# 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

3:00 PM - 4:00 PM

Hylan 1106 A

We study certain simplicial complexes, called quota complexes. A quota complex on weighted vertices is constructed by adding an -simplex if the sum of the weights of the vertices is below a given quota, . 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 th Betti number, i.e., the dimension of the th homology group, is unimodal in .

Event contact: arjun dot krishnan at rochester dot edu

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