### Graduate Student Seminar, 4:00 pm October 23, 2006; HH229

#### Speaker:

Tanya Kazakova

#### Title:

Number-theoretic consequences of ergodic theory

#### Abstract:

Every real number can be written as a continued fraction. For example, pi = [3, 7, 15, 1, 292, 1, 1, ...]. We can immediately notice that, so far, 1 appeared three times, while 13 is not on the list at all. Is it true, in general, that 1 is going to come up more often than 13? To answer this and many more number-theoretic questions, we are going to explore the patterns of pi first numerically and then analytically using tools of ergodic theory.

To volunteer to give a talk, or for any other questions regarding this schedule,
contact Sara Miller