Event Type:

Department Colloquium

Date/Time:

Wednesday, April 26, 2006 - 09:00

Location:

Kidder 364

Guest Speaker:

Institution:

University of Victoria

Abstract:

Given a measure-preserving transformation T, there has been interest in the study of ergodic averages of the form 1/N[f(T^{a_1}x)+f(T^{a_2}x)+....+f(T^{a_N}x)]. For some sequences (a_n), these averages can be shown to converge pointwise for all measure preserving transformations, whereas for other sequences they diverge. In this talk, I'll describe the maximal rate of divergence and will apply the methods to review the negative solution to an old conjecture of Khinchine's (the original conjecture was as follows: given an integrable function g on the unit circle (written additively), the averages 1/N[g(x)+g(2x)+...+g(Nx)] converge almost everywhere to the integral of g) (joint work with Mate Wierdl)