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Watch a 56-minute lecture from the Institute for Advanced Study's Special Year Seminar II where Rodica Dinu from Universität Konstanz explores the geometric aspects of Gaussian graphical models for cycles. Delve into algebraic statistics and its application of algebraic geometry, commutative algebra, and combinatorics to statistical problems, understanding how statistical models can be viewed as algebraic varieties. Examine two key conjectures: Sturmfels and Uhler's conjecture about the degree of projective variety in cycle-based Gaussian graphical models, and Drton, Sturmfels, and Sullivant's conjecture regarding maximum likelihood degree. Learn about a novel approach utilizing intersection theory of complete quadrics variety, developed through collaborative work with Michalek, Monin, and Wisniewski. The presentation draws from joint research conducted with Carlos Amendola, Mateusz Michalek, and Martin Vodicka.
