9 problems

Let $G$ be a complex reductive group with Langlands dual group $G^L$, and let $\mathcal H_G$ and $\mathcal H_{G^L}$ be their Higgs moduli spaces. Let $\sigma_G$ be an anti-holomorp…

Let a $(\mathrm{BBB})$-brane be a hyperholomorphic subvariety with a hyperholomorphic sheaf, and let a $(\mathrm{BAA})$-brane be a complex Lagrangian subvariety for the holomorphic…

Let $p$ and $q$ be integers, and consider the $(B,A,A)$-brane of ${\rm SO}(p+q,p)$-Higgs bundles and its Langlands-dual $(B,B,B)$-brane. Fix the base and hyperholomorphic bundle sp…

Let $G$ be a real group with complexification $G_{\mathbb C}$, let ${}^LG$ be its Langlands dual, and let ${mathcal M}{G}subset { mathcal M}{G{mathbb C}}$ be the $(B,A,A)$-brane of…

Langlands dual support conjecture. The support of the dual brane to $\mathcal{M}_{G}$ is the moduli space

Oper brane conjecture. The brane $A_0$ associated with the tip of the cigar is the oper brane, and homological mirror symmetry gives

Let $X=X_\Delta^3$ be a Calabi–Yau 3-fold and let $L=L_{AV}$ be an Aganagic–Vafa A-brane. Let $X^\vee\subset(\mathbb{C}^\times)^2\times\mathbb{C}^2$ be its mirror, and let $W$ be t…

Let $G_c$ be a complex reductive group with Langlands dual group $^LG_c$. Let $i_1$ be the involution whose fixed points form a $(B,A,A)$-brane in $\mathcal{M}_{G_c}$, and let…

Bulk-boundary deformation conjecture. Such a mathematical pairing should realize a bulk-boundary operator product expansion under deformation of the BRST operator, and mathematical…