AG Algebra, Geometrie und Computeralgebra

Prof. Dr. Wolfram Decker


Anschrift

Gottlieb-Daimler-Straße
Gebäude 48, Raum 435
67663 Kaiserslautern

Postfach 3049
67653 Kaiserslautern

Kontakt

Tel.: +49 631 205 2253
Fax: +49 631 205 4795
E-Mail: decker (at) mathematik.uni-kl.de

Forschungsinteressen

Ich interessiere mich für alle Aspekte der COMPUTERALGEBRA,
den Entwurf, die Implementierung und die Anwendung algebraischer
Algorithmen, wobei die ALGEBRAISCHE GEOMETRIE bei den Anwendungen
im Vordergrund steht. Mein besonderes Augenmerk gilt der ENTWICKLUNG
GROSSER COMPUTERALGEBRASYSTEME.

Dekan

Ich war von Februar 2014 bis März 2020 Dekan des Fachbereichs Mathematik.

Aktuelle Lehrveranstaltungen

Zusammen mit Gerhard Pfister biete ich regelmässig In der vorlesungsfreien Zeit Kurse am African Institute for Mathematical Sciences in Kapstadt an.

Curriculum Vitae

Software

Singular

Ich bin verantwortlich für die Entwicklung des Computeralgebrasystems SINGULAR.

OSCAR

Ich bin mitverantwortlich für die Entwicklung des Computeralgebrasystems OSCAR.

Publikationen

In Vorbereitung

  • Modular Techniques for Gröbner Bases over Rational Function Fields
    Dereje Kifle Boku, Wolfram Decker, Claus Fieker, Andreas Steenpass

Artikel

  • Computing integral bases via localization and Hensel lifting
    Janko Böhm, Wolfram Decker, Santiago Laplagne, Gerhard Pfister
    To appear in JSC Special Issue for MEGA 2019 https://doi.org/10.1016/j.jsc.2020.07.007
  • Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space
    Dominik Bendle, Janko Boehm, Wolfram Decker, Alessandro Georgoudis, Franz-Josef Pfreundt, Mirko Rahn, Pascal Wasser, Yang Zhang
    J. High Energ. Phys. 2020, 79 (2020) https://doi.org/10.1007/JHEP02(2020)079
  • Towards Massively Parallel Computations in Algebraic Geometry
    Janko Böhm, Wolfram Decker, Anne Frühbis-Krüger, Franz-Josef Pfreundt, Mirko Rahn, Lukas Ristau
    Found. Comput. Math. (2020) https://doi.org/10.1007/s10208-020-09464-x

  • Modular Techniques For Noncommutative Gröbner Bases
    Wolfram Decker, Christian Eder, Viktor Levandovskyy, Sharwan Tiwar
    Math.Comput.Sci. (2019) https://doi.org/10.1007/s11786-019-00412-9
  • Local to global algorithms for the Gorenstein adjoint ideal of a curve
    Janko Böhm, Wolfram Decker, Santiago Laplagne, Gerhard Pfister
    Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory, 51-96 (2017)
  • Bad primes in computational algebraic geometry
    Janko Böhm, Wolfram Decker, Claus Fieker, Santiago Laplagne, Gerhard Pfister
    International Congress on Mathematical Software, 93-101 (2016)
  • Current challenges in developing open source computer algebra systems
    Janko Böhm, Wolfram Decker, Simon Keicher, Yue Ren
    International Conference on Mathematical Aspects of Computer and Information, 3-24 (2015)
  • Gröbner bases over algebraic number fields
    Dereje Kifle Boku, Wolfram Decker, Claus Fieker, Andreas Steenpass
    Proceedings of the 2015 International Workshop on Parallel Symbolic Computation, 16-24 (2015)
  • The use of bad primes in rational reconstruction
    Janko Bölhm, Wolfram Decker, Claus Fieker, Gerhard Pfister
    Mathematics of Computation 84, 3013-3027 (2015)
  • Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety
    Daniel J. Bates, Wolfram Decker, Jonathon D. Hauenstein, John C. Peterson, Gerhard Pfister, Frank-Olaf Schreyer
    Applied Mathematics and Computation 231, 619-633 (2014)
  • Local analysis of Grauert--Remmert-type normalization algorithms
    Janko Böhm, Wolfram Decker, Mathias Schulze
    International Journal of Algebra and Computation 24, 69-94 (2014)
  • Parallel algorithms for normalization
    Janko Böhm, Wolfram Decker, Santiago Laplagne, Gerhard Pfister, Andreas Steenpass, Stefan Steidel
    Journal of Symbolic Computation 51, 99-114 (2013)
  • Sheaf algorithms using the exterior algebra
    Wolfram Decker, David Eisenbud
    Computations in algebraic geometry with Macaulay 2, 215-249 (2002)
  • Some introductory remarks on computer algebra
    Wolfram Decker
    European Congress of Mathematics, 121-142 (2001)
  • Computational algebraic geometry today
    Wolfram Decker, Frank-Olaf Schreyer
    Applications of algebraic geometry to coding theory, physics and computation,  65-119 (2001)
  • Non-general type surfaces in P4: Some remarks on bounds and constructions
    Wolfram Decker, Frank-Olaf Schreyer
    Journal of Symbolic Computation 29, 545-582 (2000)
  • The normalization: a new algorithm, implementation and comparisons
    Wolfram Decker, Theo de Jong, Gert-Martin Greuel, Gerhard Pfister
    Computational Methods for Representations of Groups and Algrebras, 177-185 (1999)
  • Primary decomposition: algorithms and comparisons
    Wolfram Decker, Gert-Martin Greuel, Gerhard Pfister
    Algorithmic algebra and number theory, 187-220 (1999)
  • An elliptic conic bundle in Ρ4 arising from a stable rank-3 vector bundle
    Hitachi Abo, Wolfram Decker, Nobuo Sasakura
    Mathematische Zeitschrift 229, 725-741 (1998)
  • Generating a noetherian normalization of the invariant ring of a finite group
    Wolfram Decker, Agnes E. Heydtmann, Frank-Olaf Schreyer
    Journal of Symbolic Computation 25, 727-731 (1998)
  • Gröbner bases and invariant theory
    Wolfram Decker, Theo de Jong
    London Mathematical Society Lecture Note Series, 61-89 (1998)
  • Syzygies of Abelian and Bielliptic Surfaces in P4
    Alf Aure, Wolfram Decker, Klaus Hulek, Sorin Popescu, Kristian Ranestad
    International Journal of Mathematics 8, 849-919 (1997)
  • On surfaces in P4 and 3-folds in P5
    Wolfram Decker, Sorin Popescu
    Vector Bundles in Algebraic Geometry, 69-100 (1993)
  • The Geometry of Bielliptic Surfaces in P4
    Alf Aure, Wolfram Decker, Klaus Hulek, Sorin Popescu, Kristian Ranestad
    International Journal of Mathematics 4, 873-902 (1993)
  • Construction of surfaces in P4
    Wolfram Decker, Lawrence Ein, Frank-Olaf Schreyer
    Journal of Algebraic Geometry 2, 185-237 (1993)
  • Geometry of the Horrocks bundles on P6
    Wolfram Decker, Nicolae Manolache, Frank-Olaf Schreyer
    Complex Projective Geometra: Selected Papers 179, 128 (1992)
  • Rank 2 vector bundles on P4 with c1 odd and contact curves
    Wolfram Decker, Mudumbai S. Narasimhan, Frank-Olaf Schreyer
    Mathematische Zeitschrift 205, 123-136 (1990)
  • Half-canonical surfaces in P4
    Wolfram Decker, Thomas Peternell, Joseph le Potier, Michael Schneider
    In: Sommese A.J., Biancofiore A., Livorni E.L. (eds) Algebraic Geometry, 91-110. Lecture Notes in Mathematics  1417 (1990)
  • Monads and cohomology modules of rank 3 vector bundles
    Wolfram Decker
    Algebraic Geometry, 7-17 (1990)
  • Pullbacks of the Horrocks-Mumford bundles
    Wolfram Decker, Frank-Olaf Schreyer
    Journal f. d. reine und angewandte Mathematik 382, 215-220 (1987)
  • On the uniqueness of the Horrocks-Mumford-bundle
    Wolfram Decker, Frank-Olaf Schreyer
    Mathematische Annalen 273, 415-443 (1986)
  • Stable rank 2 vector bundles with Chern-classes c1=-1, c2=4
    Wolfram Decker
    Mathematische Annalen 275, 481-500 (1984)
  • Das Horrocks-Mumford-Bündle und das Modul-Schema für stabile 2-Vektorbündel über P4 mit c1=-1, c2=4
    Wolfram Decker
    Mathematische Zeitschrift 188, 101-110 (1984)
  • Über den Modul-Raum für stabile 2-Vektor-Bündel über P3 mit c1=-1, c2=4
    Wolfram Decker
    manuscripta mathematica 42, 211-219 (1983)
  • Topologien auf Schnittmoduln kohärenter komplex-und-reell-analytischer Garben
    Wolfram Decker
    manuscripta mathematica 38, 59-76 (1982)

Bücher

  • A first course in computational algebraic geometry
    Wolfram Decker, Gerhard Pfister
    Cambridge University Press (2013)
  • Computing in Algebraic Geometry
    Wolfram Decker, Christoph Lossen
    Springer (2006)

 Tagungsbände

  • Singularities and Computer Algebra
    Wolfram Decker, Gerhard Pfister, Mathias Schulze
    Springer (2017)
  • Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory
    Gebhard Böckle, Wolfram Decker, Gunter Malle
    Springer (2017)
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