Seminar

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Koszul algebras appear in many areas of algebra, geometry and topology. Two of their

remarkable properties are that the minimal free resolution of the ground field k can be explicitly

described as a generalized Koszul complex, and there is an elegant formula relating the Hilbert

function of the algebra and the Poincare series of k. Consider the binomial edge ideal J(G) associated

to a finite simple graph G. Such an ideal is always generated by quadrics. It has a quadratic Groebner

basis if and only if the graph G is closed. There are many other cases when J(G) is Koszul. The study

of Koszul binomial edge ideals was initiated by V. Ene, J. Herzog, and T. Hibi in 2014. We characterize

the Koszul binomial edge ideals by a simple combinatorial property of G. This is joint work with 

A. LaClair, M. Mastroeni, and J. McCullough.