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: Yogeshwaran Dhandapani, Technion
Title: On the topology of some random complexes built over stationary
point processes
 
Date: Monday, November 12
Time: 14:30
Place: Schreiber 309
 
Abstract:
There has been recent interest in understanding the homology of
random simplicial complexes built over point processes, primarily
motivated by problems in applied algebraic topology. I shall describe
our new results about the growth of homology groups of Cech and
Vietoris-Rips complexes built over general stationary point
processes. Both these complexes have points of the point process as
vertices and the faces are determined by some deterministic geometric
rule. The aim of the talk shall be to explain the quantitative
differences in the growth of homology groups measured via Betti
numbers between the Poisson point process and other point processes
which exhibit repulsion such as the Ginibre ensemble, zeros of
Gaussian analytic functions, perturbed lattice etc. I shall also try
to hint at the proof techniques which involve detailed analysis of
subgraph and component counts of the associated random geometric
graphs and are applicable to similar functionals of point processes
such as Morse critical points. This is a joint work with Prof. Robert
Adler.
 
Best regards,
   Ron
Seminar webpage:
 <http://www.math.tau.ac.il/~peledron/Horowitz_seminar/Horowitz_seminar.html>
 
---------------------------------------------------------
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Ron Peled   <peledron@post.tau.ac.il>