Location: IHP, room 201
The talks are broadcasted via Zoom:
https://zoom.us/j/89445897442?pwd=QmVZWHBiM2Nwb09yUVJERnYrSHJrUT09
10:45 Julien Dardennes (Toulouse)
The coarse distance from dynamically convex to convex.
Abstract: Chaidez and Edtmair have recently found the first examples of dynamically convex domains in R^4 that are not symplectomorphic to convex domains, answering a long-standing open question. In this talk, we present new examples of such domains without referring to Chaidez-Edtmair's criterion. We also show that these domains are arbitrarily far from the set of symplectically convex domains in ℝ4 with respect to the coarse symplectic Banach-Mazur distance by using an explicit numerical criterion for symplectic non-convexity (joint work with J. Gutt, V. Ramos and J. Zhang). .
14:00 Nick Wilkins (Bonn)
Quantum Steenrod powers and Hamiltonian maps.
Abstract: Quantum Steenrod powers are a relatively new tool in the area of
symplectic geometry, with surprisingly wide-reaching connections across
mathematics. In this talk, we will highlight various applications of
quantum Steenrod powers to dynamical systems
and C^0 symplectic topology that will appear in upcoming work, joint
with E. Shelukhin. In particular, we will extend Shelukhin's previous
work to demonstrate a link between uniruledness and the quantum
deformation of the quantum Steenrod power of the point
class. We will also look at extensions of this result to
pseudorotations with hyperbolic periodic points. We will provide new
criteria for the existence of infinitely many periodic points of
Hamiltonian diffeomorphisms, using properties of the quantum Steenrod
power. Finally, we will demonstrate lower bounds for the Hofer and
C^0-norms of iterations of Hamiltonian diffeomorphisms, similarly using
properties of the quantum Steenrod power.
15:45 Dylan Cant (Orsay)
Eternal classes in symplectic cohomology.
Abstract: I will present work in progress on certain special classes in symplectic cohomology. The classes under consideration lie in the image of every continuation map (for this reason, we call them eternal classes as they are never born). We give criteria for existence and non-existence of eternal classes. Non-eternal classes in symplectic cohomology can be used to define spectral invariants for contact isotopies of the ideal boundary. The spectral invariants of non-eternal classes behave sub-additively with respect to the pair-of-pants product. This is used to define a spectral pseudo-metric on the universal cover of the group of contactomorphisms..
Next symplectix:
8/11 (Atallah, Chatterjee, Christ), 6/12 (Haney, Opshtein, Vertesi)
Other symplectic activity in Paris:
- Séminaire Nantes-Orsay- Symplectic Zoominar (every Fridays at 15:15 (except Symplectix' Fridays) Paris time)
