# Assani, Idris

Professor

Phillips Hall 305A

assani@email.unc.edu

Website

## Research Interests

Ergodic theory, probability, harmonic analysis, operator theory

## Professional Background

Bachelor, Commerce, University Paris Dauphine, France, 1981; Doctorat 3eme cycle, Pure Math, University Paris 6-France, 1981; Doctorat es Sciences, Pure Math., University Paris 6, France-1986; Post-Doctoral fellowship - University of Toronto, 1986-1988; UNC-Chapel Hill, 1988-present

## Research Synopsis

I am working on pointwise questions in dynamical systems and ergodic theory. This is quite a large field which connects several mathematical research areas, such as Probability, Harmonic Analysis, and Operator theory. Such questions naturally arise in research areas such as return times phenomena and non-conventional ergodic averages, H. Furstenberg and T. Gowers. I solved several important problems and raised others. I have also organized an Ergodic Theory and Dynamical Systems workshop on a yearly basis with NSF support since the summer 2002. Young researchers as well as topnotch researchers have been collaborating as evidenced by several published proceedings of these workshops.

## Representative Publications

*Pointwise Convergence of Ergodic Averages Along Cubes*

I. Assani,

Journal d'Analyse Mathématique, 110, 241-269, 2010

*An L1 Counting Problem in Ergodic theory*

I. Assani, Z. Buczolich and D. Mauldin ,

Journal d'Analyse Mathématique, 95, 221-241, 2005

*Strong Laws for Weigthted Sums of Ii Random Variables*

I. Assani,

Duke Mathematics Journal, 88, 2, 217-246, 1997