Monday April 7, 2003

Speaker: Dmitry Kleinbock

Title: Friendly Measures

Abstract: a lot is known about the way almost all points of Rn (with respect to Lebesgue measure) are approximated by rational points. Recently, a lot has become known about number-theoretic properties of generic points with respect to volume measures on smooth submanifolds of Rn. VERY recently, it was understood that similar properties can be established for measures satisfying certain geometric conditions - friendly measures. Besides smooth measures, examples include fractal measures on objects such as Koch's Snowflake or Sierpinski's Carpet.

I will define the `friendliness' axioms, discuss various examples, including the fractal ones, and explain why it is good to be friendly. The results (PDF) are joint with Elon Lindenstrauss and Barak Weiss.