course: Diagonalizable actions and arithmetic applications
speaker: Manfred Einsiedler (ETH Zuerich)speaker: Elon Lindenstrauss (Princeton University)
abstract: We will discuss the theory of diagonalizable group actions, and applications to number theory and other subjects, including:
Classification of measures on Gamma\G invariant under diagonalizable groups, particularly a maximal split torus (such as the full diagonal group in SL(n,Z)\SL(n,R)). The complete classification is an important open problem, we will discuss the state-of-the-art results toward this classification. We also discuss joinings and measurable factors of such actions with applications to equidistribution.
Classification of closed invariant sets under such actions: again the full classification is an important open problem, but there are substantial partial results which we will cover. We will give an application regarding values of products of n linear forms in n variables and the set of exceptions to Littlewood Conjecture.
Distribution of compact orbits of these actions, including Linnik's principle and a dynamical proof of Duke's theorem regarding equidistribution of certain collections of closed geodesics on the modular surface.
Will also investigate the connections to automorphic forms, and in particular to arithmetic quantum unique ergodicity.
We will possibly also cover quantitative aspects of equidistribution and connection to subconvexity and sparse trajectories; quantitative versions Furstenberg's theorem and possibly of other measure and orbit classification theorems.
timetable:
Wed 13 Jun, 11:00 - 12:00, Aula Dini
Fri 15 Jun, 11:00 - 12:00, Aula Dini
Tue 19 Jun, 9:30 - 10:30, Aula Dini
Thu 21 Jun, 9:30 - 10:30, Aula Dini
Tue 26 Jun, 16:00 - 17:00, Aula Dini
Thu 28 Jun, 16:00 - 17:00, Aula Dini
Fri 29 Jun, 14:00 - 15:00, Aula Dini
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