A new symbolic-numeric method to solve the multiparameter eigenvalue problem
A classical approach to solving polynomial systems is to linearize the problem and reduce it to an eigenvalue calculation. For this purpose, certain families of special matrices are used, e.g., Sylvester and Dixon matrices. Their size and structure determine how far these methods can go; therefore, it is essential to construct better matrices for the specific systems that arise in practice.
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In this talk, we focus on polynomial systems coming from the multiparameter eigenvalue problem and certain generalizations. Using the theory of resultants and Weyman complexes, we present new matrices of optimal size for solving these systems. This talk is based on joint work with Jean Charles Faugère, Angelos Mantzaflaris, and Elias Tsigaridas.
Teacher/speaker
Matías R. Bender
Since 2023, Matías R. Bender has been working as a researcher (chargé de recherche) at the project/team Tropical at INRIA Saclay – Île-de-France - CMAP, École polytechnique in Palaiseau, France. Prior to this, he was a Postdoctoral researcher in the Algorithmic Algebra group at the Institut für Mathematik, Technische Universität Berlin, led by Peter Bürgisser. In June 2019, he earned his PhD from Sorbonne Université, under the guidance of Jean-Charles Faugère and Elias Tsigaridas.
Bender's research focuses on polynomial systems, where he studies algorithms for solving them and their applications in various domains. His PhD thesis specifically dealt with effective algorithms for solving sparse polynomial systems using Gröbner bases and Resultants.
Back to the Roots Seminar Series
The ERC research project "Back to the roots of data-driven dynamical system identification", led by Prof. Dr. Bart De Moor (KU Leuven, ESAT-STADIUS), focuses on system identification, where mathematical models are derived from observed data generated by systems such as medical monitoring, electricity consumption and industrial processes. Utilizing optimization algorithms, one seeks to identify the best model in a chosen model class. This methodology finds widespread application across thousands of use cases within the AI community. However, there is no guarantee that optimization algorithms will find the best model. Present-day optimization practices are heuristic in nature, yielding results that may not be reproducible and consequently difficult to interpret.
The main objective of the Back to the Roots project is to develop a theoretical framework that combines model classes and optimization algorithms, enabling the calculation of the optimal model within the specified model class with 100% certainty.
Related courses
ESANN 2026: European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning.
Symposium - Brugge - ESANN
