23 problems

Let $\mathbf{w}$ be an invertible polynomial with admissible group of symmetries $\Gamma$, and let $\widecheck{\mathbf{w}}$ be its Berglund–Hübsch transpose with dual grading group…

The lifted complex Morse model conjecture. The induced deformation $R_{\mathfrak C_S,\gamma_S}$ is $A_\infty$-quasi-isomorphic to the directed total algebra $R_S$:

Aganagic's conjecture. Up to a degree shift involving the writhe, which is omitted here, the Khovanov homology of $\overline{\beta}$ is isomorphic to

Let $X=(\mathbb{C}^*)^n\subset\mathbb{C}^{n+1}$. A normal crossings divisor in $\mathbb{P}^n$ is the union of $n+1$ hyperplanes in general position. The categorical intersection co…

Let $\mathcal{T}$ be a massive $\mathcal{N}=(2,2)$ two-dimensional field theory with Frobenius deformation manifold $\mathcal{N}_{\mathcal{T}}$, spectral cover…

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 $\mathbf{w}$ be an invertible polynomial in two variables with admissible group of symmetries $\Gamma$, and let $\widecheck{\mathbf{w}}$ be its Berglund–Hübsch transpose with d…

Let $\mathcal{FS}_{\mathrm{orb}}(\widecheck{\mathbf{w}})$ denote the new $\mathbb{Z}/2$-graded $A_\infty$-category constructed by Cho, Choa, and Jeong as an orbifold Fukaya–Seidel…

Let $f$ be the Lefschetz fibration under consideration, let $\mathcal{F}(f)$ be its associated Fukaya–Seidel category, and let $Tw(\mathcal{F}(f))$ be its category of twisted compl…

For a tuple $a=(a_1,\ldots,a_n)$, let $-a=(a_2,\ldots,a_n)$, and let $\mathcal{A}_a$ be the directed Fukaya–Seidel $A_\infty$-category associated with the chain polynomial indexed…

Let $A$ be a configuration of points, let $\mathfrak{S}\in\operatorname{Schob}(\mathbb{C},A)$, and let $\mathfrak{g}_A(\mathfrak{S})$ be the associated $L_\infty$-algebra. For a tr…

Let $A$ be the configuration of points defining the schober, let $\mathfrak{S}\in\operatorname{Schob}(\mathbb{C},A)$, and let $({\tt{R}}^\bullet_{ij},q)$ be the $(i,j)$th infrared…

Let $M$ be the Fukaya-Seidel monad and $R$ the infrared monad, with components $M_{ij}$ and $R_{ij}$, respectively. Infrared monad deformation conjecture. Each component $M_{ij}$ o…

Under homological mirror symmetry, the derived categories of coherent sheaves for toric stacks are expected to correspond to the Fukaya–Seidel categories of their mirror Landau–Gin…

Line-bundles-are-thimbles conjecture. There is a Lagrangian thimble mirror to each line bundle on $X$.

Anticanonical tropical-division conjecture. For an appropriate choice of toric Kähler form and any small $\delta$, $\Delta^t$ is adapted to $\Sigma_{ac}$ and…

Tropical-division conjecture. $\mathcal{F}_{\Delta^t}(W_\Sigma)$ is derived equivalent to the Fukaya-Seidel category of $W_\Sigma$.

Let $D_0$ be the union of the irreducible toric divisors of $Z_0$, and let $i_{D_0}:D_0\hookrightarrow Z_0$ be the inclusion. Assume that $0\in A$ is a vertex of every maximal cell…

Let $f:(\mathbb{C}^*)^n\to\mathbb{C}$ define $H=f^{-1}(0)$, let $\mathcal{F}^\circ((\mathbb{C}^*)^n,f)$ be the Fukaya–Seidel category, and let $Z_0$ be the distinguished toric divi…

Let $f_{\mathbf{a}}:X_+^{\mathbf{a}}\dashrightarrow X_-^{\mathbf{a}}$ be a toric elementary birational cobordism specified by a lattice element $\mathbf{a}\in\mathbb{Z}^{d+2}$ sati…

Let $Q'$ be the one-vertex quotient of a wall arrangement, let ${\boldsymbol\phi}$ be a gradient polygon covering $Q'$, and let $\mathcal{M}_\zeta({\boldsymbol\phi})$ be the moduli…

Twistor-family conjecture. The moduli space of stability conditions of a Fukaya–Seidel category can be included in a one-parameter twistor family.

Let $M(\mathbb{P}^k, CY)$ be the formal scheme occurring as the zero fiber of a Stability Hodge Structure associated with a Fukaya–Seidel category having many potentials. Multiple-…