Special Year Seminar II

Algebraic statistics employs techniques in algebraic geometry, commutative algebra and combinatorics, to address problems in statistics and its applications. The philosophy of algebraic statistics is that statistical models are algebraic varieties. We will discuss two conjectures on the geometry of the Gaussian graphical model of the cycle. One conjecture is due to Sturmfels and Uhler concerning the degree of the projective variety associated to the Gaussian graphical model of the cycle. We present a new approach based on the intersection theory of the variety of complete quadrics, due to Michalek, Monin, and Wisniewski. The other conjecture is due to Drton, Sturmfels and Sullivant concerning the maximum likelihood degree of the same model.

This talk is based on joint works with Carlos Amendola, Mateusz Michalek and Martin Vodicka.