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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Attaching shortest vectors to lattice points and applications

## Attaching shortest vectors to lattice points and applicationsAdd to your list(s) Download to your calendar using vCal - An, J (Peking University)
- Wednesday 02 July 2014, 09:00-09:50
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Interactions between Dynamics of Group Actions and Number Theory We highlight a simple construction, appeared in the work of D. Badziahin, A. Pollington and S. Velani where they proved Schmidt’s conjecture, which attaches to a lattice point an integral vector that is shortest in a certain sense. Such a construction turns out to be useful in studying badly approximable vectors and bounded orbits of unimodular lattices. It can be used to prove: (1) The set $mathrm{Bad}(i,j)$ of two-dimensional badly approximable vectors is winning for Schmidt’s game; (2) $mathrm{Bad}(i,j)$ is also winning on non-degenerate curves and certain straight lines; (3) Three-dimensional unimodular lattices with bounded orbits under a diagonalizable one-parameter subgroup form a winning set (at least in a local sense). This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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