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Givental action is gauge symmetry in a homotopy Lie algebra

Dotsenko, V (Trinity College Dublin)
Thursday 04 April 2013, 11:00-12:00

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.


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