1.1. About the Ruth Lyttle Satter Prize.

The Satter Prize is awarded every two years to recognize an outstanding contribution to mathematics research by a woman in the previous five years. Established in 1990 with funds donated by Joan S Birman, the prize honours the memory of Birman's sister, Ruth Lyttle Satter. Satter earned a bachelor's degree in mathematics and then joined the research staff at AT&T Bell Laboratories during World War II. After raising a family, she received a Ph.D. in botany at the age of forty-three from the University of Connecticut at Storrs, where she later became a faculty member. Her research on the biological clocks in plants earned her recognition in the United States and abroad. Birman requested that the prize be established to honour her sister's commitment to research and to encouraging women in science. The prize carries a cash award of US$5,000.

1.2. The 2011 Selection Committee.

The Satter Prize is awarded by the AMS Council acting on the recommendation of a selection committee. For the 2011 prize, the members of the selection committee were Victor W Guillemin, Jane M. Hawkins, and Sijue Wu.

1.3. Citation for Amie Wilkinson.

The Ruth Lyttle Satter Prize in Mathematics is awarded to Amie Wilkinson for her remarkable contributions to the field of ergodic theory of partially hyperbolic dynamical systems.

Wilkinson and Burns provided a clean and applicable solution to a long-standing problem in stability of partially hyperbolic systems in the paper "On the ergodicity of partially hyperbolic systems" (Annals of Mathematics (2) 171 (1) (2010), 451-489). The study of hyperbolic systems was begun in the 1960s by Smale, Anosov, and Sinai; this work was built upon earlier achievements of Morse, Hedlund, and Hopf. The recent papers of Wilkinson, jointly with Burns, give what is considered by experts to be the optimal result that unifies much of the deep work done by mathematicians during the intervening decades to weaken the strong hypothesis of hyperbolicity in order to be widely applicable while retaining the fundamentals of the associated dynamical behaviour.

Wilkinson has played a central role in the recent major developments in many related areas as well, including making some fundamental advances in understanding generic behaviour of $C^{1}$ diffeomorphisms. In addition to her outstanding work with Burns, Wilkinson works with many co-authors, such as Avila, Bonatti, Crovisier, Masur, and Viana, with whom she has published many significant results. A problem on the centralisers of diffeomorphisms was stated by Smale more than forty years ago and is included in his list of problems for the twenty-first century; the solution in the $C^{1}$ case was provided by Wilkinson in a series of papers with Bonatti and Crovisier.

1.4. Amie Wilkinson's Response.

This is an unexpected honour for which I am very grateful. As a woman in math, I have certainly faced some challenges: shaking the sense of being an outsider, coping with occasional sexism, and balancing career and family. These difficulties were ameliorated by the support and encouragement of numerous individuals and institutions, beginning with my parents, who thought it delightful that their older daughter loved math and science (and art and cooking). Early guidance from math teachers, especially John Benson at Evanston High School, was invaluable. The people in the Math Department at Northwestern University demonstrated their faith in me early on and never wavered in their support. Northwestern protected my research time early on, was flexible in assigning duties later, and promoted me in a timely fashion. Some of this was a gamble on Northwestern's part, one that other departments might still be hesitant to make. I have been educated over the years by a string of amazing mentors and collaborators, including those mentioned in the citation. Charles Pugh, Mike Shub, Keith Burns, and Christian Bonatti have played a special role; together, they have taught me how to think, dream, and write mathematics. From early on, Lai-Sang Young (the 1993 Satter Prize winner) has been a role model; her work in dynamics and clarity of exposition has always set the standard. The joint project with Keith Burns mentioned in the citation was an immensely satisfying collaboration. Whenever I think that the intricacies of partially hyperbolic dynamics have been largely revealed, a new phenomenon arises to delight and inspire.

I also thank my husband Benson, my best friend, mathematical companion, and muse (who occasionally lets me be his muse as well), and my children Beatrice and Felix, who have forced me to take a break from mathematics when I needed it the most.

1.5. Biographical Sketch of Amie Wilkinson.

Amie Wilkinson grew up in Evanston, Illinois, received her A.B. from Harvard in 1989 and Ph.D. from Berkeley in 1995 under the direction of Charles Pugh. After serving one year as a Benjamin Peirce Instructor at Harvard, she moved to Northwestern in 1996 where she was promoted to full professor in 2005. She was the recipient of an NSF Postdoctoral Fellowship and has given AMS Invited Addresses in Salt Lake City (2002), in Rio de Janeiro (2007), and at the 2010 Joint Meetings in San Francisco. She was also an invited speaker in the Dynamical Systems session at the 2010 ICM in Hyderabad. She lives in Chicago with her husband Benson Farb and their two children.

2.1. About the Levi L Conant Prize.

The Levi L Conant Prize recognises 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.

2.2. The 2020 Award Ceremony.

The 2020 prize was awarded on Thursday, 16 January during the Joint Prize Session at the 2020 Joint Mathematics Meetings of the American Mathematical Society and the Mathematical Association of America in Denver. It was held in the Four Seasons Ballroom of the Colorado Convention Center from 4:25 to 5:25.

2.3. Citation for Amie Wilkinson.

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.(Photo by Jessica Wynne, used with permission.)

Wilkinson's exposition is original, elegant, passionate, and deep. Throughout the article, she maintains a very high standard of mathematical rigour. 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 trivialise 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.

2.4. Response of Amie Wilkinson.

I would like to thank the AMS for this great honour. 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 organising the long-term behaviour of orbits of a system. Through the mechanism of renormalisation, exponents of meta-dynamical systems direct the seeming unrelated behaviour 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 summarise, 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 barycentre 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.

2.5. 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.