GAN
9 June 2014 to 4 July 2014
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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:
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.
Images produced by Alex Barnett and Holger Then
Click here to download the programme's final scientific report
Title | Year | Programme |
---|---|---|
Best possible rates of distribution of dense lattice orbits in homogeneous spacesAuthors: Anish Ghosh, Alex Gorodnik, Amos Nevo |
2013 | GAN |
Multiparameter spherical averages of Siegel transforms and applicationsAuthors: Jayadev Athreya, Anish Ghosh, J Tseng |
2013 | GAN |
Simultaneous dense and nondense orbits and the space of latticesAuthors: R Shi, J Tseng |
2013 | GAN |
30 June 2014 to 4 July 2014
Monday 9th June 2014 | |||
---|---|---|---|
14:30 to 15:30 | Room 2 |
Tuesday 10th June 2014 | |||
---|---|---|---|
14:30 to 15:30 |
On continued fraction expansion of potential counterexamples to mixed Littlewood conjecture. |
Room 2 |
Thursday 12th June 2014 | |||
---|---|---|---|
11:30 to 12:30 |
Distribution of values of linear maps on quadratic surfaces. |
Room 2 | |
14:30 to 15:30 | Room 2 |
Friday 13th June 2014 | |||
---|---|---|---|
11:30 to 12:30 |
On continued fraction expansion of potential counterexamples II |
Room 2 | |
14:30 to 15:30 | Room 2 |
Monday 16th June 2014 | |||
---|---|---|---|
16:00 to 17:00 |
Spectral gap in simple Lie groups : Clay Mathematics Institute Senior Scholar Lecture. |
Room 1 |
Wednesday 18th June 2014 | |||
---|---|---|---|
11:30 to 12:30 | Room 2 | ||
14:30 to 15:30 |
Effective Ratner Theorem for ASL(2, R) and the gaps of the sequence \sqrt n modulo 1 |
Room 1 |
Thursday 19th June 2014 | |||
---|---|---|---|
14:30 to 15:30 |
Fourier analysis of multiplicative functions and a combinatorial application. |
Room 2 |
Friday 20th June 2014 | |||
---|---|---|---|
10:30 to 11:30 | Discussion Room | ||
11:30 to 12:30 | Room 1 | ||
14:30 to 15:30 |
Asymptotical behavior of piecewise contractions of the interval. |
Room 2 |
Tuesday 24th June 2014 | |||
---|---|---|---|
14:30 to 15:30 |
Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces. |
Room 2 | |
15:45 to 16:45 |
Stationary Measures and Invariant Subsets of Homogeneous Spaces: Part I |
Room 2 |
Friday 27th June 2014 | |||
---|---|---|---|
11:30 to 12:30 | Room 2 | ||
14:30 to 15:30 | Room 2 | ||
15:45 to 16:45 |
Stationary Measures and Invariant Subsets of Homogeneous Spaces: Part II |
Room 2 |
Monday 30th June 2014 | |||
---|---|---|---|
08:30 to 08:55 | No Room Required | ||
08:55 to 09:00 | Room 1 | ||
09:00 to 09:50 |
Gap Distributions, Homogeneous Dynamics, and Random Lattices |
Room 1 | |
10:00 to 10:50 | Room 1 | ||
11:00 to 11:30 | No Room Required | ||
11:30 to 12:20 |
Quasirandom Groups, Minimally Almost Periodic Groups and Ergodic Ramsey Theory |
Room 1 | |
12:30 to 13:30 | No Room Required | ||
13:30 to 14:20 | Room 1 | ||
14:30 to 15:00 | No Room Required | ||
16:00 to 16:50 | Room 1 | ||
17:00 to 18:00 | No Room Required |
Tuesday 1st July 2014 | |||
---|---|---|---|
09:00 to 09:50 |
The Hausdorff dimension of not uniquely ergodic 4-IETs has codimension 1/2. |
Room 1 | |
10:00 to 10:50 | Room 1 | ||
11:00 to 11:30 | No Room Required | ||
11:30 to 12:20 |
Inhomogeneous multiplicative Littlewood conjecture and logarithmic savings |
Room 1 | |
12:30 to 13:30 | No Room Required | ||
13:30 to 14:20 | Room 1 | ||
14:30 to 15:00 | No Room Required | ||
15:00 to 15:50 | Room 1 | ||
16:00 to 16:50 |
Effective equidistribution for twisted averages of the horocycle flow |
Room 1 | |
18:30 to 19:30 | No Room Required |
Wednesday 2nd July 2014 | |||
---|---|---|---|
09:00 to 09:50 |
Attaching shortest vectors to lattice points and applications |
Room 1 | |
10:00 to 10:50 |
Dimension of Self-similar Measures and Additive Combinatorics |
Room 1 | |
11:00 to 11:30 | No Room Required | ||
12:30 to 13:30 | No Room Required | ||
13:30 to 14:20 |
Lattice points counting and Diophantine approximable on manifolds |
Room 1 | |
14:30 to 15:00 | No Room Required | ||
15:00 to 15:50 | Room 1 | ||
16:00 to 16:50 | Room 1 | ||
19:30 to 22:00 |
Conference Dinner at Cambridge Union Society hosted by Cambridge Dining Co. |
No Room Required |
Thursday 3rd July 2014 | |||
---|---|---|---|
09:00 to 09:50 | Room 1 | ||
10:00 to 10:50 | Room 1 | ||
11:00 to 11:30 | No Room Required | ||
11:30 to 12:20 |
Metric Diophantine approximation: the well approximable theory on manifolds |
Room 1 | |
12:30 to 13:30 | No Room Required | ||
13:30 to 14:20 |
Hausdorff dimension estimates for bounded orbits on homogeneous spaces of Lie groups |
Room 1 | |
14:30 to 15:00 | No Room Required | ||
15:00 to 15:50 |
Limiting distributions of translates of curves on homogeneous spaces |
Room 1 | |
17:00 to 18:00 | Centre for Mathematical Sciences | ||
18:00 to 19:15 | No Room Required |
Friday 4th July 2014 | |||
---|---|---|---|
10:00 to 10:50 | Room 1 | ||
11:00 to 11:30 | No Room Required | ||
11:30 to 12:20 |
Spectral gap properties for random walks on homogeneous spaces: examples and consequences |
Room 1 | |
12:30 to 13:30 | No Room Required | ||
13:30 to 14:20 | Room 1 | ||
14:30 to 15:00 | No Room Required | ||
15:00 to 15:50 | Room 1 | ||
16:00 to 16:50 | Room 1 |
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