Tuesday, November 26, 14:00, 7.527
Vladimir Dotsenko (Strasbourg), Rational homotopy type of the moduli space of
stable rational curves.
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.