Konstantinos Efstathiou

During the week of July 13–17, I am participating in the workshop Geometric Structures and Differential Equations — Symmetry, Singularity, and Applications, held at the Research Institute of Mathematical Sciences of Kyoto University. At the workshop, I present recent work on the Tavis–Cummings system with an $A_2$ singularity. I am grateful to Daisuke Tarama and the other organizers for the invitation to present my work and for putting together an exciting program.

I am visiting the University of Antwerp to serve as a member of the PhD defense committee for Pedro Santos. In connection with the defense, Pedro Santos and Sonja Hohloch are organizing a mini-workshop on Invariants and Integrable Systems. As part of the workshop, I presented recent work on the Tavis–Cummings system with an $A_2$ singularity.

The article Maslov $S^1$ Bundles and Maslov Data with Bohuan Lin and Holger Waalkens has been accepted for publication in the Journal of Mathematical Physics. In the article we introduce the notion of Maslov $S^1$ bundles over general symplectic manifolds, generalizing similar constructions on cotangent bundles. We analyze the properties of Maslov $S^1$ bundles and define a generalization of the Maslov index when the Maslov bundle is trivial. In the case where the Maslov bundle over the manifold $M$ is not trivial, but there is a symplectic $S^1$ action on $M$, we introduce the notion of Maslov data which serves as a non-integrable version of the Maslov index. Finally, we use Maslov bundles to prove results about homogeneous spaces and monotone symplectic manifolds, and we consider applications to integrable Hamiltonian systems.