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Diophantine approximation for algebraic numbers

Advances in Homogeneous Dynamics May 11, 2015 - May 15, 2015

May 12, 2015 (03:50 PM PDT - 04:40 PM PDT)
Speaker(s): Hillel Furstenberg (The Hebrew University of Jerusalem)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • well-approximable numbers

  • Diophantine approximation

  • Liouville number

  • transcendental number theory

  • homogeneous dynamics orbit

  • Raghunathan's theorem

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14241

Abstract

A number is well approximable (WA) if the error when approximatin by p/q can be made small compared to the sqare of 1/q. Almost all reals are WA. For good reasons quadratic irrationals are not.  Nothing is known for cubic irrationals.  We show how this relates to special orbits in homogeneous dynamics.

Supplements
23524?type=thumb Furstenberg. Notes 128 KB application/pdf Download
Video/Audio Files

14241

H.264 Video 14241.mp4 361 MB video/mp4 rtsp://videos.msri.org/data/000/023/450/original/14241.mp4 Download
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