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