(From Divisibility to RSA Cryptosystems)
Lecture Notes, 47+ii pp, pdf (German)
Joint Work with L. Mischke, W. Pöttker
(Elementary Cartography)
Textbook, (German) - in progress
(Elementary Analysis: A Three-Term Course)
Lecture notes, 343 pp, pdf (German)
(Differential Geometry I: Curves and Surfaces)
Lecture notes, 130 pp, pdf (German)
(Preliminary course in mathematics)
Lecture notes, 105 pp, pdf (German)
(Linear algebra on spaces with anti-commuting coefficients)
Lecture notes, 29 pp, pdf (German)
(Linear algebra on spaces with anti-commuting coefficients)
Notes from a lecture given at a joint seminar of the groups Differential Geometry and Theoretical Physics III, TU Dortmund
Lecture notes, 14 pp, pdf
(Teaching material for math classes)
Teil 1:
Grundlagen I (Arithmetik), Grundlagen II (Algebra)
Teil 2:
Analysis I (Funktionenklassen), Analysis II (Differentiation und Integration)
Teil 3:
Geometrie I (Elementargeometrie), Geometrie II (Analytische Geometrie)
Teil 4:
Statistik, Stochastik und Elementare Zahlentheorie
(Teaching material for physics classes)
Teil 1: Grundlagen
Teil 2: Dynamik: Kraft und Energie
Teil 3: Kinematik: Einfache Bewegungen
Teil 4: Hydrostatik
(Useful properties of Möbius transformations)
pdf (German), 5 pp
(On the property \( (AB)^{+} = B^{+}A^{+} \) of the Moore-Penrose Inverse)
pdf (German), 5 pp
(Trace free matrices as commutators)
pdf (German), 9 pp
(The Gauß line)
pdf (German), 4 pp
(An efficient way to calculate a basis of sum and intersection of two vector spaces)
pdf (German), 4 pp
Math. Semesterber. 64 (2017) no. 1, 25-39
Joint work with R. Gäer, Schniewindt GmbH & Co. KG and C. Eggert, ThyssenKrupp Rothe Erde GmbH
Abstract:
(An optimized smoothing method motivated by a technical problem)
Math. Semesterber. 59 (2012) no. 1, 29-55, German
Joint work with G. Skoruppa, in cooperation with W. Kranz, Kranz Software Engineering
Abstract:
Technische Universität Dortmund, 2013 (Advisor: Prof. Dr. Lorenz Schwachhöfer)
Abstract:
In this work, we systematically analyze supersymmetry on solvable Lorentzian
symmetric spaces. We provide explicit conditions under which spinor connections admit supersymmetry
by describing the underlying Lie bracket structure. We introduce the necessary notions and tools for
flat connections and, on this basis, establish that in all dimensions up to eleven, nontrivial and at
most canonically restricted irreducible supersymmetries exist. Moreover, we extend the examples known
from the literature to a complete classification and supplement it with a full catalogue of N=2
extended natural supersymmetries.
By presenting further examples—including cases with N>2, non-natural, non-canonically restricted,
and non-flat supersymmetries—we illustrate how our framework applies to the general situation.
In particular, we demonstrate that in any dimension admitting an irreducible super extension, a
nontrivial 3/4-restricted supersymmetry is possible.
Universität Leipzig, 2003 (Advisor: Prof. Dr. Hans-Bert Rademacher)
Abstract:
In this thesis, we combine the notions of supergeometry with supersymmetry. We construct a
special class of supermanifolds whose reduced manifolds are (pseudo-)Riemannian manifolds,
thereby allowing vector fields and spinor fields to be treated as equivalent geometric objects.
This serves as the starting point for our definition of supersymmetric Killing structures.
The latter combines subspaces of vector fields and spinor fields, provided they satisfy certain
field equations. This naturally leads to a superalgebra that extends the supersymmetry algebra
to the setting of non-flat reduced spaces.
We examine in detail the additional terms that arise in this structure, the so-called center
of the supersymmetric Killing structure. Furthermore, we provide numerous examples, emphasizing
those in which the center takes a particularly simple form.
(Connections on Principal Bundles and Instantons on S⁴)
Universität Osnabrück, 2000 (Advisor: Prof. Dr. Heinz Spindler)
Abstract:
In the first part of the thesis, the various concepts of connections in differential
geometry are examined. It is shown that connections on manifolds and on vector bundles
are in one-to-one correspondence with those on principal bundles.
The second part focuses on a special class of connections: the self-dual connections on
SU(2)-principal bundles over the four-sphere S4 with integral second Chern class c2=−k.
These are the k-instantons.
(Kepler's barrel rule and numerical quadrature)
2010, 28 pp, pdf (German)
A preprint of sections 1+2 has been published in Mathematik-Seminar des Freistaates Sachsen, Heft Sayda, Leipzig, 2001.
Abstract:
Wir präsentieren hier einen Vorschlag für eine motivierende Einführung in die Volumenberechnung mit
Integralen sowie in die Theorie der Quadraturformeln. Der Übergang zwischen beiden Schwerpunkten
erfolgt durch eine ausführliche Diskussion der Keplerschen Fassregel.
Der Text richtet sich einerseits an Lehrende im Übergangsfeld zwischen Schule und Studium,
und andererseits an mathematikinteressierte Schülerinnen und Schüler mit Grundkenntnissen über
Zahlenfolgen sowie in der Differentialrechnung.
Die Kapitel 1 und 2 basieren auf einer erprobten Lehreinheit im Rahmen eines Wochenendseminars
der Leipziger Schülergesellschaft für Mathematik in Bennewitz (Oktober 2000).
Die vorliegende Fassung stellt eine erweiterte Ausarbeitung eines Seminars im Schülerzirkel
der Technischen Universität Dortmund (September 2009) dar.
(Appendix to "Supersymmetric Killing structures")
2003, 4 pp, pdf
Abstract: We use the notations introduced in [Klinker, F.: Supersymmetric Killing Structures] to explain how we derive the signs cf. Table 3 therein. The calculations below constitue an extended version of the calculations for the Lorentzian case are based on [Scherk, J.: Extended supersymmetry and extended supergravity theories].
2002, 7 pp, arXiv:math.DG/0212058
Abstract: In this note, we compare the spinor bundle of a Riemannian manifold (M = M1 ×· · ·× MN , g) with the spinor bundles of the Riemannian factors (Mi, gi). We show that - without any holonomy conditions - the spinor bundle of (M, g) is for a certain class of metrics isomorphic to a bundle obtained by tensoring the spinor bundles of (Mi, gi) in an appropriate way. For N=2 and a one dimensional factor, this construction was developed in [Baum 1989a]. Although this fact for general factors is frequently used in the physics literature, to the best of our knowledge, a proof has been missing.