**THE MALLAT
FAMILY FUND FOR RESEARCH IN MATHEMATICS **

**invites**** you to a**

**SPECIAL LECTURE SERIES**** **

**to**** be
presented by**

**Professor
Paul**** H Rabinowitz**** **** **

University of
Wisconsin–Madison

Member of the

The lectures will be
held in

Room
232

Technion -
Israel Institute of Technology

**
**

Lecture
I:

**Towards an Aubry-Mather Theory
for PDE's I**

(a) The work of Moser and then
of Bangert towards a PDE version of the Aubry-Mather
theory of invariant curves for self maps of an annulus

and

(b) The recent developments
due to Rabinowitz and Stredulinsky
which introduce renormalized functionals to the
Moser-Bangert setting
and use them to obtain a large variety of solutions of the PDE's.

Lecture
II:

**Towards an Aubry-Mather Theory for PDE's II**

This lecture will both discuss
some results not given in the first lecture and sketch the proofs of some of
the surveyed results.

Lecture
III:

**Homoclinic**** Solutions of Hamiltonian
Systems with
Double Well Potentials**

A survey will be given of existence
results for heteroclinic and homoclinic
solutions of the Hamiltonian system

q" + V_q(t,q) =0

where q is in R^n and
V is either a periodic or double well potential in q. Some recent work on a
case in which the bottoms
of the wells are are different levels will be discussed
in more detail.

Due to
construction in the