Giulio Tiozzo and Tristan C. Collins are awarded the 2021 André Aisenstadt Prize

Giulio Tiozzo (University of Toronto) and Tristan C. Collins (Massachusetts Institute of Technology) are winners of the 2021 André Aisenstadt prize. Many brilliant mathematicians were in the running for the André Aisenstadt prize this year. Once again, the CRM International Scientific Committee was particularly impressed with the achievements of two nominees and thus decided that both be awarded the prize. This rare situation is an expression of the high caliber of their work.

Giulio Tiozzo (University of Toronto)

Entropy along the Mandelbrot set

Summary: The notion of topological entropy, arising from information theory, is a fundamental tool to understand the complexity of a dynamical system.  When the dynamical system varies in a family, the natural question arises of how the entropy changes with the parameter.
In the last decade, W.  Thurston introduced these ideas in the context of complex dynamics by defining the “core entropy” of a quadratic polynomials as the entropy of a certain forward-invariant set of the Julia set (the Hubbard tree). As we shall see, the core entropy is a purely topological/combinatorial quantity which nonetheless captures the