5 problems

Determinant de Rham formula.

Let $X$ be a smooth complex quasi-projective variety and let $\mathbb V$ be a local system of geometric origin on $X$. Let $(V,\nabla)$ be the associated algebraic flat vector bund…

Quantum-connection identification conjecture. The differential operators $\hbar\,{}^B\nabla_{\partial_t}$ and $\hbar\,{}^B\nabla_{\hbar\partial_\hbar}$ preserve $\bar G_0^{W_t}$. M…

Gauss–Manin mirror symmetry conjecture. The function $W_t$ is expected to define a Gauss–Manin connection that recovers the connections defined on the $A$-model side by Dubrovin an…

The torsion conjecture. For every $j,t\geqslant 0$, the equality