Department of Mathematics

Prof. Dr. Wolfram Decker

Contact

Tel.: +49 631 205 2253
Fax: +49 631 205 4795 

E-Mail: wolfram.decker (at) rptu.de

Address

Gottlieb-Daimler-Straße
Building 48, Room 435
67663 Kaiserslautern

Research Interests

I am interested in all aspects of computer algebra,
the design, implementation and application of algebraic
algorithms, focussing on algebraic geometry in the applications.

I am particularly interested in the development of large computer algebra systems.


Algebra, Geometry and Computer Algebra Group

Publications

In Vorbereitung / In Preparation
  • Modular Techniques for Gröbner Bases over Rational Function Fields
    Dereje Kifle Boku, Wolfram Decker, Claus Fieker, Andreas Steenpass
Artikel / Articles
  • Commutative algebra and algebraic geometry
    Janko Böhm, Wolfram Decker, Frank-Olaf Schreyer
    Chapter in: The Computer Algebra System OSCAR: Algorithms and Examples, 21-79 (2025)
  • Invariant Theory
    Wolfram Decker, Lakshmi Ramesh, Johannes Schmitt
    Chapter in: The Computer Algebra System OSCAR: Algorithms and Examples, 297-331 (2025)
  • Module Intersection for the Integration-by-Parts Reduction of Multi-Loop Feynman Integrals
    Dominik Bendle, Janko Boehm, Wolfram Decker, Alessandro Georgoudis, Franz-Josef Pfreundt, Mirko Rahn, Yang Zhang
    To appear in the proceedings of the conference "MathemAmplitude 2019" in Padova, Italy (Proceedings of Science) https://arxiv.org/abs/2010.06895
  • 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 / Books
  • The Computer Algebra System OSCAR: Algorithms and Examples
    Wolfram Decker, Christian Eder, Claus Fieker, Max Horn, Michael Joswig, eds.
    Algorithms and Computation in Mathematics, Springer (2025)
  • 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 / Conference Proceedings
  • 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)

Curriculum Vitae

1953  born in Kusel
1971-1977 Studied mathematics at the University of Kaiserslautern
1977  Diploma in Mathematics
1978-1984 Research assistant at the University of Kaiserslautern
1984 Ph.D. at the University of Kaiserslautern
1984-1990 Assistant Professor (C1) at the University of Kaiserslautern
1989  Habilitation at the University of Kaiserslautern
1990-2009  Professor (C3) at Saarland University
2000-2004 Chair of the programme management committee of EAGER
since 2009 Professor (W3) at TU Kaiserslautern (today: RPTU)
2010-2016 Coordinator of the DFG-SPP 1489
2014-2020 Dean of the Department of Mathematics
2017-2024 Co-Speaker of the SFB-TRR 195
2019-2023 Senior research professor at TU Kaiserslautern (today: RPTU)
since 2009 Leading member of the SINGULAR development team
since 2018 Leading member of the OSCAR development team

  1. Sorin Popescu (1993): "On Smooth Surfaces of Degree ≥ in P4".
  2. Michael Messollen (1998): "Polynomfaktorisierung und charakteristische Mengen über endlichen Körpern".
  3. Hirotachi Abo (2002): "Rank Two and Rank Three Vector Bundles on the Projective Fourspace".
  4. Holger Cröni (2002): "Zur Berechnung von Kovarianten von Quantiken".
  5. I. Made Sulandra (2003): "Über Gröbnerwalkalgorithmen".
  6. Michael Kunte (2008): "Gorenstein Modules of Finite Length".
  7. Ngoc Anh Pham (2013): "Implementing Intersection Theory".
  8. Hiep Tuan Dang (2014): "Intersection theory with applications to the computation of Gromov-Witten invariants".
  9. Andreas Steenpaß (2014): "Algorithms in SINGULAR: Parallelization, Syzygies, and Singularities".
  10. Dereje Kifle Boku (2014): "Gröbner Bases over Extension Fields of Q".
  11. Sharwan Kumar Tiwari (2017): "Algorithms in Noncommutative Algebras: Gröbner Bases and Hilbert Series".
  12. Isabel Christine Stenger (2018): "A Homological Approach to Numerical Godeaux Surfaces".
  13. Lukas Ristau (2019): "Using Petri nets to parallelize algebraic algorithms".