29 problems

Barannikov–Kontsevich conjecture. The Frobenius structure $(S',\eta_F|_{S'},\Phi_F|_{S'})$ should be a Frobenius submanifold of the Frobenius manifold constructed by Barannikov–Kon…

Equivariant abelian/nonabelian correspondence. Let $\varphi:P\longrightarrow N$ be the isomorphism of formal schemes over $N(X//{\bf G})\otimes{\mathbb C}[\lambda]$ defined by…

Let $M$ be the base space of an unfolding $F$ of a singularity with a CDV-structure, let $R\subset M$ be the real analytic exceptional subvariety, let $E+\overline E$ be the associ…

Let $(W,G)$ be an admissible Landau–Ginzburg pair, where $W$ is an invertible polynomial with at most two variables and $G$ is an admissible group. Semisimplicity conjecture. The F…

Hertling's conjecture. For any $p\in M$, the set $R$ does not contain the $\mathcal{E}+\overline{\mathcal{E}}$ orbit of $p$. Far enough along the flow of…

Frobenius-manifold Lyashko–Looijenga degree conjecture. The degree of the map $LL(\mathcal{F}_g)$ equals

Let a semisimple Frobenius manifold have an associated Principal Hierarchy, and let $(P_0,P_1)$ be a tau-symmetric bihamiltonian deformation of that hierarchy. The deformation has…

Consider a deformation of the bihamiltonian structure of the Principal Hierarchy, and let its central invariants be the functions parametrizing the infinitesimal deformation. The a…

Let the Principal Hierarchy be associated to a semisimple Frobenius manifold, and consider a deformation of its bihamiltonian structure with constant central invariants. Denote the…

Let $W$ be an invertible Calabi–Yau polynomial in three variables, and let $(W,G)$ be an admissible Landau–Ginzburg pair. Semisimplicity conjecture for three-variable Calabi–Yau LG…

Let $M$ be a semisimple Frobenius manifold, let its principal hierarchy have tau function $Z_M$, and let $L_m$ be the operators defining the Virasoro symmetries by … A super tau-co…

Frobenius-manifold and stability-condition isomorphism conjecture. There should exist an isomorphism

Let $(M,t^0)$ be an irreducible germ of a generically semisimple F-manifold. A generically semisimple F-manifold structure conjecture. The existence and parametrization assertions…

Quantum symplecticity conjecture. For any $u\in\mathcal C$, the function $H_{\hbar}(z,u)$ is valued in the group $L^{(2)}GL(h)_\hbar$.

Orbifold mirror conjecture. With the notation of the preceding Toda mirror construction,

Let $\mathfrak{g}$ be a simple Lie algebra, let $\bar i$ be a marked simple root, and let…

Let $M$ be a semisimple Frobenius manifold, and let its Dubrovin–Zhang integrable hierarchy be the associated hierarchy. Dubrovin–Zhang fermionic reformulation conjecture. There is…

Let $M$ be a semisimple Frobenius manifold, let its Dubrovin–Zhang integrable hierarchy be the hierarchy associated with $M$, and let the spectral curve of $M$ be constructed using…

Let $M$ be an $N$-dimensional semisimple Frobenius manifold such that it possesses a holomorphic genus one potential $\mathrm dG$. Global extension conjecture. There exists a conve…

Consider the constrained KP hierarchy and its extension obtained by adjoining the additional set of flows associated with the logarithm of its Lax operator. Let the associated Frob…

Existence conjecture. For each non-general multiplet $A$, there exists a Frobenius structure satisfying conditions (i), (ii), (iii), (v), and (vi) of Theorem 1, but not condition (…

Let $H$ be a non-degenerate Hamiltonian on $M$, let $U$ be the base of the associated Frobenius structure on a vector bundle $E$, and let $X_E$ be its Euler vector field. The 'eige…

Let $H$ be a non-degenerate Hamiltonian on $M$, let $\tilde U_{\xi}$ be the associated space, and let $\star:T U\rightarrow \operatorname{End}(E)$ be the Frobenius structure over…

Genus two G-function vanishing conjecture. For every such $M$,

Let $\mathbb{P}^1$ be an orbifold of ADE type, with orbifold-point multiplicities $p$, $q$, and $r$, and let $t_n$ denote the distinguished coordinate appearing in the genus-zero F…