U. of Haifa Colloquium 15/6/21
Speaker: Michael Farber (University of London)
Topic: Ample simplicial complexes.
Place: This is an online seminar. Please email Yuval Ginosar “ginosar at math dot haifa dot ac dot il” for the Zoom ID and password.
Date: Tuesday, June 15, 2021
Motivated by potential applications in network theory, engineering and computer science, we study r-ample simplicial complexes. These complexes can be viewed as finite approximations to the Rado complex which has a remarkable property of indestructibility, in the sense that removing any finite number of its simplexes leaves a complex isomorphic to itself.
We prove that an r-ample simplicial complex is simply connected and 2-connected for r large.
We use the probabilistic method to establish the existence of r-ample simplicial complexes.
We introduce the iterated Paley simplicial complexes, which are explicitly constructed r-ample
simplicial complexes with nearly optimal number of vertexes.
The talk is based on a joint work with C. Even-Zohar and L. Mead.