Brief History of the Boltzmann-Sinai Hypothesis


October 12, 2018 | 2:30 - 3:30 p.m.


Campbell Hall 443


Dr. Nandor Simanyi


The Boltzmann-Sinai Hypothesis dates back to 1963 as Sinai’s modern formulation of Ludwig Boltzmann’s statistical hypothesis in physics, actually as a conjecture: Every hardball system on a flat torus is (completely hyperbolic and) ergodic (i. e. ”chaotic”, by using a nowadays fashionable, but a bit profane language) after fixing the values of the obviously invariant kinetic quantities. In the half century since its inception, quite a few people have worked on this conjecture, made substantial steps in the proof, created useful concepts and technical tools, or proved the conjecture in some special cases, sometimes under natural assumptions. Recently I was able to complete this project by putting the last, missing piece of the puzzle to its place, getting the result in full generality. In the talk, I plan to present the brief history of the proof by sketching the most important concepts and technical tools that the proof required.