FB 6 Mathematik/Informatik/Physik

Institut für Mathematik


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SS 2024

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10.04.2024 um 17:15 Uhr in Raum 69/125

Prof. Dr. Bram Petri (Institut Universitaire de France)

Highly Connected Hyperbolic Surfaces

Hyperbolic surfaces are surfaces equipped with a complete Riemannian metric of constant negative sectional curvature. Equivalently, these are surfaces that are locally isometric to the hyperbolic plane. These surfaces and their moduli spaces appear naturally in many places in mathematics. In this talk I will talk about connectivity questions on hyperbolic surfaces and how probability theory can help approach these questions. This is joint work with Thomas Budzinski and Nicolas Curien. I will not assume any familiarity with hyperbolic geometry.

24.04.2024 um 17:15 Uhr in Raum 69/125

Prof. Dr. Carlos Améndola Cerón(TU Berlin)

Likelihood Geometry of Reflexive Polytopes

We study the problem of maximum likelihood (ML) estimation for statistical models defined by reflexive polytopes. Our focus is on the ML degree of these models as a way of measuring the algebraic complexity of the corresponding optimization problem. We compute the ML degrees of all 4319 classes of three-dimensional reflexive polytopes and prove formulas for several general families, which include the hypercube and the cross-polytope in any dimension. We find some surprising behavior in terms of the gaps between ML degrees and degrees of the associated toric varieties, and we encounter some models of ML degree one. This is joint work with Janike Oldekop.