7 problems

Let $\operatorname{IGrass}(n,V)$ be the Lagrangian Grassmannian with $\dim V=2n$, and let $\mathcal{R}$ be its tautological bundle. The defining exact sequence is … A relation betw…

Let $LG(n)$ be the Lagrangian Grassmannian, and let $\lambda^1,\ldots,\lambda^s$ be strict partitions forming Lagrangian Schubert data, so that … For distinct real numbers…

Secant nondefectivity conjecture. The variety $\mathbb{S}ec_h(\mathcal{LG}(n,2n))$ has the expected dimension except when $(n,h)\in\{(4,3),(4,4)\}$.

Cohomological tameness conjecture. The function $W_t$ is cohomologically tame, and the elements $[p_\lambda\omega]$ freely generate $G_0^{W_t}$.

Gauss–Manin mirror symmetry conjecture. The function $W_t$ is expected to define a Gauss–Manin connection that recovers the connections defined on the $A$-model side by Dubrovin an…

Let $LG(n)$ be the Lagrangian Grassmannian, let $F_\bullet(t)$ be the isotropic osculating flag, and let $X_{\boldsymbol{\kappa}}F_\bullet$ be the Schubert variety indexed by a str…

Let $\Lambda$ be the Lagrangian Grassmannian and let $M^5\subset\Lambda$ be a generic five-dimensional hypersurface. Its conformal metric $Q_{M^5}$ and conformal cubic form…