9 problems

Let $M$ and $M^{\vee}$ be open Calabi–Yau manifolds that are mirror to each other in the sense of homological mirror symmetry. A ring isomorphism is an isomorphism preserving the p…

Riemannian F-manifold conjecture. The flat structures associated with linear $a_0$ are bi-flat, and the bi-flat structures associated with the special linear solutions above come f…

Let $a_0$ be a solution of the integrable hierarchy equation defining an F-manifold with compatible connection. A solution is linear when $a_0$ is linear in the coordinates, and th…

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…

Let $G$ be a finite Coxeter group, and let $\mathcal{H}$ be the collection of reflecting hyperplanes of its reflection representation. Write $|\mathcal{H}/G|$ for the number of orb…

A pre-Lie commutative algebra has a symmetric associative product $\circ$ and a not-necessarily-symmetric product $\cdot$ satisfying the pre-Lie commutative algebra relations. Ever…

Let $((M,0),\circ,e,E)$ be an irreducible germ of a generically semisimple $F$-manifold, meaning that the multiplication is semisimple at generic points, and suppose that…

A cohomology F-manifold is the structure defined in the paper by its cohomological vector field and associated tensor operations. The additional integrability condition is the cond…

Let $M$ and $M^{\vee}$ be open Calabi–Yau manifolds that are mirror to each other in the sense of homological mirror symmetry. Write $SH^*(M)$ for the symplectic cohomology of $M$,…