**Unfortunately this talk is postponed, along with the rest of Guillem’s visit. We will rearrange for later in the term.**

Guillem Cazassus (Oxford) will talk in the geometry seminar at 11am in the Salle des Profs on 31/01/2023. **Note the unusual time**! This talk is part of an Oxbridge double bill, with Jack Smith’s talk following in the afternoon at our usual time of 2pm. Guillem’s title is “Hamiltonian actions on Floer homology and Fukaya categories” and his abstract is below.

*I will talk about some algebraic structures arising onLagrangian Floer homology and Fukaya categories in the presence of aHamiltonian action of a compact Lie group. Specifically, the relevantstructure is (our version of) A-infinity bialgebras, a strong homotopyversion of bialgebras. If time permits, I will also outline how todefine a strong homotopy version of Hopf algebras.On the one hand, this should be related to a conjecture of Teleman,motivated by Homological Mirror Symmetry. On the other hand, ourmotivation comes from gauge theory in low dimensions, and is part of aprogram aimed at recasting Donaldson-Floer theory into an extendedfield theory. More speculatively, we also expect these structures toarise in higher dimensional gauge theory, following theDonaldson-Segal program, and in relation with the Moore-Tachikawafield theories.This is based on two joint works in progress, one with Paul Kirk, MikeMiller-Eismeier and Wai-Kit Yeung, and another with Alex Hock andThibaut Mazuir.*