Renormalization has become a central philosophy in low-dimensional dynamics. Among its many applications are Kolmogorov-Arnold-Moser principle, interval trade transformations (where it is named Rauzy-Veech induction), Feigenbaum-type universality, and even fluid dynamics. This course will function an introduction to renormalization magic, utilizing the key instance of analytic homeomorphisms of the circle. The prerequisites are a regular course in advanced analysis, and some primary familiarity with the notions of discrete-time dynamics.
- This course might be an introduction to the subject with a spotlight of deformation concept and purposes to moduli areas.
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- The objective of this course is to offer an introduction to the mathematical theory of General Relativity via the lens of the research of wave propagation on black holes.
- This class provides an introduction to classical subjects in ergodic concept, with applications to dynamical systems.
- Roughly speaking, the theme of the course is to investigate the connection between differential geometry and algebraic geometry in Kahler geometry.
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