Our very own Pranav Chakravarthy will speak in the differential geometry seminar at 2pm on Monday 16th October, in the Salle des Profs (9th floor of building NO). Pranav’s title is “Homotopy type of equivariant symplectomorphisms of rational ruled surfaces” and his abstract is below.
In this talk, we present results on the homotopy type of the group of equivariant symplectomorphisms of S^2 x S^2 and CP^2 blown up once under the presence of a Hamiltonian circle actions. We prove that the group of equivariant symplectomorphisms is homotopy equivalent to either a torus, or to the homotopy pushout of two tori depending on whether the circle action extends to a single toric action or to exactly two nonequivalent toric actions. Our results rely on J-holomorphic techniques, on Delzant’s classification of toric actions, and on Karshon’s classification of Hamiltonian circle actions on 4-manifolds. Time permitting, we will explain results of a similar flavor on the homotopy type of Z_n equivariant symplectomorphisms for a large family of finite cyclic groups in the Hamiltonian group. This is based on joint work with Martin Pinsonnault.