Publications

(Zentralblatt MATH, MathSciNet, Google Scholar, arXiv)

Preprints

1	H. Chau Nguyen, Sébastien Designolle, Mohamed Barakat and Otfried Gühne, Symmetries between measurements in quantum mechanics.

Refereed publications

23	Mohamed Barakat, Robin Brüser, Claus Fieker, Tobias Huber and Jan Piclum, Feynman integral reduction using Gröbner bases. Journal of High Energy Physics volume 2023, Article number: 168 (2023).
22	Mohamed Barakat and Lukas Kühne, Computing the nonfree locus of the moduli space of arrangements and Terao’s freeness conjecture. Math. Comp. 92 (2023), 1431-1452.
21	Mohamed Barakat and Markus Lange-Hegermann, An algorithmic approach to Chevalley’s Theorem on images of rational morphisms between affine varieties. Math. Comp., 91(333), (2022), 451–490.
20	Mohamed Barakat, Reimer Behrends, Christopher Jefferson, Lukas Kühne and Martin Leuner, On the generation of rank 3 simple matroids with an application to Terao’s freeness conjecture. SIAM J. Discrete Math., 35(2), (2021), 1201–1223.
19	Mohamed Barakat and Markus Lange-Hegermann, A constructive approach to the module of twisted global sections on relative projective spaces. Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, Springer, (2017) 23-49.
18	Takuro Abe, Mohamed Barakat, Michael Cuntz, Torsten Hoge, and Hiroaki Terao, The freeness of ideal subarrangements of Weyl arrangements. Journal of the Eur. Math. Soc. 18,6 (2016), 1339-1348.
17	Mohamed Barakat, On subdirect factors of a projective module and applications to system theory. Multidimensional Systems and Signal Processing 26,2 (2015), 339-348.
16	Mohamed Barakat and Markus Lange-Hegermann, On the Ext-computability of Serre quotient categories. Journal of Algebra 420 (2014), 333-349.
15	Mohamed Barakat and Markus Lange-Hegermann, Characterizing Serre quotients with no section functor and applications to coherent sheaves. Appl. Categor. Struct. 22,3 (2014), 457-466.
14	Mohamed Barakat and Markus Lange-Hegermann, On monads of exact reflective localizations of Abelian categories. Homology, Homotopy and Applications 15,2 (2013), 145-151.
13	Mohamed Barakat and Michael Cuntz, Coxeter and crystallographic arrangements are inductively free. Adv. Math. 229, no. 1 (2012), 691-709.
12	Mohamed Barakat and Markus Lange-Hegermann, An Axiomatic Setup for Algorithmic Homological Algebra and an Alternative Approach to Localization. J. Algebra Appl. 10, no. 2 (2011), 269-293.
11	Mohamed Barakat and Simon Görtzen, Simplicial cohomology of smooth orbifolds in GAP. Proceedings of the ICMS (Kobe, Japan), Lecture Notes in Computer Science 6327 (2010), 46-49.
10	Mohamed Barakat, Conley Index Theory. Proceedings of the MTNS (Budapest, Hungary) (2010), 1645-1651.
9	Mohamed Barakat, Purity Filtration and the Fine Structure of Autonomy. Proceedings of the MTNS (Budapest, Hungary) (2010), 1657-1661.
8	Mohamed Barakat and Stanislaus Maier-Paape, Computation of connection matrices using the software package conley. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 19, no. 9 (2009), 3033-3056.
7	Mohamed Barakat and Daniel Robertz, conley: computing connection matrices in Maple. J. Symbolic Comput. 44, no. 5 (2009), 540-557.
6	Mohamed Barakat and Daniel Robertz, homalg - A Meta-Package for Homological Algebra. J. Algebra Appl. 7, no. 3 (2008), 299-317.
5	Mohamed Barakat and Daniel Robertz, Computing invariants of multidimensional linear systems on an abstract homological level. MTNS Proceedings, Kyoto, Japan (2006), 542-559.
4	Mohamed Barakat and Daniel Robertz, homalg: First steps to an abstract package for homological algebra. EACA Proceedings, Sevilla, Spain (2006), 29-32.
3	Mohamed Barakat, The existence of Cartan connections and geometrizable principal bundles. Arch. Math. 83, no. 2 (2004), 159-163.
2	Mohamed Barakat, jets. A MAPLE-package for formal differential geometry. Computer algebra in scientific computing, (EACA Konstanz), Springer, Berlin (2001), 1-12.
1	Mohamed Barakat and Martin Oberlack, Reduction and long time behaviour of homogeneous turbulence under spatially constant mean-velocity gradient. Advances in turbulence VIII: Proc. of the 8th European Turbulence Conference, Barcelona, Spain (2000), 865-868.

Non-refereed publications

13	Mohamed Barakat, Robin Brüser, Tobias Huber and Jan Piclum, IBP reduction via Gröbner bases in a rational double-shift algebra. Proceedings of Science (Loops and Legs in Quantum Field Theory).
12	Mohamed Barakat, Tom Kuhmichel, and Fabian Zickgraf, CompilerForCAP - A category theory aware compiler; Building and compiling towers of categories.
11	Mohamed Barakat and Lukas Kühne, Investigating Terao’s freeness conjecture with computer algebra. Computeralgebra-Rundbrief (2021), 8-11.
10	Mohamed Barakat, Markus Lange-Hegermann and Sebastian Posur, Elimination via saturation.
9	Mohamed Barakat and Markus Lange-Hegermann, Gabriel morphisms and the computability of Serre quotients with applications to coherent sheaves.
8	Mohamed Barakat, Max Horn, Frank Lübeck, Oleksandr Motsak, Max Neunhöffer, and Hans Schönemann, The GAP package SingularInterface. Computeralgebra-Rundbrief (2014), 29-33.
7	Mohamed Barakat, Computations of unitary groups in characteristic 2. (for J.-P. Serre) (2013).
6	Mohamed Barakat, Computing Ext in Serre quotient categories. Mini-Workshop: Constructive Homological Algebra with Applications to Coherent Sheaves and Control Theory, MFO report no. 57 (2013), 19-21.
5	Mohamed Barakat and Markus Lange-Hegermann, The homalg project. Computeralgebra Rundbrief (2012), 6-9.
4	Mohamed Barakat, Jet groupoids and the invariance of geometric structures. Mini-Workshop: Algebraic and Analytic Techniques for Polynomial Vector Fields, MFO report no. 57 (2010), 19-21.
3	Mohamed Barakat, Spectral Sequences and Effective Computations. Mini-Workshop: Formal Methods in Commutative Algebra: A View Toward Constructive Homological Algebra, MFO report no. 50 (2009), 7-12.
2	Mohamed Barakat, Spectral filtrations via generalized morphisms.
1	Mohamed Barakat and Barbara Bremer, Higher extension modules and the Yoneda product.

Theses

Pro-nilpotente Lie Algebren. Diploma thesis, Lehrstuhl B für Mathematik, RWTH-Aachen University (October 1997).

Functional Spaces. A Direct Approach. PhD thesis, RWTH-Aachen University (January 2002).

The Homomorphism Theorem and Effective Computations. Habilitation thesis, RWTH-Aachen University (April 2009).