Probability, Ergodic Theory, Mathematical Physics Seminar

Unimodality of Bernoulli Random Quota Complexes

Erin Crossen, University of Rochester

Friday, February 28th, 2020
3:00 PM - 4:00 PM
Hylan 1106 A

We study certain simplicial complexes, called quota complexes. A quota complex on \(N+1\) weighted vertices is constructed by adding an \(n\)-simplex \([v_0,\dots,v_n]\) if the sum of the weights of the vertices is below a given quota, \(q\). In this talk, the weights of the vertices are chosen i.i.d. with a Bernoulli distribution. The main result of this talk is that the expectation of the \(m\)th Betti number, i.e., the dimension of the \(m\)th homology group, is unimodal in \(m\).

Event contact: arjun dot krishnan at rochester dot edu