ALCYON lab
ALgorithms forCombinatorics,
geometrY,
Optimization and
Number theory
| Home | Members | Projects | Publications | SCIM | Theses topics | Alumni |
In ALCYON (Algorithms for Combinatorics, Geometry, Optimization and Number Theory) we work on Symbolic Computation.
Both on the mathematics to improve algorithms and on the efficient (high performance) implementations of algorithms
in order to push mathematics further.
Symbolic Computation lies in the intersection of mathematics and computer science.
This means that it is both 100% mathematics and 100% computer science.
If you want to join us, fill in this form.
ALCYON participates in the Symbolic Computation Istanbul Meetings
If you are interested to work on a project (graduation project, master thesis, PhD, research project),
you can check possible thesis topics.
Computer Algebra
Algorithmic methods in commutative algebra is one of the main areas we work on. For example, in recent years we study the resultant system in detail.
Effective Algebraic Geometry
We work on singularities and algorithmic tools for their exploration.
Optimization
A major forus of our research is on Integer Linear Optimization (ILP). On one hand using Polhedral Omega for ILP, on the other hand using ILP for improving polynomial multiplication algorithms.
Polyhedral Geometry
We develop algorithms for efficient computation in polyhedral geometry. We also use polyhedral geometry to improve algorithms in different fields, e.g., combinatorics.
Number Theory
We are interested mostly in problems involving Integer Partitions. This rich area of number theory offers many scomputational challenges but also provides beautiful algorithmic tools.
News
| 01 July 2025 | ACA 2025 - Applications of Computer Algebra |
Events
| Applications of Computer Algebra 2025 | 01 July 2025 | Greece |
| Symbolic Computation: Algorithms, Learning and Engineering 2022 | 08 August 2022 | Turkey |
| Computer Algebra in Scientific Computing 2022 | 26 August 2022 | Turkey |
| Applications of Computer Algebra 2022 | 15 August 2022 | Turkey |
Members
| Fatma Karaoğlu | Faculty | Gebze TU |
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| Tulay Ayyildiz | Faculty | Gebze TU |
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| Elias Tsigaridas | Associate Faculty | Inria/IMJ-PRG |
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| Mohan Ravichandran | Associate Faculty |
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| Zafeirakis Zafeirakopoulos | Researcher | University of Geneva |
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| Deniz Naz Demirel | MSc Student | Middle East Technical University |
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| Baran Solmaz | MSc Student | Gebze TU |
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| Başak Karakaş | MSc Student | Gebze TU |
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| Ismail Tapan | Undergraduate Student | Gebze TU |
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Projects
| Ongoing | |||
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| 2022 Oct- 2025 Oct |
Polyhedral Omega: Generalizations and Applications - POGA | TUBITAK 1001 | ~50k euro |
| Concluded | |||
| 2019 Jun- 2022 Jun |
Gröbner Bases, Resultants and Polyhedral Geometry - GRAPE | Bilateral Project with France - TUBITAK 2509 | ~50k euro |
| 2017 Mar- 2019 Jul |
A system for efficient representation of mathematical data and benchmarking of mathematical software and algorithms | TUBITAK 3001 | ~17k euro |
| 2017 Oct- 2020 Oct |
Heterogeneous Algorithms for Combinatorics, Geometry, Optimization and Number Theory - HALCYON | TUBITAK 3501 | ~80k euro |
| 2019 Nov- 2021 Nov |
Zero dimensional Hermite method | TUBITAK 3501 | ~25k euro |
| 2018 Oct- 2020 Feb |
Algebraic Motion Planning | Reasearch Council of Gebze Technical University | ~3k euro |
| 2016 Aug- 2017 Feb |
Parallel Computation of Discrete and Continuous Volume | Reasearch Council of Gebze Technical University | ~3k euro |
Publications
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| 2020 | Daniel Slamanig, Elias P. Tsigaridas, Zafeirakis Zafeirakopoulos - "Mathematical Aspects of Computer and Information Sciences - 8th International Conference, MACIS 2019" - Springer LNCS. |
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| Journal Papers | ||||||||
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| 2023 | Christina Katsamaki, Fabrice Rouillier, Elias P. Tsigaridas, Zafeirakis Zafeirakopoulos - "PTOPO: Computing the geometry and the topology of parametric curves" - Journal of Symbolic Computation. |
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| 2017 | Felix Breuer, Zafeirakis Zafeirakopoulos - "Polyhedral Omega: a New Algorithm for Solving Linear Diophantine Systems" - Annals of Combinatorics. |
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| 2016 | Matthias Beck, Benjamin Braun, Matthias Köppe, Carla D. Savage, Zafeirakis Zafeirakopoulos - "Generating Functions and Triangulations for Lecture Hall Cones" - SIAM Journal on Discrete Mathematics. |
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| 2014 | Matthias Beck, Benjamin Braun, Matthias Köppe, Carla D. Savage, Zafeirakis Zafeirakopoulos - "s-Lecture hall partitions, self-reciprocal polynomials, and Gorenstein cones" - The Ramanujan Journal. |
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| 2014 | Angelos Mantzaflaris, Hamid Rahkooy, Zafeirakis Zafeirakopoulos - "Efficient computation of dual space and directional multiplicity of an isolated point" - Computer Aided Geometric Design. |
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| 2011 | Christos Koukouvinos, Veronika Pillwein, Dimitris E. Simos, Zafeirakis Zafeirakopoulos - "On the average complexity for the verification of compatible sequences" - Information Processing Letters. |
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| Talks (Invited & Symposia w/o Proceedings) |
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| Theses | ||||||||
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| 2019 | Nurdan Ünlü - "Toric h-numbers of dual hypersimplices and Chow-Betti numbers abd Ehrhart polynomials of Minkowski sums with segments" - MSGSU. |
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| 2019 | Büşra Sert - "A Study on the Chamber Complex" - MSGSU. |
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| 2012 | Zafeirakis Zafeirakopoulos - "Linear Diophantine Systems: Partition Analysis and Polyhedral Geometry" - Research Institute for Symbolic Computation / DK-compmath. |
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| 2008 | Zafeirakis Zafeirakopoulos - "Study and Benchmarks for Real Root Isolation methods" - Departments of Informatics and Telecommunication. |
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