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Houston Summer School on Dynamical Systems

May 18-26, 2016

The Department of Mathematics at University of Houston will host the fourth annual Houston Summer School on Dynamical Systems from May 18-26, 2016.

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 Poincaré sections 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:
  1. 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.
  2. 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.
  3. 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.         NSF logo

Videos of lectures: Probability in dynamics, decay of correlations
Hyperbolic dynamics and beyond(Rodriguez Hertz)
Multiplicative ergodic theory and application (Quas)

Poincaré sections for diagonal actions (Cheung)

Schedule of lectures

Evening and weekend options

Lorenz attractor videos Exercises List of project papers

Further references for spectral approach

Notes for Multiplicative Ergodic Theorem lectures

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