AbstractQuantum Ergodicity (QE) is a classical topic in spectral geometry, which states that on a compact Riemannian manifold whose geodesic flow is ergodic with respect to the Liouville measure, the Laplacian has a density one subsequence of eigenfunctions that tends to be equidistributed. In this talk, we present the QE for unitary flat bundles. By using a mixture of semiclassical and geometr...
AbstractIt has long been conjectured that the classical Lorenz attractor supports a unique measure of maximal entropy. In this talk, we will give a positive answer to this conjecture and its higher-dimensional counterpart by considering the uniqueness of equilibrium states for H\"older continuous functions on a sectional-hyperbolic attractor. we will prove that on every compact manifold with di...