Amie Wilkinson to Receive the 2020 Conant Prize#
The 2020 Levi. L. Conant prize will be awarded to Amie Wilkinson for the article "What are Lyapunov exponents, and why are they interesting?
", published in the Bulletin of the American Mathematical Society in 2017. The article provides a broad overview of the modern theory of Lyapunov exponents and their applications to diverse areas of dynamical systems and mathematical physics.
Wilkinson's exposition is original, elegant, passionate, and deep. Throughout the article, she maintains a very high standard of mathematical rigor. At the same time, she provides a great deal of geometric intuition through the use of well-chosen examples and striking visuals. Definitions of abstract concepts are followed by examples and special cases that are natural and relatively simple, but do not trivialize the subject and offer interesting phenomena for analysis.
The explanations are clear and accessible to a wide audience. This is an impressive feat, given that this area of research has a reputation for being very technical and difficult to explain to non-experts. The article could be skimmed for a quick introduction to a fascinating part of mathematics, but it also lends itself to careful and repeated study, rewarding the more invested reader with a deeper understanding of the subject. We expect that it will be a valuable resource for many years to come.
Biographical Sketch of Amie Wilkinson:#
Amie Wilkinson has been a professor of mathematics at the University of Chicago since 2011, working in ergodic theory and smooth dynamics. Her research is concerned with the interplay between dynamics and other structures in pure mathematics--geometric, statistical, topological, and algebraic.
Wilkinson was the recipient of the 2011 AMS Satter Prize, and she gave an invited talk in the Dynamical Systems section at the 2010 International Congress of Mathematicians. In 2013 she became a Fellow of the AMS for "contributions to dynamical systems," and in 2019 she was elected to the Academia Europaea.
Response of Amie Wilkinson:#
I would like to thank the AMS for this great honor. The exponential growth rates measured by Lyapunov exponents are a powerful and yet elusive predictor of chaotic dynamics, and they aid in the fundamental task of organizing the long-term behavior of orbits of a system. Through the mechanism of renormalization, exponents of meta-dynamical systems direct the seeming unrelated behavior of highly structured systems like rational billiard tables and barycentric subdivision. Lyapunov exponents can deliver delightful surprises as well, leading to crazy geometric structures such as the pathological foliations Mike Shub and I have studied. To summarize, I love the subject of this article and am delighted that I might have conveyed this affection to the reader.
I have many colleagues to thank for their input and support; three of them in particular I'd like to mention by name. Artur Avila, whose work was the guiding inspiration for this article, has in many ways shaped how I view Lyapunov exponents and has opened my eyes to their power and versatility. Curtis McMullen explained to me his beautiful analysis of the barycenter problem, which served as the perfect introduction to the subject. Svetlana Jitormirskaya was instrumental in helping me get the facts straight on ergodic Schrödinger operators. Finally, I would like to thank the AMS for first inviting me to talk on the work of Artur Avila at the AMS Current Events Bulletin in 2016, a lecture on which this article was based.
About the Prize:#
The Levi L. Conant Prize recognizes the best expository paper published in either the Notices of the AMS or the Bulletin of the AMS in the preceding five years. Prize winners are invited to present a public lecture at Worcester Polytechnic Institute - where Conant spent most of his career - as part of the institute's Levi L. Conant Lecture Series, which was established in 2006.
The 2020 prize will be awarded Thursday, January 16 during the Joint Prize Session at the 2020 Joint Mathematics Meetings in Denver.
