Abstract: Knowing When to Stop
In many basic processes in science (and the rest of life) there is an
element of chance involved, and a crucial problem is deciding when to
stop. The process could be waiting to buy Google stocks, proofreading
a paper, deciding when to switch medications, or interviewing for a
new secretary (or spouse). At some point you need to stop, and your
objective is to do it in a way that optimizes your reward (e.g.
maximum expected profit or minimum expected cost). This talk will
briefly review the mathematical theory of optimal stopping (also
known in the literature as Secretary, Marriage, Dowry, or Best-Choice
Problems), which has a long and colorful history complete with
excellent rules of thumb, counterintuitive surprises, colorful
paradoxes and unsolved problems.
Included will be Gnedin’s solution of the Game of Googol, and very
recent results by Stadje and by Medina and Zeilberger on a still-open
famous problem of optimal stopping in fair-coin tossing. Talk will be
aimed for the non-specialist.
Abstract: Digits, dynamics, and distortion – A tour of Benford’s Law
 Benford’s Law, a notorious gem of mathematics folklore, asserts that
leading digits of numerical data are usually not equidistributed, as
might be expected, but rather follow one particular logarithmic
distribution. Since first recorded by Newcomb, this apparently
counter-intuitive phenomenon has attracted much interest from
scientists and mathematicians. This talk will provide a friendly
introduction to some of the intriguing aspects of Benford’s Law,
relating them in particular to problems in number and probability
theory and, above all, dynamics.