 |
|
|
|
|
|
|
|
|
|
(For) Students
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Hot Topics (contact me if you're interested)
|
|
Testing quasi-freeness of divisors
|
|
|
Local algorithms in D-module theory: standard bases over Weyl algebras,
local Bernstein data (like local Bernstein-Sato polynomial).
|
|
|
Gröbner bases for bimodules, bisyzygies and biresolutions
|
|
|
Normal forms for matrices over Euclidean Ore domains (e.g. Jacobson form over a
simple algebra and especially forms over non-simple algebras); Jacobson,
Hermite, Popov and other forms
|
|
|
Multivariate polynomial factorization in non-commutative algebras of operators,
admitting nontrivial gradings
|
|
|
Purity filtration of finitely presented modules, applications to module
decompositions, compatibility of purity filtration with central character
decomposition of a module.
|
|
|
Classification and description of groups of K(q)- and K-linear automorphisms of
quantum algebras (e.g. coordinate ring of quantum affine space, quantum Weyl
algebra). Actions of subgroups of the descibed above on quantum algebras.
|
|
|
Classification and isomorphy types of K-algebras, generated by x,y
subject to the relation yx= xy + f(y), f(y) in K[y].
|
|
|
|
Ph.D. Theses
|
|
|
Master or Diploma Theses
|
|
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,
"Computation of the central elements and centralizers of sets of elements in
non-commutative polynomial algebras" , 2006
|
|
|
Olexander Motsak
(with Prof. Dr. Serhiy Ovsienko), National Kyiv Shevtchenko University, 2004
|
|
|
|
Bachelor Theses
|
|
