THE REES DISTINGUISHED LECTURER SERIES

Prof. Keith Ball

University College, London, England

 Pools of Blood and the End of the Universe

Thursday April 21, 2005

126 Alfred Lerner Hall
3:30 - 4:30

This talk is an introduction to the concept of disorder or uncertainty as it appears in mathematics and physics. I shall begin by illustrating the probabilistic or information-theoretic idea of uncertainty by means of a (real-life) example from diagnostic blood testing. I shall then indicate how this probabilistic uncertainty fits with the classical concept that arose in thermodynamics during the 19th century. The talk is intended to be accessible to a very broad audience: no technical knowledge beyond pre-calculus will be assumed.

 

 

Friday April 22, 2005

104 Gore Hall
3:30 - 4:30

The aim of this talk is to give an overview of the recent solution of a problem that goes back to the work of Shannon and Linnik in the late 40’s and 50’s. The second law of thermodynamics asserts that entropy increases with time. It has long been believed that the central limit theorem of probability should be driven by an analogous principle: that entropy should increase along the central limits process. This was recently proved by the speaker and his collaborators using a new, variational characterization of the entropy. The first half of the talk will be a brief introduction to information-theoretic entropy and the central limit theorem. The second half of the talk will explain the proof of the “second law”. The only technical prerequisites will be basic probability theory (random variables, variance), the divergence theorem, the Cauchy-Schwartz inequality and (a vague recollection of) the heat equation.

 

Refreshments served immediately after talk in Ewing 436.