Laurentiu Maxim (University of Wisconsin) : A proof of the Huh-Sturmfels involution conjecture in likelihood geometry

Séminaire « Géométrie algébrique »
Salle Kampé de Feriet (Bâtiment M2, 1er étage)
Maximum likelihood estimation in statistics leads to the problem of finding the critical points of a likelihood function on a complex algebraic variety. The number of critical points of a general likelihood function is called the maximum likelihood (ML) degree of the algebraic variety. The ML degree can be understood in terms of the topology of the variety, as the Euler characteristic of a certain constructible function (local Euler obstruction) which measures the complexity of singularities.
In this talk, I will discuss how a geometric interpretation of Chern-Mather classes together with an involution formula of Aluffi lead to a proof of a 2013 conjecture of June Huh and Berndt Sturmfels on the relation between two natural generalizations of the ML degree: sectional ML degrees and ML bidegrees. (Joint work with J. Rodriguez, B. Wang and L. Wu.)

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