Pure Math Grad Student Seminar (PuMaGraSS)
Friday, September 28, 2018 at 12:00am to 1:00pm
2-449
Speaker: Christian Gaetz
Title: Combinatorial applications of the Hard-Lefschetz Theorem and Hodge-Riemann relations
Abstract: In the 1980's Richard Stanley used the Hard-Lefschetz theorem from algebraic geometry to solve two famous open problems in combinatorics: the Erdos-Moser conjecture about subset sums and McMullen's g-conjecture for simplicial polytopes. Recently, Adiprasito, Huh, and Katz strengthened these methods by developing "Hodge theory for matroids" and resolved several longstanding conjectures in matroid theory, graph theory, and network theory. The ideas behind these methods and their implications will be discussed.
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