Abstract:
Let X be a smooth complex projective manifold,
$G^{eq}(X)\subset GL(H(X))$ – the image of the group $Aut(D(X))$ in the
group of automorphisms of $H(X)$. First I will explain about the
relation of the group $G^{eq}(X)$ and the Neron-Severi Lie algebra.
Then I plan to discuss the conjecture of Kontsevich on the relation
of the group $G^{eq}(X)$ (if $X$ is CY) with the monodromy group of the
mirror symmetric family.