# Interactions between Dynamics of Group Actions and Number Theory

Created: | 2014-06-10 14:04 |
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Institution: | Isaac Newton Institute for Mathematical Sciences |

Description: | 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. |

# Media items

This collection contains 47 media items.

### Media items

#### Adelic equidistribution and property (tau)

Einsiedler, M (ETH Zürich)

Tuesday 01 July 2014, 10:00-10:50

**Collection**:
Interactions between Dynamics of Group Actions and Number Theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 11 Jul 2014

#### Applications of Thin Orbits

Kontorovich, A (Yale University)

Wednesday 02 July 2014, 11:30-12:20

**Collection**:
Interactions between Dynamics of Group Actions and Number Theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 11 Jul 2014

#### Asymptotical behavior of piecewise contractions of the interval.

Nogueira, A (Aix Marseille Université)

Friday 20 June 2014, 14:30-15:30

**Collection**:
Interactions between Dynamics of Group Actions and Number Theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 10 Jul 2014

#### Attaching shortest vectors to lattice points and applications

An, J (Peking University)

Wednesday 02 July 2014, 09:00-09:50

**Collection**:
Interactions between Dynamics of Group Actions and Number Theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 11 Jul 2014

#### Counting and equidistribution of common perpendiculars: arithmetic applications

Paulin, F (Université Paris-Sud)

Monday 30 June 2014, 15:00-15:50

**Collection**:
Interactions between Dynamics of Group Actions and Number Theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 11 Jul 2014

#### Dimension of Self-similar Measures and Additive Combinatorics

Hochman, M (Hebrew University of Jerusalem)

Wednesday 02 July 2014, 10:00-10:50

**Collection**:
Interactions between Dynamics of Group Actions and Number Theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 11 Jul 2014

#### Diophantine property in groups

Varjú, P (University of Cambridge)

Friday 04 July 2014, 10:00-10:50

**Collection**:
Interactions between Dynamics of Group Actions and Number Theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 15 Jul 2014

#### Distribution of values of linear maps on quadratic surfaces

Sargent, O (University of Bristol)

Thursday 12 June 2014, 11:30-12:30

**Collection**:
Interactions between Dynamics of Group Actions and Number Theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 18 Jun 2014

#### Divisibility properties in higher rank lattices

Mozes, S (Hebrew University of Jerusalem)

Monday 30 June 2014, 10:00-10:50

**Collection**:
Interactions between Dynamics of Group Actions and Number Theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 11 Jul 2014

#### Effective equidistribution for twisted averages of the horocycle flow

Forni, G (University of Maryland)

Tuesday 01 July 2014, 16:00-16:50

**Collection**:
Interactions between Dynamics of Group Actions and Number Theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 11 Jul 2014

#### Effective Ratner equidistribution for SL(2,R)⋉(R2)⊕k and applications to quadratic forms

Strombergsson, A (Uppsala Universitet)

Thursday 26 June 2014, 13:30-14:30

**Collection**:
Interactions between Dynamics of Group Actions and Number Theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 11 Jul 2014

#### Effective Ratner Theorem for ASL(2, R) and the gaps of the sequence \sqrt n modulo 1

Vinogradov, I (University of Bristol)

Wednesday 18 June 2014, 14:30-15:30

**Collection**:
Interactions between Dynamics of Group Actions and Number Theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 10 Jul 2014

#### Escape of mass in positive characteristics

Shapira, U (Technion - Israel Institute of Technology)

Wednesday 02 July 2014, 15:00-15:50

**Collection**:
Interactions between Dynamics of Group Actions and Number Theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 11 Jul 2014

#### Every flat surface is Birkhoff and Osceledets generic in almost every direction: Clay Mathematics Institute Senior...

Eskin, A (University of Chicago)

Monday 30 June 2014, 16:00-16:50

**Collection**:
Interactions between Dynamics of Group Actions and Number Theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 11 Jul 2014

#### Expansion properties of linear groups

Salehi Golsefidy, A (University of California, San Diego)

Monday 30 June 2014, 13:30-14:20

**Collection**:
Interactions between Dynamics of Group Actions and Number Theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 11 Jul 2014

#### Fourier analysis of multiplicative functions and a combinatorial application.

Host, B (Université de Marne-la-Vallée)

Thursday 19 June 2014, 14:30-15:30

**Collection**:
Interactions between Dynamics of Group Actions and Number Theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 10 Jul 2014

#### Gap Distributions, Homogeneous Dynamics, and Random Lattices

Athreya, J (University of Illinois)

Monday 30 June 2014, 09:00-09:50

**Collection**:
Interactions between Dynamics of Group Actions and Number Theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 11 Jul 2014

#### Gauss maps for simultaneous approximation

Cheung, Y (San Francisco State University)

Thursday 03 July 2014, 10:00-10:50

**Collection**:
Interactions between Dynamics of Group Actions and Number Theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 11 Jul 2014

#### Hall rays for Lagrange spectra of Veech surfaces

Ulcigrai, C (University of Bristol)

Monday 23 June 2014, 13:30-14:30

**Collection**:
Interactions between Dynamics of Group Actions and Number Theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 11 Jul 2014

#### Hausdorff dimension estimates for bounded orbits on homogeneous spaces of Lie groups

Kleinbock, D (Brandeis University)

Thursday 03 July 2014, 13:30-14:20

**Collection**:
Interactions between Dynamics of Group Actions and Number Theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 11 Jul 2014