## EVENT DETAILS AND ABSTRACT

**Eigenfunctions Workshop**
**Title:** Semiclassical measures for the SchrÃ¶dinger equation on the torus (joint work with F. Macia)

**Speaker:** Nalini Anantharaman

**Speaker Info:** Orsay

**Brief Description:**

**Special Note**:

**Abstract:**

Our main result is the following : let $(u_{n})$ be a sequence in $L^{2}(\mathbb{T}^{d})$, such that $
orm{u_n}_{L^{2}(\mathbb{T}^{d})}=1$ for all $n$. Consider the sequence of probability measures $
u_{n}$ on $\mathbb{T}^{d}$, defined by $
u_{n}(dx)=(\int_{0}^{1}|e^{it\Delta /2}u_{n}(x)|^{2}dt) dx. $ Let $
u$ be any weak limit of the sequence $(
u_{n})$: then $
u$ is absolutely continuous. This generalizes a former result of Bourgain and Jakobson, who considered the case when the functions $u_{n}$ are eigenfunctions of the Laplacian. Our approach is different from theirs, it relies on the notion of (two-microlocal) semiclassical measures, and the properties of the geodesic flow on the torus.

**Date:** Thursday, June 10, 2010

**Time:** 9:30am

**Where:** Lunt 105

**Contact Person:** Jared Wunsch

**Contact email:**

**Contact Phone:**

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