Vladimir Dotsenko (Strasbourg), Rational homotopy type of the moduli space of stable rational curves.

Abstract:

In 2004, Manin asked whether the cohomology of the moduli space of stable rational curves with n marked points (= the Deligne-Mumford compactification of the moduli space of smooth genus zero curves with n marked points) is a Koszul algebra. This question remained open since. I shall present a solution to it, proving that the answer is positive for all n. An immediate consequence of my result is a complete description of rational homotopy groups of these spaces, and the Whitehead (-Bott-Samelson) Lie algebra structure on the rational homotopy groups.