9 problems

Let $z:=\phi^3$, let $\theta:=z\frac{d}{dz}$, and let $I_3$ be the logarithmic solution of the Picard–Fuchs equation described in the source. Define … where $I^{(0)}_2$ is the holo…

Let $X$ be a noncompact toric Calabi–Yau threefold with $\dim H_4(X,\mathbb{Z})=0$, and let $\{l^1,\dots,l^m\}$ define $X$ via symplectic quotient. Define … where … and … If…

Consider the A-model on a Calabi–Yau threefold $X$. Let $u_i$ be the logarithm of the B-model complex deformation parameter $z_i$ obtained from the toric construction of the mirror…

Let $R\subset\mathbb{C}$ be a finitely generated $\mathbb{Z}$-algebra, let $f:X\to S$ be a smooth proper morphism of smooth $R$-schemes, fix $s\in S(R)$, and let $\widehat{S}$ and…

Hauptmodul and monodromy-group conjecture. Then $k^n$ is a Hauptmodul for $\Gamma^b$,

Let $\mathcal{P}$ be a Picard–Fuchs operator of a family of Calabi–Yau threefolds with a MUM point at $0$, and suppose that its associated local system is irreducible. For a loop…

Degree and ramification conjecture. The following hold:

Consider the differential equation … An integral solution means a solution of this equation whose coefficients are integral. Zagier-type conjecture. Any integral solution to this d…

Mirror symmetry of variations of Hodge structures. For any Fano variety $X$ there exists a one-parameter family