Flows on homogeneous spaces

The notes below are based on the class I taught on this subject in the spring of 2010

Please use them with care. If you find them useful, please let me know (it will give me an incentive to type them up eventually)

• Syllabus
• Notes on Siegel sets, reduced lattices, Mahler Criterion
  Notes showing SL(n,Z) is a lattice
• Ergodicity and mixing for SL(2)
• Equidistibution properties of horocycle flow (part 1)
  (part 2)
  exercises (due April 26)
• Quantitative nondivergence estimates on the space of lattices
  I have been loosely following Kleinbock's notes Quantitative nondivergence and its Diophantine applications available here.
• The Oppenheim Conjecture
  notes for Uri Shapira's lecture
• A special case of Ratner's measure classification theorem
• Introduction to the action of the diagonal group