Viktor Levandovskyy (For) Students
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All flavours of non-commutative Gröbner and standard bases
Algorithms for finitely presented algebras
Algorithms for Ore localized algebras and for torsion
Local algorithms in D-module theory: standard bases over Weyl algebras, local Bernstein data (such as local Bernstein-Sato polynomial).
Normal forms for matrices over Euclidean Ore domains (especially over non-simple algebras) like Jacobson, Hermite, Popov and other forms
Multivariate polynomial factorization in non-commutative algebras of operators
Equidimensional (aka purity) filtration of finitely presented modules, applications to module decompositions, compatibility of purity filtration with central character decomposition of a module.
Ph.D. Theses
Johannes Hoffmann, RWTH Aachen, 2019: "Left saturation closure. Theory and algorithms"
Grischa Studzinski, RWTH Aachen, 2013: "Implementation and Applications of Fundamental Algorithms relying on Gröbner Bases in Free Associative Algebras"
Daniel Andres , RWTH Aachen, 2013: "Noncommutative Computer Algebra with Applications in Algebraic Analysis"
Kristina Schindelar (with Prof. Dr. Eva Zerz), RWTH Aachen, 2010 : "Algorithmic aspects of algebraic system theory"
Christian Dingler (with Prof. Dr. Gerhard Pfister), TU Kaiserslautern, 2010 : "Ein symbolischer Ansatz für finite Differenzenverfahren partieller Differentialgleichungen"
Master or Diploma Theses
Tobias Metzlaff, RWTH Aachen, 2019: "Computational Improvements for Non-Commutative Gröbner bases over Z/mZ"
Ömer Sali, RWTH Aachen, 2016: "Homomorphisms between equidimensional modules and applications"
Johannes Hoffmann, RWTH Aachen, 2016: "Ore localization, associated torsion and algorithms".
Malte Klegraf (with Prof. Dr. Eva Zerz), RWTH Aachen, 2015: Applications of general linear programming methods to monomial orderings in G-algebras.
Robert Löw (with Prof. Dr. Eva Zerz), RWTH Aachen, 2015: Bernstein-Sato ideals, associated stratifications, and computer-algebraic aspects.
Niclas Kruff (with Prof. Dr. Eva Zerz), RWTH Aachen, 2015: Ore localization with applications in D-module theory .
Florian Drescher (with Prof. Dr. Eva Zerz), RWTH Aachen, 2012 : "Constructive Theory of Bimodules with Applications. Gröbner basis theory of bimodules over the free algebra"
Ann Christina Foldenauer (with Prof. Dr. Eva Zerz), RWTH Aachen, 2012 : "Gröbner Bases for Bimodules and its Applications. Jacobson normal form in centerless Ore extensions and Gröbner Basis theory for Bimodules in G-algebras"
Albert Heinle (with Prof. Dr. Eva Zerz), RWTH Aachen, 2012 : "Factorization, Similarity and Matrix Normal Forms over certain Ore domains"
Christian.Schilli (with Prof. Dr. Eva Zerz), RWTH Aachen, 2012 : "Algorithmen zur Berechnung der Reinheitsfiltrierung eines Moduls und Anwendungen"
Daniel Andres (with Prof. Dr. Eva Zerz), RWTH Aachen, 2010 : "Algorithms for the computation of Sato's b-functions in algebraic D-module theory"
Grischa Studzinski (with Prof. Dr. Eva Zerz), RWTH Aachen, 2010 : "Dimension Computations in Non-Commutative Associative Algebras"
Olexander Motsak (with Prof. Dr. Gert-Martin Greuel), TU Kaiserslautern, 2006 : "Computation of the central elements and centralizers of sets of elements in non-commutative polynomial algebras"
Olexander Motsak (with Prof. Dr. Serhiy Ovsienko), National Kyiv Shevtchenko University, 2004
Bachelor Theses
Eva Maria Rehr, RWTH Aachen, 2021: "Systeme linearer Differenzengleichungen und deren Desingularisierung"
Lilly Nadol, RWTH Aachen, 2019: "Desingularisierung von Systemen linearer Differentialgleichungen"
Alexandra Schnitzer (with Prof. Dr. Eva Zerz and Dr. Johannes Hoffmann), RWTH Aachen, 2019: "Charakterisierung von Ringen über homologische Moduleigenschaften"
Karim Abou Zeid (with Prof.~Dr.~Erika Abraham), RWTH Aachen, 2019: "Letterplace Gröbner Bases, their Implementation and Applications"
Leonard Schmitz, RWTH Aachen, 2018: "Semiautomatisches Beweisen der algebraischen Matrizenidentitäten"
Johannes Hoffmann (with Prof. Dr. Eva Zerz), RWTH Aachen, 2014: "Konstruktive Berechnungen in Ore-lokalisierten G-Algebren"
Andre Ranft (with Prof. Dr. Eva Zerz), RWTH Aachen, 2014: "Hilbertpolynome von Moduln über nichtkommutativen G-Algebren"
Niclas Kruff (with Prof. Dr. Eva Zerz), RWTH Aachen, 2013: "Die Lazard-Methode zur Standardbasisberechnung in lokalen Weyl-Algebren"
Rene Kempen (with Prof. Dr. Eva Zerz), RWTH Aachen, 2013: "A Lie algebra approach to the Z-graded Weyl algebra"
Bastian Haase (with Prof. Dr. Eva Zerz), RWTH Aachen, 2013: "Multi-Letterplace Ring, Multi-Gradings and Applications"
Albert Heinle (with Prof. Dr. Eva Zerz), RWTH Aachen, 2010 : "Factorizing polynomials in a class of noncommutative algebras"
Jan Hackfeld (with Prof. Dr. Eva Zerz), RWTH Aachen, 2010 : "SAGBI bases for subalgebras generated by commuting elements"
University of Kassel Faculty10 Mathematik und NaturwissenschaftenInstitut für Mathematik