Invited Talks
We are proud to present the invited speakers of CASC conference:
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Abdul Jarrah, American University of Sharjah, UAE
Title of the talk: Invariants of Polynomial Systems of ODEs
This talk will present recent algorithmic methods from computational algebra for studying polynomial systems of ordinary differential equations (ODEs) with emphasis on invariants, first integrals, time-reversibility, and their relation to Poincaré-Dulac normal forms. Algorithms for identifying generators of algebras of monomial and polynomial first integrals for systems with diagonal linear parts, including those with algebraic complex eigenvalues, will be presented. The talk will also explore the relationship between invariants of certain group actions and time-reversibility in two-dimensional polynomial systems with a resonant singularity, proposing algorithms to generate and analyze the Sibirsky ideal. These computational methods provide effective tools for studying integrability, symmetries, and invariant properties in nonlinear polynomial ODE systems.
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Ilias Kotsireas, Wilfrid Laurier University, Canada
Title of the talk: Constructive Combinatorics and Computer Algebra
The importance of interdisciplinary research can hardly be overstated. Cross-fertilization of research areas within Mathematics, Computer Science, Physics, and Engineering has been responsible for several such success stories. The objective of this talk is to present an instance of this phenomenon, that permeates the research career of the author for more than twenty years. In particular, we will discuss advances on periodic Golay pairs, an extremely challenging combinatorial problem, that can be formulated as a series of systems of polynomial equations, as a Linear Algebra problem, and as a Big Data problem. In the recently published work [1], we uncovered new structural properties of these objects, using Computer Algebra and high-performance computing. In recent unpublished on-going work [2], we are taking advantage of novel SAT formulations to tackle the search problem for these objects.
References
[1] New results on periodic Golay pairs
Tyler Lumsden, Ilias Kotsireas and Curtis Bright;
Math. Comp. DOI: https://doi.org/10.1090/mcom/4096
Published electronically: April 15, 2025.
[2] SAT formulations for periodic Golay pairs
Bernhard Andraschko, Ilias Kotsireas, Martin Kreuzer
(work in progress).