Viktor Levandovskyy (For) Students
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Hot Topics (contact me if you're interested)
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
Purity filtration of finitely presented modules, applications to module decompositions, compatibility of purity filtration with central character decomposition of a module.
Ph.D. Theses
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
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
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"
RWTH Aachen University Division of Mathematics Lehrstuhl B für Mathematik