6 problems

SYZ conjecture. Under this equivalence, the mirror cycles of line bundles, respectively skyscraper sheaves, on $\mathbb{P}_{\mathbf{\Sigma}}$ should be Lagrangian sections, respect…

Let $(Y_t,D_t)$, $t\in (0,1]$, be a $1$-parameter family of pairs of del Pezzo surfaces $Y_t$ of degree $d$ with smooth anti-canonical divisors $D_t$. Assume that…

Yau–Auroux conjecture. There exists a special Lagrangian fibration on $X$.

Let $\mathcal{M}^{0}$ be the local Ooguri–Vafa model, let $Q$ be the quotient group defining its SYZ mirror $\bar{\mathcal{M}}^{0}=\mathcal{M}^{0}/Q$, and fix sufficiently large…

Consider a family of Calabi–Yau varieties undergoing a large complex degeneration, with the associated SYZ fibrations and metric degeneration. Family SYZ degeneration conjecture. S…

Let $X$ be a Calabi–Yau manifold with a B field $\mathcal{B}$, and let $\check{X}$ be its mirror. SYZ mirror symmetry conjecture. There should exist a possibly singular special Lag…