Tel Aviv University
 
Dear all,
 
This week at the Horowitz seminar on Probability, Ergodic Theory and
Dynamical Systems at Tel Aviv University we are happy to have:
 
Speaker: Omer Bobrowski, Technion
Title: Distance functions, critical points and topology for some
random complexes
 
Date: Monday, January 30
Time: 14:30
Place: Schreiber 309
 
Abstract:
In this talk we focus on the distance function from a random set of
points P in the Euclidean space. The distance function is continuous,
however, it is not everywhere differentiable. Nevertheless, one can
accurately define critical points and then apply Morse theory to it.
We study the number of critical points in small neighborhoods around
P. Specifically, we are interested in the case where the number of
points in P goes to infinity, and the size of the neighborhoods goes
to zero. We present limit theorems for the number of critical points
and show that it exhibits a phase transition, depending on how fast
the size of the neighborhoods goes to zero. A similar phase
transition was presented recently by Kahle and Meckes who studied the
Betti-numbers of random geometric complexes. We show that this is
more than just a coincidence, and discuss the connection between the
distance function and geometric complexes.
 
Best regards,
   Ron
 
Seminar webpage:
 <http://www.math.tau.ac.il/~peledron/Horowitz_seminar/Horowitz_seminar.html>
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Ron Peled   <peledron@gmail.com>