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Session S24 - Symbolic Computation: Theory, Algorithms and Applications

Tuesday, July 13, 12:30 ~ 12:55 UTC-3

On the Fundamental Theorem of Tropical Partial Differential Algebraic Geometry

Sebastian Falkensteiner

RISC Hagenberg, Johannes Kepler University Linz, Austria   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Tropical Differential Algebraic Geometry considers difficult or even intractable problems in Differential Equations and tries to extract information on their solutions from a restricted structure of the input. The Fundamental Theorem of Tropical Differential Algebraic Geometry and its extensions state that the support of power series solutions of systems of partial differential equations can be obtained either, by solving a so-called tropicalized differential system, or by testing monomial-freeness of the associated initial ideals instead of analyzing the given system itself. Tropicalized differential equations work on a very simple algebraic structure which may help in theoretical and computational questions, particularly on the existence of solutions.

The content of the talk will be the introduction of the underlying algebraic structures, and the presentation of the precise statement of the Fundamental Theorem and the latest results on its extension and generalization.

Joint work with Cristhian Garay-Lopez (Centro de Investigacion en Matematicas, Mexico), Mercedes Haiech (Institut de recherche mathematique de Rennes, France), Marc Paul Noordman (Bernoulli Institute, University of Groningen, Netherlands) and Francois Boulier (Univ. Lille, CNRS, France).

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