Vladimir Dotsenko: Rational homotopy type of the moduli space of stable rational curves

Abstract: The moduli space of stable rational curves, also known as the Deligne-Mumford compactification \(\bar{M}_{0,n}\) of the moduli space of rational curves with marked points has been studied in many different areas of mathematics for decades, but some questions about it have remained open until now. An instance of such question is rational homotopy type of this space. I shall show that the rational cohomology of this space is a Koszul algebra (answering a question of Yu. I. Manin, D. Petersen and V. Reiner), and explain how this allows one to compute the rational homotopy Lie algebra of this space in a very explicit way. If time permits, some generalisations will be discussed.