[Binghamton Geometry/Topology Seminar] Geometry/Topology Seminar - Dean's Lecture in Geometry and Topology

[Christoforos Neofytidis]

BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR
Dean's Lecture in Geometry and Topology

   Date: Thursday, October 27th, 2016

   Time: 2.50 pm

   Place: Whitney Hall, Room 100E

   Speaker: Boris Hasselblatt (Tufts University)

   Title: Statistical properties of deterministic systems by elementary means

Abstract: The Maxwell-Boltzmann ergodic hypothesis aimed to lay a
foundation under statistical mechanics, which is at a microscopic scale a
deterministic system. Similar complexity was discovered by Poincaré in
celestial mechanics and by Hadamard in the motion of a free particle in a
negatively curved space. We start with a guided tour of the history of the
subject from various perspectives and then discuss the central mechanism
that produces pseudorandom behavior in these deterministic systems, the
Hopf argument. It has been known to extend well beyond the scope of its
initial application in 1939, and we show that it also leads to much
stronger conclusions: Not only do time averages of observables coincide
with space averages (which was the purpose for making the ergodic
hypothesis), but any finite number of observables will become decorrelated
with time. That is, the Hopf argument does not only yield ergodicity but
mixing, and often mixing of all orders.

NOTE:  The seminar has a webpage where the semester's program is listed:

http://www2.math.binghamton.edu/p/seminars/topsem