A Positivity Phenomenon in Elsers Gaussian-cluster Percolation Model

Start Date: May 13, 2020
Event Start Time: 1:00 PM
Event End Time: 2:00 PM
Seminar Series: Graduate Combinatorics Seminar
Presenter(s): Julie Vega - University of Kentucky
Event Location: Online Event
Event Additional Info: SPECIAL NOTE: This seminar is presented online only.You can join via ZOOM with Meeting ID: 268 276 468 or by clicking this link https://brown.zoom.us/j/268276468For further information see: https://sites.google.com/view/gocc-combinatorics/home
Presentation Type: Stand Alone Presentation
Abstract:
Veit Elser proposed a random graph percolation model in which physical dimension appears as a parameter. From this model, numerical graph invariants els_k (G) , called Elser numbers, naturally arise and Viet Elser conjectured that els_k (G) > 0 for all graph G and integers k > 2. In this talk we will interpret the Elser numbers as Euler characteristics of nucleus (simplicial) complexes and prove Elser’s conjecture.

This is joint work with Galen Dropalen-Barry, Cyrus Hettle, David Livingston, Jeremy Martin, George Nasr, and Hays Whitlatch.

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