infsurfmorelia2013@gmail.com

Teichmüeller theory is an important area of modern mathematics with links to many other subjects. Much of the theory focusses on Riemann surfaces of finite analytic type, but in this mini-course we will survey results in Teichmüller theory which hold for all Riemann surfaces, and in particular in the case of infinite analytic type. We will discuss the topics including:

Wind-tree models are 2D Boltzmann gas models where a point-particle moves at unit speed with perfect bounces off rectangular obstacles in the plane. Paul and Tatiana Ehrenfest introduced them in 1912 with randomly placed obstacles; in the 1980s J. Hardy and J. Weber introduced lattice-periodic wind-tree models: obstacles at integer points, sides horizontal and vertical.

By relating these models to infinite-area translation surfaces and using the dynamics of genus two translation surfaces, explored and explained in great detail in recent years, one can gain insight into the following dynamical questions:

- Does a generic trajectory come back arbitrarily near its starting point? (recurrence versus transience)
- How fast does a particle explore the billiard? (diffusion)
- Do particles explore every portion of the space? (minimality and ergodicity)

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Registration via this page is closed.
If you want to attend this conference please send an email to infsurfmorelia2013@gmail.com

FIRST DEADLINE (FOR EARLY CONSIDERATION): 3 APRIL, 2013.

Final Deadline 19 May 2013.

We have funding for travel and accomodations. Please specify your needs in the pre-registration form.