8 problems

Let $\mathcal{T}$ be a four-dimensional $\mathcal{N}=2$ field theory with Coulomb branch $B$, discriminant locus $\Delta$, Seiberg–Witten integrable system $(M,\Omega_I)$, holomorp…

Let $X$ be a compact Calabi–Yau 3-fold degenerating to $X_1\cup_\Sigma X_2$, where $X_1$ and $X_2$ are Fano 3-folds transversally glued along an anticanonical K3 surface $\Sigma$.…

Let $X$ be a compact 3-manifold with Heegaard splitting $X=X_1\cup_\Sigma X_2$ along a compact surface $\Sigma$, and let $G_\mathbb{C}$ be the complexification of a compact Lie gro…

Let $(M,\Omega_I)$ be holomorphic symplectic, set $\omega_u=\operatorname{Re}(u^{-1}\Omega_I)$ and $B_u=\operatorname{Im}(u^{-1}\Omega_I)$, and let $F(M,\omega_u,B_u)$ be the corre…

Let $L$ be an exact Kähler manifold, let $W$ be a holomorphic Morse function on $L$, and let $L'$ be the graph of $dW$ in $T^*L$. Cotangent-bundle Fueter–Fukaya–Seidel conjecture.…

Let $M$ be a holomorphic symplectic manifold with complex structure $I$ and holomorphic symplectic form $\Omega_I$. For $I$-holomorphic Lagrangian submanifolds $L_1,L_2\subset M$,…

Let $B$ be the base of a Seiberg–Witten integrable system $(M,\Omega_I)$, let $\Delta$ be its discriminant locus, and let $\Gamma_b$ be the charge group over…

A four-dimensional $\mathcal{N}=2$ quantum field theory has a corresponding Seiberg–Witten integrable system, and its holomorphic Floer theory is defined for that system. BPS spect…