Event № 75
The k-th expansion constant h_k(X) of a simplicial complex X is a natural k-dimensional extension of the Cheeger constant of a graph. Roughly speaking, h_k(X) measures the distance of X from complexes Y that have non-trivial k-cycles.
We will describe this notion and some of its applications.
In particular, we'll discuss:
1) A probabilistic construction of 2-dimensional expanders with bounded edge degree. This involves a concentration inequality on the space of random Latin squares. (joint work with A. Lubotzky).
2) Expansion of building-like complexes (Joint work with A. Lubotzky and S. Mozes).
No prior knowledge will be assumed.