M2-brane theories, respectively. The relevant worldvolume…

Let $Y$ be a target space-time and let $Z_{D3}(Y)$ denote the path integral of a perturbative D3-brane theory, with contributions summed over fundamental closed orientable $4$-mani…