Modul:   MAT760  Ergodic theory and dynamical systems seminar

Ergodicity of frame flows in low-rank

Vortrag von Dr. Thibault Lefeuvre

Sprecher eingeladen von: Dr. Mihajlo Cekić

Datum: 05.06.23  Zeit: 13.30 - 14.30  Raum: ETH HG G 43

The aim of this talk is to study the ergodicity of a class of partially hyperbolic flows constructed by taking unitary extensions to vector bundles of the geodesic flow over a closed negatively-curved manifold. We will show that, when the rank of the vector bundle is small compared to the dimension of the manifold, ergodicity can be completely characterized in geometric terms -- a certain connection admits no holonomy reduction. The proof combines classical hyperbolic dynamics, harmonic analysis, and, more surprisingly, real algebraic geometry (classification of polynomial maps between sphere). Joint work with Mihajlo Cekić.