On the Theta-simplicity conjecture for the Kontsevich-Zorich cocycle
Ergodic Theory and Dynamical Systems Seminar
19th March 2026, 2:00 pm – 3:00 pm
Fry Building, G.07
The foundational works of Masur and Veech in 1982 on interval exchange transformations and translation flows gave birth to the so-called Teichmuller dynamics: in a nutshell, it amounts to study a class of parabolic systems thanks to the hyperbolic features of a renormalization procedure on an appropriate moduli space.
Many concrete applications of Teichmuller dynamics ideas rely on the nature of the Lyapunov spectrum of the Kontsevich-Zorich cocycle with respect to SL(2,R)-invariant probability measures. For the Masur-Veech measures, the simplicity of the Lyapunov spectrum was proved by Avila and Viana in 2007. Nonetheless, some examples by Forni, Filip, Avila, Yoccoz and myself show the Lyapunov spectra of other SL(2,R)-invariant probability measures often display a much richer behavior.
In this talk, we will discuss a joint work with F. Arana-Herrera, J. DeWitt, A. Eskin, V. Gadre, R. Gutiérrez-Romo, Y. Lima, K. Rafi and S. Schleimer showing that the Lyapunov spectrum of the Kontsevich-Zorich cocycle with respect to any SL(2,R)-invariant probability measure is always Theta-simple (i.e., as simple as it is allowed by the monodromy).
Comments are closed.