Homogeneous dynamics, unitary representations, and Diophantine exponents
50 mins 36 secs,
193.49 MB,
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About this item
| Description: |
Nevo, A (Technion - Israel Institute of Technology)
Thursday 03 July 2014, 16:00-16:50 |
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| Created: | 2014-07-11 18:41 |
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| Collection: | Interactions between Dynamics of Group Actions and Number Theory |
| Publisher: | Isaac Newton Institute |
| Copyright: | Nevo, A |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
|
| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | We will describe an explicit quantitative form of the duality principle in homogeneous dynamics. This allows the reduction of a diverse set of quantitative equidistribution problems on homogeneous spaces G/H to the problem of giving explicit spectral bounds for the restriction of automorphic representations of G to the stability subgroup H. We will demonstrate this approach by deriving bounds for Diophantine approximation exponent on homogeneous varieties, a problem raised by Serge Lang already in 1965, but which have seen little progress since then. The Diophantine exponents we derive are in many cases best possible, a remarkable fact that follows from an important and useful representation-theoretic phenomenon which we will highlight. Based on Joint work with Alex Gorodnik (Bristol University) and on joint work with Anish Ghosh (TIFR Mumbai) and Alex Gorodnik. |
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