Random Linear Algebra and the Vanishing Threshold for Integer Homology

Wednesday, April 2, 2014 - 1:30pm - 2:30pm
Lind 305
Matthew Kahle (The Ohio State University)
There are a few different approaches now to
homology-vanishing theorems for random simplicial complexes: (1)
cocycle counting, (2) spectral gap methods, and a new approach, (3)
random linear algebra. In this talk I will talk about the third
approach, and new joint work with Hoffman and Paquette, giving the
vanishing threshold for homology with integer coefficients. This was a
problem that had resisted attempts by the other methods for several
years, and the approach is also elementary. (This is a follow up to an
earlier talk, but this talk will also aim to be self contained.)