Arne Lorenz
From 2005 to 2009, I was a PhD student at Lehrstuhl B für Mathematik.
Contact
Research Areas
- Formal Theory of PDEs
- Differential Geometry
- Algebraic Geometry
Teaching
Publications
(arXiv)
- Articles (refereed)
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- Theses
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Jet Groupoids, Natural Bundles and the Vessiot Equivalence
Method, PhD thesis, March 2009 (pdf).
-
Leptoproduktion von t\bar{t} Quarks in der QCD bis zur Ordnung
alpha_s^2: Helizitätsamplituden für die Drei- und
Vierpartonzustände, June 2005, unpublished (Diploma
thesis in German), (pdf).
Projects (or contributions)
- jets (joined 2005 as coauthor, still active)
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http://wwwb.math.rwth-aachen.de/~barakat/jets
- Jet Groupoids (started 2005, still active)
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- homalg (joined the team
in 2008, see the seminar section)
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Talks
- Laplace Invariants
via Vessiot Equivalence Method
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Talk at the Workshop Differential Equations by Algebraic
Methods on February 6th, 2009 at RISC Linz (Austria).
The visit to RISC was financially supported by the SCIence project.
- Vessiot's Equivalence
Method Applied to Linear Partial Differential Operators
-
Talk in the Computer
Algebra Seminar on May 5th, 2008 at RISC Linz (Austria).
- Abstract de Rham Theorem
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Summer School on "Algorithmic
D-module theory", 3-7 September 2007, Kleinwalsertal (Austria).
- Generalities About Sheaves
(together with Sebastian Jambor)
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Summer School on "Algorithmic
D-module theory", 3-7 September 2007, Kleinwalsertal (Austria).
- Integrabilitätsbedingungen
in der Geometrie (in German)
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Kollegseminar Graduiertenkolleg
"Hierarchie und Symmetrie in mathematischen Modellen",
15.12.2007, Aachen.
Seminars
In summer term 2006, the article "Sheaf Algorithms Using the Exterior Algebra" [1] was
treated in the
institute seminar. See also [2] for additional information.
Together with Mohamed Barakat,
we produced some seminar notes (partly in
German). I have also implemented the algorithms to compute sheaf cohomology in a
Maple package `SheafAlgorithms` which uses the Maple version of homalg. It contains procedures to
calculate the Tate resolution described in [1]. An example worksheet may be
found here.
To compute sheaf cohomology, the package JanetOre by Daniel
Robertz was extended to support the exterior algebra.
All packages may be obtained from our software server http://wwwb.math.rwth-aachen.de:8040.
Literature
- [1] W. Decker, D. Eisenbud; Sheaf Algorithms Using the Exterior Algebra;
in: Computations in Algebraic Geometry with Macaulay 2; D. Eisenbud,
D. R. Grayson, M. Stillman, B. Sturmfels (Eds.)
- [2] D. Eisenbud, G. Fløystad und F. Schreyer; Sheaf Cohomology
and Free Resolutions over Exterior Algebras; Trans. AMS,
355(11):4297-4426
Physics
In june 2005, I graduated in physics at the
Institut für Theoretische
Physik E
under supervision of Professor W. Bernreuther.
Together with Marc Hitschfeld (now at: Universität
zu Köln, Fachgruppe Physik) I have written a Maple package TensorReduce for the reduction
of tensor integrals occurring in one-loop QFT calculations. The
package can be obtained from our software server.
Interesting Links
last modification: 2009/04/20,
Disclaimer
