9 problems

Let $m$ be even and let $\{S_{\pi}\}$ be a collection of cells of $Gr^+_{k+m/2,n}$. Generalized T-duality conjecture. The collection gives a triangulation, respectively dissection,…

Consider regular positroidal subdivisions $\{\Gamma_{\pi}\}$ and $\{\Gamma_{\pi'}\}$ of $\Delta_{k+1,n}$ and corresponding subdivisions $\{Z_{\hat{\pi}}\}$ and $\{Z_{\hat{\pi'}}\}$…

A regular positroidal subdivision of $\mathcal{A}_{n,k,2}$ is a positroidal dissection of the form $\{S_{\hat{\pi}}\}$, where $\{S_{\pi}\}$ is a regular positroidal subdivision of…

Let $\{S_{\pi}\}$ be a collection of cells of $Gr^+_{k+1,n}$, and let $\{S_{\hat{\pi}}\}$ be its T-dual collection. Good T-duality correspondence conjecture. The collection…

Let $S_{\pi^{(1)}}$ and $S_{\pi^{(2)}}$ be positroid cells in $Gr^+_{k,n}$ corresponding to coloopless permutations $\pi^{(1)}$ and $\pi^{(2)}$, with … and…

Let $\{S_{\pi}\}$ be a collection of cells of $Gr^+_{k+1,n}$, and let $\{S_{\hat{\pi}}\}$ be its T-dual collection in $Gr^+_{k,n}$. T-duality conjecture. The collection…

Let $S_{\pi}$ be a loopless $(n-c)$-dimensional cell of $Gr^+_{k+1,n}$ with $c$ connected components, where $c$ is a positive integer. Then $S_{\hat{\pi}}$ is a coloopless…

Parametrised T-duality trivialisation conjecture. The diagram

Let $X$ and $\check{X}$ be Calabi–Yau manifolds which are mirror to each other. A special Lagrangian torus fibration is a fibration with torus fibers calibrated by the special Lagr…