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Fachbereich
Institut für Mathematik
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Oberseminar Diskrete Mathematik, Geometrie und Optimierung

Termin und Ort:

Dienstags, 16 c.t., Raum 711 gr., Robert-Mayer-Str. 10

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Veranstalter: 

Raman Sanyal und Thorsten Theobald

Diskrete Mathematik, Geometrie und Optimierung

Feb 11 2025
16:15

Dr. Sebastian Debus: Symmetric function inequalities and superdominance

TU Chemnitz

Abstract: In this talk we consider inequalities of homogeneous symmetric functions, i.e., inequalities that hold in any number of variables. Therefore, we study the cones of symmetric sums of squares and nonnegative functions for fixed degrees. In polynomial optimization one is interested in the set-theoretic differences between the cones of sums of squares and nonnegative polynomials. A theorem of V. Kostov allows us to understand the extremal
rays of the cones for symmetric quartics. We find a symmetric quartic that is nonnegative but not a sum of squares in any non-trivial number of variables. To analyze higher degrees we investigate the tropicalization of the cones and discover a hidden combinatorial structure that can also be naturally expressed in terms of the superdominance order. This order turns out to completely characterize the valid inequalities of products of power sums on the nonnegative orthant.
This is joint work with J. Acevedo, G. Blekherman and C. Riener.

Diskrete Mathematik, Geometrie und Optimierung

Jan 28 2025
16:15

Kamillo Ferry: Tropical combinatorics of max-linear Bayesian networks

TU Berlin

Abstract: Max-linear Bayesian networks are a type of graphical statistical model that are described by a weighted directed graph.
As a further consequence, the set of possible observation of any MLBN forms a polytrope, a tropical polyhedron that is also classically convex. In joint work with Améndola, we classify the combinatorial types of MLBNs via their associated polytropes.