Dynamical Developments: A Conference in Complex Dynamics and Teichmuller Theory

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This award supports the participation of U.S.-based researchers in the international conference "Dynamical Developments: A Conference in Complex Dynamics and Teichmüller theory," taking place August 17-21, 2015, at Jacobs University in Bremen, Germany. Dynamical systems are all around us: the motion of the planets, the weather, the stock market, and the ecosystems in which we live. These systems depend on a variety of parameters, and as these parameters change, the corresponding system is affected. Often, "complexifying" a dynamical system and its corresponding parameter space, that is, regarding the salient quantities as complex numbers rather than (the more highly restricted) real numbers, leads to new insights and tools for investigating the underlying mathematics. Complex dynamics is a very active field that has experienced tremendous progress over the past few decades. This conference will bring together a diverse group of participants, ranging from various experts in these fields to younger researchers who are beginning their studies, for an intense and focused meeting to discuss exciting new developments, ideas, and directions for the subject.Complex dynamics has thrived over the past 25 years. This period of development has led to deep results on certain one-parameter model families (quadratic polynomials, for example). The time is ripe for the subject to advance to a more general theory, which will inevitably involve related fields such as Teichmüller theory, moduli spaces, dynamics in several complex variables, self-similar groups, arithmetic dynamics, symbolic dynamics, hyperbolic and algebraic geometry, and statistical physics. The conference will feature presentations by leading experts in complex dynamics and Teichmüller theory and will provide ample time for discussions. In addition to the formal scientific program, this conference will have two aspects less common to current mathematics conferences: there will be a young researchers seminar in which more junior participants can share their work with the community of mathematicians attending the conference, and there will be a computer program tutorial, showcasing some of the latest software used in the field. Conference web site : http://www-personal.umich.edu/~kochsc/H70.html