Symbolic computation lab · Athens & Istanbul
ALCYON stands for ALgorithms for Combinatorics, geometrY, Optimization and Number theory. We improve the mathematics behind algorithms and turn it into fast, careful software. We do this from two nodes, in Athens and Istanbul.
Athens node Αθήνα
The Athens node sits in the Department of Mathematics of the University of Athens. It works on the mathematics behind our algorithms, from polyhedral geometry and generating functions to symbolic linear algebra, and on mathdata, our system for representing mathematical objects.
Istanbul node İstanbul
The Istanbul node is where ALCYON started, at Gebze Technical University. It works on computer algebra and effective algebraic geometry, including real solving and Hermite methods, hosts most of our funded projects and theses, and ran the Symbolic Computation Istanbul Meetings (SCIM) from 2021 to 2023.
Algorithmic methods in commutative algebra, including the study of resultant systems.
Singularities, real solving and the algorithmic tools needed to explore them, such as Hermite matrices and their signatures.
Integer linear optimization. We use Polyhedral Omega to solve ILPs, and ILP to improve polynomial multiplication algorithms.
Efficient computation with polyhedra, and polyhedral methods that improve algorithms across combinatorics and algorithm design.
Computational questions and algorithmic tools arising from integer partitions.
Zafeirakis Zafeirakopoulos gives the talk Generating functions and interpolation at the 96th Séminaire Lotharingien de Combinatoire in Strobl, Austria.
Eugenia Maria Betsani, an undergraduate student in the Athens node, presents joint work with Zafeirakis Zafeirakopoulos at CASC 2026 in Bath, UK: Sparse multivariate interpolation and rational generating functions of polyhedra, on using sparse interpolation to efficiently compute rational generating functions of lattice points in polyhedra.
Our work with Mahmut Levent Doğan and Elias Tsigaridas, Small Resultant Systems via Linear Combinations, is now on arXiv.
Tülay Ayyıldız visits Sorbonne Université, Paris, in August–September 2026, hosted by Elias Tsigaridas, with a PRESTIJ Research Fellowship from the Embassy of France in Türkiye.
Sparse multivariate interpolation and rational generating functions of polyhedra
CASC 2026, 28th International Workshop on Computer Algebra in Scientific Computing, Bath, UK, 2026
Certified Real Eigenvalue Location
27th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2025), pp. 30–36, 2025
A Julia Package for Polyhedral Omega and Applications
ACM Communications in Computer Algebra 58(2) (ISSAC 2024 software presentation), 2024
PTOPO: Computing the geometry and the topology of parametric curves
Journal of Symbolic Computation, 2023 · PDF
