# Roger Jones

DePaul University

## Talk 1:

Title: When does a sequence of operators diverge?

In this talk I will describe various conditions that imply a sequence of
operators diverge. These conditions will be used to show ergodic averages
along lacunary sequences, convolution powers of certain measures, and
other kinds of averages can diverge. A discussion of Bourgain's entropy
method will be included.

## Talk 2:

Title: Convergence of convolution powers

In this talk I will discuss what is known about ergodic averages obtained
by taking convolution powers of a fixed measure. The $L^2$ result will be
obtained, and used to obtain the weak type (1,1) result. It will be shown
how to obtain a ``good - $\lambda $'' inequality between the maximal
operator associated with this sequence of operators, and the usual ergodic
maximal function. Some open problems will be mentioned.

## Talk 3:

Title: Oscillation inequalities in ergodic theory

In this talk I will look at the oscillation of the sequence of classical
ergodic averages, and establish norm inequalities for the oscillation
operators. Some of the results will be extended to other settings, and
applications will be discussed.