Speaker:  Benjamin Schroeter, University of Binghamton
Title: Correlation bounds of fields and matroids
Time: 2:30 PM, Monday, November 25, 2019
Place:  Malott 206

Abstract: Given a finite connected graph and two of its edges $e$ and $f$. Choose a spanning tree $T$ uniformly at random. It follows from work of Kirchhoff on electrical networks that the events $e\in T$ and $f\in T$ are negatively correlated. A combinatorial generalization of graphs and vector spaces are matroids. We will discus an analog of the above situation for general matroids, thus introduce as a measure of the correlation in a matroid its correlation constant. We use Hodge theory to bound these constants and explicit constructions of realizable matroids with positively correlated elements. This is joined work with June Huh and Botong Wang.


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