- Series
- Analysis Seminar
- Time
- Wednesday, November 18, 2009 - 2:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Matt Bond – Michigan State University
- Organizer
- Brett Wick

It is well known that a needle thrown at random has zero
probability of intersecting any given irregular planar set of finite
1-dimensional Hausdorff measure. Sharp quantitative estimates for fine open
coverings of such sets are still not known, even for such sets as the
Sierpinski gasket and the 4-corner Cantor set (with self-similarities 1/4
and 1/3). In 2008, Nazarov, Peres, and Volberg provided the sharpest known
upper bound for the 4-corner Cantor set. Volberg and I have recently used
the same ideas to get a similar estimate for the Sierpinski gasket. Namely,
the probability that Buffon's needle will land in a 3^{-n}-neighborhood of
the Sierpinski gasket is no more than C_p/n^p, where p is any small enough
positive number.