# 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