Construction of random points in moduli spaces and their geometry
Central software project: Interaction, high-performance and support (OSCAR)
SINGULAR: A new level of abstraction and performance

EU Horizon 2020 Projekt OpenDreamKit

EPSRC Grant Classification, Computation, and Construction: New Methods in Geometry

Algebraische Geometrie

TRR-Seminar Numerical Algebraic Geometry

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

In Vorbereitung

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

Artikel

• 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 2019https://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)