Abstract

Renormalization ideas were introduced in dynamics in the late 1970s. By now, renormalization is one of the most important methods of asymptotic analysis in the theory of dynamical systems. This talk serves as an introduction to dynamical renormalization. I'll also discuss closely connected rigidity theory and formulate some open problems. No previous knowledge of renormalization will be assumed.

Biography

Professor Khanin is a distinguished scholar in statistical mechanics and dynamical systems. He earned his PhD from the Landau Institute of Theoretical Physics in Moscow, where he subsequently worked as a Research Associate until 1994. He later held academic positions at Princeton University, the Isaac Newton Institute in Cambridge, and Heriot-Watt University, before joining the University of Toronto in 2005. In 2024, he joined the Beijing Institute of Mathematical Sciences and Applications (BIMSA). Professor Khanin has authored over 100 papers published in leading journals, including Annals of Mathematics, Inventiones Mathematicae, Journal of the American Mathematical Society, Annales Scientifiques de l'École Normale Supérieure, GAFA, and Communications in Mathematical Physics. He has been an invited speaker at several major conferences, including the International Congress of Mathematicians in 2008, the 3rd European Congress of Mathematics in 2000, and twice at the International Congress of Mathematical Physics. His honors include the Humboldt Research Award (2021), the Jean Morlet Chair (2017), and the Simons Fellowship (2014, 2021). Since 2020, he has served as Editor-in-Chief of the journal Nonlinearity.