**A Symposium in memory of Professor Jal R. Choksi**

McGill University

Department of Mathematics and Statistics

June 6, 2012

BURNSIDE HALL 920

**09:30**

**Jacques Hurtubise, Chair - McGill University**

Opening Remarks

**09:40**

**Donald Dawson – Carleton University**

Metrics, measures and the structure of populations

Over the past twenty-five years a number of new mathematical objects have emerged from the study of the structure and evolutions of populations. In this lecture, starting with the classical Galton-Watson branching process, we outline the development of three of these, namely the continuum random tree (CRT), super-Brownian motion (SBM) and the integrated super excursion (ISE) and the relations among them, as well as the associated invariance principles and their universality classes.

**10:10**

**Cesar Silva – Williams College**

On measurable sensitivity for nonsingular and measure-preserving systems

We will discuss measurable notions of sensitivity for nonsingular and measure-preserving systems including a characterization theorem for such systems.

**10:40 Coffee break – BURNSIDE HALL 911**

**11:00**

**Stanley Eigen – Northeastern University**

The Pascal-Adic Transformation and its Infinite Measure Preserving Source

Three representations of the Pascal-adic transformation are given: via a cutting and stacking procedure; as a map on symbol space; as an adic-transformation. It is then shown how they arise naturally in the study of infinite measure preserving transformations.

**11:30**

**Jean-Marc Belley – Université de Sherbrooke**

Existence of antiperiodic solutions of Josephson’s impulsive equation with Henstock-Kurzweil integrable forcing

Under weak conditions, Josephson’s state dependent impulsive equation with Henstock-Kurzweil integrable forcing is shown to admit an absolutely continuous antiperiodic generalized solution with Lebesgue integrable first derivative and Henstock-Kurzweil integrable second derivative. A uniqueness condition is also given. This is joint work with P. Morales.

**Lunch break**

**14:00**

**Andres del Junco - University of Toronto**

Rigid and non-recurrent sequences for measure-preserving automorphisms of a probability space

The main focus here is to find conditions on a sequence n

_{m}of positive integers which ensure that for some weakly mixing automorphism*T*on a probability space (X, μ) we have lim_{m}μ(*T*^{n}_{m }A Δ A) = 0 for every measurable A. (This phenomenon is called rigidity). The problem can be rephrased as a question in harmonic analysis. We use both harmonic analysis and direct constructions, as well as combinations of the two, to find the desired*T*. Many open questions remain. Example: For any integer a ≥ 2 n_{m}= a^{m}is rigid for some weakly mixing*T*. We do not know if this is the case for n_{m}= 2^{m}+ 3^{m}. It is not the case for n_{m}= 2^{m}+ m^{2}.This is joint work with V. Bergelson, M. Lemanczyk and J. Rosenblatt.

**14:30**

**Raj Prasad – UMass Lowell**

Tilings of the integers arising from a class of infinite measure preserving transformations

There are many infinite sequences of integers associated to an infinite measure preserving transformation: weakly wandering sequences, exhaustive weakly wandering (EWW) sequences and strongly weakly wandering sequences. EWW sequences give rise to an infinite tiling of the integers. We consider a class of ergodic transformations of an infinite measure space with no recurrent sequences (this class includes simple random walk on the integers) and study their hereditary tilings of the integers. This is joint with Eigen, Hajian, and Keane.

**15:00 Coffee break – BURNSIDE HALL 911**

**15:30**

**Maria Isabel Cortez – Universidad de Santiago de Chile**

Orbit equivalence and invariant measures of generalized Toeplitz subshifts

In this talk we will show that every possible set of invariant probability measures is realizable among the class of the Toeplitz subshifts given by the action of an infinite, countable, amenable and residually finite group G. This is an extension of the result due to T. Downarowicz for G = Z. Furthermore, we will see that in every topological orbit equivalence class associated to a Toeplitz Z-subshift there is a Toeplitz Z

^{n}-subshift, for every n > 1.This is a joint work with S. Petite.

**16:00**

**Karin Reinhold – SUNY, Albany**

Random ergodic theorems

We study convergence of random ergodic averages when the weights are given by random variables which are not identically distributed.

**16:30**

**Niky Kamran – McGill University**

Energy decay theorems for Dirac operators on Lorentzian manifolds with ends

We present a general approach to the proof of local energy decay for the solutions of the Dirac equation with L

^{2}initial data, on globally hyperbolic Lorentzian manifolds foliated by cylindrical space-like submanifolds with asymptotically Euclidean and hyperbolic ends.**17:00**

**Jacques Hurtubise, Chair - McGill University**

Closing Remarks

**18:30**Reception – L’Orchidée de Chine

2017 Peel