Interactions between Dynamics of Group Actions and Number Theory: Recent Episodes

Cambridge University

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.

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

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

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

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

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

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Pollicott, M (University of Warwick) Friday 04 July 2014, 09:00-09:50

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Kleinbock, D (Brandeis University) Thursday 03 July 2014, 13:30-14:20

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Shah, N (Ohio State University) Thursday 03 July 2014, 15:00-15:50

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Velani, S (University of York) Thursday 03 July 2014, 11:30-12:20

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Nevo, A (Technion - Israel Institute of Technology) Thursday 03 July 2014, 16:00-16:50

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Cheung, Y (San Francisco State University) Thursday 03 July 2014, 10:00-10:50

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Shapira, U (Technion - Israel Institute of Technology) Wednesday 02 July 2014, 15:00-15:50

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Wooley, T (University of Bristol) Thursday 03 July 2014, 09:00-09:50

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

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Beresnevich, V (University of York) Wednesday 02 July 2014, 13:30-14:20

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Kontorovich, A (Yale University) Wednesday 02 July 2014, 11:30-12:20

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Forni, G (University of Maryland) Tuesday 01 July 2014, 16:00-16:50

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An, J (Peking University) Wednesday 02 July 2014, 09:00-09:50

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Hochman, M (Hebrew University of Jerusalem) Wednesday 02 July 2014, 10:00-10:50

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Nelson, P (EPFL - Ecole Polytechnique Fédérale de Lausanne) Tuesday 01 July 2014, 15:00-15:50

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Flaminio, L (Université Lille 1) Tuesday 01 July 2014, 13:30-14:20

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Einsiedler, M (ETH Zürich) Tuesday 01 July 2014, 10:00-10:50

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Vishe, P H (University of York) Tuesday 01 July 2014, 11:30-12:20

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Chaika, J (University of Utah) Tuesday 01 July 2014, 09:00-09:50

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Eskin, A (University of Chicago) Monday 30 June 2014, 16:00-16:50

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Paulin, F (Université Paris-Sud) Monday 30 June 2014, 15:00-15:50

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Salehi Golsefidy, A (University of California, San Diego) Monday 30 June 2014, 13:30-14:20

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Mozes, S (Hebrew University of Jerusalem) Monday 30 June 2014, 10:00-10:50

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Athreya, J (University of Illinois) Monday 30 June 2014, 09:00-09:50

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Shi, R (Xiamen University) Friday 27 June 2014, 11:30-12:30

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Bengoechea, P (University of York) Friday 27 June 2014, 14:30-15:30

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Strombergsson, A (Uppsala Universitet) Thursday 26 June 2014, 13:30-14:30

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Ulcigrai, C (University of Bristol) Monday 23 June 2014, 13:30-14:30

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Ramirez, F (University of York) Monday 23 June 2014, 11:00-12:00

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Nogueira, A (Aix Marseille Université) Friday 20 June 2014, 14:30-15:30

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Host, B (Université de Marne-la-Vallée) Thursday 19 June 2014, 14:30-15:30

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Vinogradov, I (University of Bristol) Wednesday 18 June 2014, 14:30-15:30

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Maucourant, F (Université de Rennes 1) Wednesday 18 June 2014, 11:30-12:30

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Benoist, Y (Université Paris-Sud 11) Monday 16 June 2014, 16:00-17:00

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Gadre, V (University of Warwick) Tuesday 17 June 2014, 11:30-12:30

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Kra, B (Northwestern University) Tuesday 17 June 2014, 14:30-15:30

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Badziahin, D (Durham University) Friday 13 June 2014, 11:30-12:30

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Zorin, E (University of York) Friday 13 June 2014, 14:30-15:30

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Ward, T (Durham University) Thursday 12 June 2014, 14:30-15:30

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Badziahin, D (Durham University) Tuesday 10 June 2014, 14:30-15:30

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Tseng, J (University of Bristol) Wednesday 11 June 2014, 11:30-12:30

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Sargent, O (University of Bristol) Thursday 12 June 2014, 11:30-12:30