Introduction:

The ideas of renormalization were introduced into the theory of dynamical systems by M. Feigenbaum almost 50 years ago. By now renormalization is one of the main methods of studying asymptotic behavior of dynamical systems.
In this course we will introduce the ideas of the renormalization theory in different settings, including unimodal maps, homeomorphisms of the unit circle, KAM theory to name a few. We shall also discuss Ergodic theory aspects of renormalization, the thermodynamic formalism, and basic results in the theory of hyperbolic dynamical systems. It is expected that by the end of the course students will be able to take on research projects focused on renormalization and related problems.

Lecturer Intro:

Khanin received his PhD from the Landau Institute of Theoretical Physics in Moscow and continued working there as a Research Associate until 1994.[2] Afterwards, he taught at Princeton University, at the Isaac Newton Institute in Cambridge, and at Heriot-Watt University before joining the faculty at the University of Toronto. Khanin was an invited speaker at the European Congress of Mathematics in Barcelona in 2000. He was a 2013 Simons Foundation Fellow. He held the Jean-Morlet Chair at the Centre International de Rencontres Mathématiques in 2017, and he was an Invited Speaker at the International Congress of Mathematicians in 2018 in Rio de Janeiro. In 2021 he was awarded The Humboldt Prize, also known as the Humboldt Research Award, in recognition of his lifetime's research achievements.

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