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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.
CASC 2020  Computer Algebra in Scientific Computing 
ALCYON lab Opening! See you there! 
NEMO kick off 
Machine Learning and Computer Algebra  18 July 2020  Greece 
Polytopes  Algebra  Computation  18 July 2020  Greece 
NEMO kickoff  23 January 2020  GTU 
Zafeirakis Zafeirakopoulos  Faculty  Gebze TU 


Elias Tsigaridas  Associate Faculty  Inria/IMJPRG 


Mohan Ravichandran  Associate Faculty  Bogazici University 


Tulay Ayyildiz Akoglu  Associate Faculty  Karadeniz TU 


Gizem Süngü  PhD Student  Gebze TU 


Başak Karakaş  MSc Student  Gebze TU 


Meryem Özkan  MSc Student  Gebze TU 


Umutcan Önal  MSc Student  Gebze TU 


Nurgül Kangal  Undergraduate Student  MSGSU 

Büşra Sert  MSc Student  MSGSU 


Nurdan Ünlü  MSc Student  MSGSU 

Ongoing  

2019 Jun 2021 Jun 
Gröbner Bases, Resultants and Polyhedral Geometry  GRAPE  Bilateral Project with France  TUBITAK 2509  ~50k euro 
2017 Oct 2020 Oct 
Heterogeneous Algorithms for Combinatorics, Geometry, Optimization and Number Theory  HALCYON  TUBITAK 3501  ~80k euro 
2018 Oct 2020 Feb 
Algebraic Motion Planning  Reasearch Council of Gebze Technical University  ~3k euro 
Concluded  
2017 Mar 2019 Jul 
A system for efficient representation of mathematical data and benchmarking of mathematical software and algorithms  TUBITAK 3001  ~17k euro 
2016 Aug 2017 Feb 
Parallel Computation of Discrete and Continuous Volume  Reasearch Council of Gebze Technical University  ~3k euro 
2019 

Journal Papers  

2014  Matthias Beck, Benjamin Braun, Matthias Köppe, Carla D. Savage, Zafeirakis Zafeirakopoulos  "sLecture hall partitions, selfreciprocal polynomials, and Gorenstein cones"  The Ramanujan Journal. 


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. 


2017  Felix Breuer, Zafeirakis Zafeirakopoulos  "Polyhedral Omega: a New Algorithm for Solving Linear Diophantine Systems"  Annals of Combinatorics. 


2014  Angelos Mantzaflaris, Hamid Rahkooy, Zafeirakis Zafeirakopoulos  "Efficient computation of dual space and directional multiplicity of an isolated point"  Computer Aided Geometric Design. 


2014  Christos Koukouvinos, Veronika Pillwein, Dimitris E. Simos, Zafeirakis Zafeirakopoulos  "On the average complexity for the verification of compatible sequences"  Information Processing Letters. 

Talks (Invited & Symposia w/o Proceedings) 

Theses  

2012  Zafeirakis Zafeirakopoulos  "Linear Diophantine Systems: Partition Analysis and Polyhedral Geometry"  Research Institute for Symbolic Computation / DKcompmath. 


2008  Zafeirakis Zafeirakopoulos  "Study and Benchmarks for Real Root Isolation methods"  Departments of Informatics and Telecommunication. 

Use machine learning for predicting statistics or properties of polynomials. The main goal is to find appropriate encodings of polynomials and answer questions such as the number of real roots, the distance of the closest real roots, the existence of double roots etc.
You have to try and compare different architectures and design an interface that will be easy to use for the predictions you cover.
Design a system that parses code in Python and C/C++ in order to create a list of citations. Functions in libraries will be decorated by something like: @citation{KnuthTAOCP} Then your system will compile a list of all citations used by an input program (based on which functions are called).
You need basic understanding of compilation, programming in C/C++ and Python. For the citations we will use the standard bibtex format.