### 16 maj, kl 13.15-14.15, KTH, sal D33.

###
Nalini Anantharaman (Ecole Polytechnique):
Entropy and localization of eigenfunctions

**Abstract.**
On a compact negatively curved manifold, we study the
asymptotic behaviour of the eigenfunctions $(\phi_n)$ of the
laplacian, when the eigenvalue $\lambda_n$ goes to infinity. The
Quantum Unique Ergodicity conjecture says that the probability
measures $|\phi_n(x)|^2dx$ should converge weakly to the riemannian
volume (the uniform measure). We prove a result going in this
direction, saying that the `dynamical' entropy of these measures is
asymptotically positive.
This is a follow-up talk to the colloquium, and will give more details
about the proof and recent developments.