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>