New York Number Theory Seminar
December 14, 200, at 3:30 p.m.
Elon Lindenstrauss, Institute for Advanced Study
- Title:
- Rigidity of hyperbolic Z^n actions and some questions in number
theory and quantum chaos.
- Abstract:
- For many nice algebraic actions of Z^n or R^n (n > 1) there is a
remarkable (and as yet little understood, and in most cases only
conjectural) scarcity of closed invariant sets and invariant measures (this
is to be contrasted with hyperbolic Z or R actions which have uncountably
many wild closed invariant sets and invariant probability measures). A proof
of these conjectures would have profound number theoretic implications (e.g.
Littlewood's conjecture) and on some cases of Rudnick and Sarnak's quantum
unique ergodicity conjecture.