Nándor Simányi (University of Alabama)

The ergodicity of typical hard sphere systems in 2D: geometric aspects.

Abstract. In my recent proof of the Boltzmann-Sinai Ergodic Hypothesis for typical hard sphere systems (in 2D) I used some interesting geometric arguments, such as

1) the possibility of an infinite, neutral, singularity-free translation (other than in the direction of the flow!) of any phase point $x_\infty$that is actually an $\omega$-limit point of the trajectory of a separating phase point (in any neighborhood of which one finds two ergodic components);

2) the classical Sylvester-Gallai theorem from combinatorial geometry, claiming that for any finite subset X of the Euclidean plane, if no line intersects X in exactly two points, then X is contained by a single line.

The emphasis of my talk will be put on these geometric aspects.