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Speaker: Sam Spiro (Rutgers)

Title: Extremal Problems for Random Objects 

Abstract: Broadly speaking, extremal combinatorics studies how ``large'' combinatorial objects can be, such as determining the maximum number of edges that a graph with a given set of properties can have.  In contrast, the field of probabilistic combinatorics studies properties of random discrete objects, such as random graphs and random permutations.  In this talk, we study several problems at the intersection of these areas.  In particular, we consider the maximum expected score one can obtain in a certain card guessing game, as well as the problem of finding large $F$-free subgraphs of random graphs.