Mike Hochman's Homepage

I am a Veblen Research Instructor at the math department at Princeton University.

During the fall of 2008 I'll be visiting MSRI for the special semester on ergodic theory and additive combinatorics.

email: hochman /a/t/ math dot princeton dot edu
office: 303 @ MSRI
Tel. (510) 643 6022
Fax. (510) 642 8609

Mailing address:
The Mathematical Sciences Research Institute
17 Gauss Way
Berkeley, CA 94720-5070
USA

Teaching

I'm on leave this year.

In Fall 2007 I taught Math 201 (multivariate calculus). In Spring 2008 I taught Math 202 (linear algebra with applications). For more information see the blackboard website.

Research interests

I am interested in ergodic theory and topological dynamics, both classical Z-actions and actions of other groups (especially Z^d but also amenable groups). A lot of my work involves entropy theory (and the "dual" notion of determinism). Recently I have been working on the symbolic dynamics in higher dimensions, specifically SFTs and sofic shifts, and I'm also started working in infinite ergodic theory.

It's not so easy to explain what I do to someone who isn't an expert in the field. Here is my attempt to explain it. At the end there's a list of recommended reading if you want to know more.

Publications and preprints

Here are my papers on Mathscinet, here are some preprints on the arxiv

Determinism and invertibility in topological dynamics, in preparation.
A note On universality in multidimensional symbolic dynamics, preprint (submitted)
On the dynamics and recursive properties of multidimensional symbolic systems , preprint, to appear in Inventiones Mathematicae
On the automorphism group of multidimensional SFTs, preprint (submitted)
A ratio ergodic theorem for multiparameter actions, to appear in Journal of the European Mathematical Society, preprint
A Characterization of the Entropies of Multidimensional Shifts of Finite Type, with Tom Meyerovitch, to appear in Annals of Mathematics , arxiv
Upcrossing inequalities for stationary sequences and applications to entropy and complexity, arxiv (submitted)
2008 On processes which cannot be distinguished by finitary observation, with Yonatan Gutman, Israel Journal of Mathematics , arxiv .
2008 Genericity in Topological Dynamics, Ergodic Theory and Dynamical Systems , arxiv. Here are some related slides from a talk I gave at the 2006 CSWDDS workshop
2007 Averaging sequences and abelian rank in amenable groups, Israel Journal of Mathematics, arxiv.
2006 Return times, recurrence densities and entropy for actions of some discrete amenable groups, Journal d'Analyse, arxiv.

Graduate Work

I did my graduate work (M.A. and Ph.D.) under the guidance of Professor Benjamin Weiss, at the math department at the Hebrew University of Jerusalem in Israel.

My paper Return times, recurrence densities and entropy for actions of some discrete amenable groups represents my M.A. thesis work.

My Ph.D. thesis consists of three of the above papers: Averaging sequences and abelian rank in amenable groups , Genericity in topological dynamics , and Upcrossing inequalities for stationary sequences and applications .

Calculus Textbook

Together with my friends Yonatan Harel, Ittay Weiss and Ofek Shilon, I have written a calculus textbook to accompany the first year course given at the Hebrew University (the book is in Hebrew, of course). Here is the table of contents. The book is available from Academon Press. Corrections can be found on the book site.