Rankin Lecture 2026: Repellers of random walks
Professor Marcelo Viana (IMPA, Rio de Janeiro, Brazil)
Monday 9th February 11:00-12:00
Abstract
The School of Mathematics and Statistics is delighted to invite you to the Rankin Lecture 2026, to be given by Professor Marcelo Viana of the Institute for Pure and Applied Mathematics (IMPA) in Rio de Janeiro, Brazil. The lecture, entitled Repellers of random walks, will be held on Monday 9th February 2026, 11am-12pm GMT, with a light lunch to follow at 12pm (open to all registered attendees).
To attend, please register in advance at https://rankin- lecture-2026.eventbrite.co.uk
As this is a catered event, we particularly encourage early registration before 5pm Sunday 1st February to give us an accurate estimate of numbers for catering.
More details are below.
Location: Lecture Theatre 116 of the Mathematics and Statistics Building (map here)
Date/Time: Monday 9th February 2026, 11am-12pm, with a light lunch to follow at 12pm
Speaker: Professor Marcelo Viana (Institute for Pure and Applied Mathematics, Rio de Janeiro, Brazil)
Title: Repellers of random walks
About the speaker
Marcelo Viana is a professor of mathematics and the current director of IMPA - Institute for Pure and Applied Mathematics in Rio de Janeiro. His work in the fields of dynamical systems and ergodic theory earned him several academic distinctions, such as Louis D. Scientific Grand Prize from the Institut de France, and the inaugural Ramanujan Prize from the International Centre for Theoretical Physics and the International Mathematical Union. He has mentored 42 doctoral students to date. In addition to his research publications, he has written a handful of textbooks on differential equations, ergodic theory and dynamical systems. Viana is a member of the academies of sciences of Brazil, Chile, and Portugal, and of TWAS - The World Academy of Sciences. He was president of the Brazilian Mathematical Society and vice president of the International Mathematical Union. He led the organization of the 2018 International Congress of Mathematicians in Rio de Janeiro. He writes a weekly column about science in Folha de S.Paulo, Brazil's most prominent newspaper, and is also the author of popularization books in mathematics.
Abstract
Consider a sequence of invertible dxd matrices picked at random (independently) according to some probability distribution and multiply them successively. What can be said about the product as the number of factors goes to infinity? In a seminal 1960 paper, Furstenberg and Kesten proved that the norm and the co-norm have well-defined exponential rates of growth that are actually deterministic, i.e., independent of the random choices. They are called extremal Lyapunov exponents. In a recent joint paper with Artur Avila and Alex Eskin we prove that the Lyapunov exponents vary continuously with the underlying probability distribution, relative to a suitable topology. The proof is based on a detailed analysis of the dynamics of the random walk defined on projective space by the probability distribution.
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