Combinatorics: Zur Luria (ETH Zurich), "Random designs and high dimensional expanders"

Expander graphs have many wonderful properties, and have been an immensely useful and fruitful area of research in both applicative and theoretical fields. There has been a lot of interest recently in the study of higher dimensional generalizations of expanders to d-uniform hypergraphs. Many competing definitions have been proposed, and different definitions may be appropriate depending on the property of expanders that we wish to preserve.
Designs are a combinatorial object with a long history. They may be viewed as a generalization of regular graphs. Until recently, for all but a small collection of parameters, designs were not known to exist. Amazingly, recent papers by Peter Keevash established the existence of designs for every set of parameters obeying certain necessary conditions, and even proved an asymtotic estimate on their number.


Mon, 02/11/2015 - 11:00 to 13:00