Margulis, G (Yale University)
Wednesday 02 July 2014, 16:00-16:50

Oppenheim conjecture and related problems

In the last decade there have been several important breakthroughs in Number Theory and Diophantine Geometry, where progress on long-standing open problems has been achieved by utilising ideas originated in the theory of dynamical systems on homogeneous spaces. Dynamical systems techniques are applicable to a wide range of number-theoretic objects that have many symmetries. In particular:

various question in Diophantine approximation have been studied using recurrence properties of flows on the space of unimodular lattices
diagonal flows have played an important role in recent advances on quantum chaos and in the proof of the quantum unique ergodicity conjecture for arithmetic surfaces
flows on homogeneous spaces of nilpotent groups have been used to produce new estimates on exponential sums and to study prime solutions of systems of linear equations
the distribution of periodic orbits is connected to behaviour of period integrals of automorphic forms and to the problem of establishing subconvexity bounds for L-functions
The aim of this programme is to bring together researchers working in Number Theory and Homogeneous Dynamics to discuss the recent developments and open problems that lie at the crossroads of these fields and to encourage more interaction among people working in these diverse areas.

Mohammadi, A (University of Texas at Austin)
Friday 04 July 2014, 15:00-15:50

Unipotent flows on infinite volume manifolds

Guivarch, Y (Université de Rennes 1)
Friday 04 July 2014, 11:30-12:20

Spectral gap properties for random walks on homogeneous spaces: examples and consequences

Benoist, Y (Université Paris-Sud 11)
Friday 04 July 2014, 16:00-16:50

Random walk on p-adic flag varieties

Dani, S G (Indian Institute of Technology)
Friday 04 July 2014, 13:30-14:20

Multi-dimensional metric approximation by primitive points

Varjú, P (University of Cambridge)
Friday 04 July 2014, 10:00-10:50

Oppenheim conjecture and related problems

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