Location: IHP, room 201
The seminar will take place in presence, but will be broadcasted via zoom:
https://us02web.zoom.us/j/89445897442?pwd=QmVZWHBiM2Nwb09yUVJERnYrSHJrUT09
10:45 Gabriele Benedetti (Amsterdam)
Zoll magnetic flows on the two-torus: a Nash-Moser construction.
Abstract: In recent years, tools from contact and symplectic geometry have been very effective in studying systolic questions arising from metric and convex geometry. In particular, under general assumptions the local maximizers of the systolic ratio are Zoll flows, namely those flows generating a free circle action. Therefore, it is interesting to construct Zoll flows in specific classes of systems. In 1976, Guillemin used the Nash-Moser implicit function theorem to construct an infinite-dimensional family of Zoll geodesic flows on the two-sphere close to the round metric. In this talk, we build on Guillemin's idea and we construct an infinite-dimensional family of integrable Zoll magnetic flows on the two-torus, a case which presents new analytical difficulties. This is joint work in progress with Luca Asselle and Massimiliano Berti.
14:00 Arnaud Maret (Jussieu)
Action-angle coordinates for character varieties à la Kapovich--Millson.
Abstract: We study a moduli space of triangle chains in the hyperbolic plane with prescribed angles and relate it to a character variety of surface group representations in PSL(2,R). We will explain how to describe action-angle coordinates on the above-mentioned moduli space for the Goldman symplectic structure. There is a natural action of a mapping class group that preserves the symplectic structure. We will see that this action is ergodic. .
15:45 Théo Marty (Bonn)
Reeb-Anosov flows in dimension 3.
Abstract: Geodesic flows are important examples of both Reeb flows and Anosov
flows (on hyperbolic surfaces). Others Reeb-Anosov flows have been
constructed by Dehn surgery on already existing Reeb-Anosov flows. But
the set of Reeb-Anosov flows was not well understood until recently. I
will present of combination of recent results: an Anosov flow is
topologically equivalent to a Reeb-Anosov flow if and only if it admits
an open book decomposition, if and only if its orbit space is R-covered
and skewed..
Next Symplectix:
TBA !
Other symplectic activity in Paris:
- Séminaire Nantes-Orsay- Symplectic Zoominar (every Fridays except Symplectix' Fridays at 15:15, Paris time)
