Recent progress on the quantum unique ergodicity conjecture

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


We report on some recent striking advances on the quantum unique ergodicity, or QUE conjecture, concerning the distribution of large frequency eigenfunctions of the Laplacian on a negatively curved manifold. The account falls naturally into two categories. The first concerns the general conjecture where the tools are more or less limited to microlocal analysis and the dynamics of the geodesic flow. The second is concerned with arithmetic such manifolds where tools from number theory and ergodic theory of flows on homogeneous spaces can be combined with the general methods to resolve the basic conjecture as well as its holomorphic analogue. Our main emphasis is on the second category, especially where QUE has been proven. This note is not meant to be a survey of these topics, and the discussion is not chronological. Our aim is to expose these recent developments after introducing the necessary backround which places them in their proper context.

Original languageEnglish (US)
Pages (from-to)211-228
Number of pages18
JournalBulletin of the American Mathematical Society
Issue number2
StatePublished - 2011

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


Dive into the research topics of 'Recent progress on the quantum unique ergodicity conjecture'. Together they form a unique fingerprint.

Cite this