Givental action is gauge symmetry in a homotopy Lie algebra
Seminar Room 1, Newton Institute
In this talk, I shall explain the mystery of hypercommutative algebras (=genus 0 cohomological field theories): it has been known for a while that the space of hypercommutative algebra structures on a given vector space possesses an unusually large group of symmetries. I shall explain how that appears naturally as a group of gauge symmetries of Maurer--Cartan elements in a certain homotopy Lie algebra. The existence of that homotopy algebra is still a result of several wonderful coincidences, but somehow I shall explain precisely what coincidences one should be hunting for in order for that sort of phenomena to occur.