# Mini-Workshop on Symplectic Geometry, Vrije Universiteit Amsterdam, September 30, 2016

## Titles and abstracts for the talks

### Urs Frauenfelder:

Periodic orbits in the restricted three body problem and Arnold's J^+ invariant

This is joint work with Kai Cieliebak. After regularization periodic orbits in the restricted three body problem become knots in RP^3. Their projection to position space is a curve in the plane. We show that Arnold's J^+ invariant is invariant under homotopies of periodic orbits and gives an additional invariant to their knot type in RP^3.

### Alexander Ritter:

The symplectic cohomology of toric varieties, and generation results for the Fukaya category

I will explain why the symplectic cohomology of (non-compact) Fano toric varieties recovers the Jacobian ring. Then I will explain how this can be used to obtain generators of the Fukaya category. A key ingredient is the definition and the structural properties of the open-closed string map, obtained in joint work with Ivan Smith.

### Lev Buhovski:

Towards the C^0 flux conjecture

I will talk about the C^0 flux conjecture, and some extension of a previous result of Lalonde, McDuff and Polterovich.

### Hansjörg Geiges, colloquium talk:

Geometry of the Kepler problem in celestial mechanics

In this colloquium talk I shall discuss some elementary geometric aspects of the Kepler problem. In particular, I want to show how Kepler's first law of planetary motion can be derived from a surprising (and surprisingly obscure) duality of force laws involving conformal transformations of the complex plane. In its basic form, this duality was known to Newton; a more general version was found by Bohlin and Kasner some 100 years ago; its modern interpretation in terms of Maupertuis's principle is due to Arnold.

### Hansjörg Geiges, second talk:

Traps and plugs in symplectic dynamics

The year is 2016 AD. Mathematicians studying dynamical systems are entirely occupied with finding periodic orbits. Well, not entirely... One small band of indomitable plumbers actually tries to block periodic orbits with plugs. This is their story, which started in 1966, and is based partly on joint work with Nena Röttgen and Kai Zehmisch.