Higher-dimensional Givental symmetries

Vortrag von Prof. Dr. Vladimir Dotsenko

Datum: 20.10.25  Zeit: 13.30 - 14.30  Raum: ETH HG G 19.1

Some 20 years ago, Chen, Gibney and Krashen introduced beautiful algebraic varieties parametrizing "pointed trees of projective spaces"; these varieties generalize the celebrated Deligne-Mumford compactifications of moduli spaces of genus zero curves with marked points. In the latter case, the homology operad encodes the tree level part of a cohomological field theory. It follows from the work of Givental and many others that the space of all such structures on a given graded vector space has a very rich symmetry group; this fact has been used in many different research areas. In this talk, I shall prove that the homology of the operad made of Chen-Gibney-Krashen spaces possesses many interesting properties, and in particular, there are higher-dimensional Givental symmetries that emerge in this story. Curiously enough, this leads to new results on classical Givental symmetries as well. This is joint work with Eduardo Hoefel, Sergey Shadrin and Grigory Solomadin.