Distinguished Lecture Series
Professor of Mathematics, the University of Chicago
Wednesday, 4/13, McGuinn 121, 4:00 p.m.
Title: "What are the odds?"
Abstract: How do we think about the chances of rare events occurring, and are unlikely events really all that unlikely? This talk will explore two complementary themes: 1) the emergence of apparent structure and order from completely random processes; and 2) how non-random, deterministic processes can produce seemingly random output.
Thursday, 4/14, Fulton 110, 3:30 p.m.
Title: "The Ergodic Hypothesis: the general case"
Abstract:The celebrated Ergodic Theorems of George Birkhoff and von Neumann in the 1930's gave rise to a mathematical formulation of Boltzmann's Ergodic Hypothesis in thermodynamics. This reformulated hypothesis has been described by a variety of authors as the conjecture that ergodicity -- a form of randomness of orbit distributions -- should be``the general case" in conservative dynamics. I will discuss remarkable discoveries in the intervening century that show why such a hypothesis must be false in its most restrictive formulation but still survives in some contexts. In the end, I will begin to tackle the question, "When is ergodicity and other chaotic behavior the general case?"
Friday, 4/15, Fulton 110, 3:30 p.m.
Title: "The Ergodic Hypothesis: robust mechanisms for chaos"
Abstract: What are the underlying mechanisms for robustly chaotic behavior in smooth dynamics? In addressing this question, I'll focus on the study of diffeomorphisms of a compact manifold, where "chaotic" means "mixing" and and "robustly" means "stable under smooth perturbations." I'll describe recent advances in constructing and using tools called "blenders" to produce stably chaotic behavior with arbitrarily little effort.