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What is the maximum number of edges in a graph on n vertices without triangles? Mantel’s answer in 1907—that at most half of the edges can be present—started a new field: extremal combinatorics. More generally, what is the maximum number of edges in an n-vertex graph that does not contain any subgraph isomorphic to H? What about if you consider hypergraphs instead of graphs? I will introduce the technique of sums of squares and discuss how it can be used to attack such problems.

Internship interviews can be stressful, but they don’t have to be. Join us to learn how to best prepare for interview day, to answer challenging questions and to present yourself in a professional manner. *This workshop will fulfill the Internship Preparation Workshop requirement for the Charles Hamilton Houston Internship Program.*