The school is designed for graduate students and
will use short lecture courses, tutorial and
discussion sessions, and student projects to
explore some of the fundamental concepts of
dynamical systems. It will be accessible
to students without a background in dynamics,
but is also intended for students who have begun
studying dynamics and wish to learn more about
this field.
The school is
funded by an NSF grant, which will cover
travel and local expenses for all accepted
participants.
For videos of the lectures see the list to the right.
The following short
courses are planned:
Decay of correlations in dynamical
systems (University of Houston
dynamics group: Vaughn Climenhaga, Matt
Nicol, Will Ott, Andrew Torok) These lectures will introduce the
notion of decay of correlations for a
dynamical system and will describe three
important methods for establishing a rate
of decay: spectral gap (Perron--Frobenius
theory); coupling techniques; and Birkhoff
cones.
Hyperbolic dynamics and beyond
(Federico Rodriguez Hertz, Pennsylvania
State University)
In these lectures we plan to develop the
basic theory of hyperbolic systems,
including, stable manifolds,
linearization, local stability, etc. Then
we shall show how to apply the theory to
general systems, like random smooth
systems, non uniformly hyperbolic systems,
etc. Time permitting we plan to move on to
group actions and show how this theory can
be applied to handle actions with "some
hyperbolic behavior".
Multiplicative ergodic theory and
applications (Anthony Quas, University
of Victoria)
The multiplicative ergodic theorem (MET),
proved by Oseledets in the 1960s plays a
key role in differentiable dynamical
systems, geometry, and other areas. In
these lectures, we will understand the key
ideas of the MET, and discuss applications
to atmospheric dynamical systems.
Poincaré sections for diagonal actions
(Yitwah Cheung, San Francisco State
University)
We begin with the geodesic flow on the
modular surface and recall its connection
to continued fractions and the interplay
between dynamics and number theory.
We shall examine the role of Poincarésections in this context (e.g. using
it to prove the existence of
Khintchin-Levy's constant with the help of
the ergodic theorem) and elaborate on two
different ways the use of Poincaré
sections can be generalized, first by
considering more general one-parameter
diagonal actions, then by considering
higher dimensional diagonal actions.
Students participating
in the school should be familiar with the
following prerequisite material: measure theory,
basic functional analysis, basic theory of
smooth manifolds. There will be background
sessions during the school to give a brief
review of the most relevant parts of these
topics.
To apply for participation in the summer school,
please send an email to uh.summer.school@gmail.com
with a short CV containing the following
information:
Your name, current institution, and
program and year of study. Please also
include the name and email address of your
Ph.D. advisor or of another mathematician
who can serve as a reference if necessary.
A list of recent mathematics courses you
have taken and the grades earned.
Please indicate your background in the
prerequisite topics of measure theory,
functional analysis, and smooth manifold
theory.
A brief description of your mathematical
interests, particularly as they relate to
the topic of the summer school.
The deadline for applications to be guaranteed
full consideration is February
29, 2016. Funding for this event
is provided by NSF grant
DMS-1600737.
