Louis Theran (St. Andrews): Algebraic matroids and secant varieties

The algebraic matroid of an irreducible variety X in P^N is a combinatorial object that captures dependencies among the coordinates in the ideal of X, or, equivalent, how X is aligned with the coordinate axes.  Interest in algebraic matroids has picked up in recent years due to applications in rigidity theory, algebraic statistics and chemical reaction networks, among others.

I will talk about the relationship between the algebraic matroid M(X) of X and the algebraic matroids M(X^{s}) of its secant varieties X^{s}, in particular, the relationship between M(X^{s}) and the matroid union s M(X), plus some interesting examples and non-examples of when these are equal.

This is joint work with F. Mohammadi and J. Sidman