Office: 726
Phone: +61 8 8313 6184
eMail: wolfgang.globke @ adelaide.edu.au
The University of Adelaide
School of Mathematical Sciences
Adelaide SA 5005
Australia
arXiv:1706.08735
Differential Geometry and its Applications 54 B, 2017, 475-489 (also arXiv:1611.08662)
Journal of Algebra 487, 2017, 200-216 (also arXiv:1606.01643)
to appear in International Mathematics Research Notices (also arXiv:1507.02575)
Journal of Geometry and Physics 108, 2016, 83-101 (also arXiv:1410.3572)
New York Journal of Mathematics 20, 2014, 441-446 (also arXiv:1312.2210)
Israel Journal of Mathematics 202, 2014, 255-274 (also arXiv:1211.1111)
Advances in Mathematics 240, 2013, 88-105 (also arXiv:1205.3285)
Proceedings of the American Mathematical Society 140, 2012, 2479-2488 (also arXiv:1009.3383)
Karlsruhe Institute of Technology, 2011
There are MuPAD files available to facilitate computations involving the non-abelian holonomy groups in dimensions 8 (geodesically incomplete) and 14 (geodesically complete) from part II of my thesis.
Universität Karlsruhe (TH), 2007
Addendum: The file Tables of Prehomogeneous Modules (pdf) contains all tables from my diploma thesis.
English translation of the course notes below, but still work in progress. Comments and corrections are very welcome!
Course Notes in German, 2012
This is a translation of Josef Dorfmeister and Max Koecher's long treatise on homogeneous domains and the associated relative invariants and algebras. I took the liberty of changing some of the fonts to be more to my liking, but the letters used to denote the objects in the text remained the same.
This is a translation of Hans Freudenthal's paper on octonion geometry (or "octaves", as he calls them) published in 1985.
This is a translation of Jacques Helmstetter's paper on left-symmetric algebras. The French original is difficult to obtain.
Jacques Helmstetter's second paper on left-symmetric algebras, which is a collection of several fundamental results in this field.
Hermite was the first to prove the transcendence of the Euler number in this article. The techniques developed to study the transcendence of numbers are to a large part inspired by Hermite's approach here.
This is a translation of the classical German paper Über eine bemerkenswerte Hermitesche Metrik written in 1932 by Erich Kähler. In this paper he introduced the special class of Riemannian metrics nowadays called Kähler metrics in his honour. Kähler's prose resembles that of a 19th century German academic, meaning it consists mostly of seemingly endless convoluted sentences. In translating I tried to stay as close as possible to his original notation and wording – after all, just because you do not speak German it does not mean you should not have to suffer, does it?
Another literary masterpiece by Erich Kähler from 1962. This paper develops the inner differential calculus, nowadays unfortunately often named geometric algebra. Kähler's contribution is often overlooked, even though he developed the theory independently of and more rigorously than similar developments at around the same time.
Max Koecher's curious text relates Riccati differential equations to Jordan algebras.
This is a translation of Domingo Luna's paper on closed orbits for reductive groups given the existence of an invariant scalar product, published in 1972.
Luna improves the previous paper and finds a slice theorem for the action of reductive algebraic groups on affine varieties, analogous to the slice theorem for compact Lie groups on differentiable manifolds.
A paper on Lie rings associated to finite groups. I thought this might be interesting, but now I'm not so sure.
A translation of Carl Ludwig Siegel's text Über Riemanns Nachlaß zur analytischen Zahlentheorie from 1932. This survey of Riemann's lost papers on his ideas and calculations on the zeta function was a kickstarter for the Riemann hypothesis business.
Wüstholz's seminal paper in the theory of transcendental numbers. Unfortunately it cites a lot from other papers that are available in German only.
This is a translation of Hans Zassenhaus's seminal paper on small group elements. It has become very influential in the theory of discrete subgroups of Lie groups. This paper is often mistakenly assigned the year 1938, but the issue was indeed published in 1937. Some typos were fixed and a few additional comments added.
This is a translation of a paper published in 1948 by Hans Zassenhaus. He develops an algorithm to generate all the space groups (crystallographic groups) for a given dimension n. In the translation I slightly changed the original notation for rings and fields by using the modern notation \(\mathbb{Z}\), \(\mathbb{Q}\) and \(\mathbb{R}\) for integer, rational and real numbers, respectively. Some typos were corrected and an index was added.
An analysis of Louis Auslander's infamous 1964 paper on flat affine manifolds. This paper gave rise to the conjecture that the fundamental group of every compact complete flat affine manifold is virtually polycyclic.
Mobile Robotics Lab (University of Karlsruhe), 2005
Seminar on Medical Simulation Systems (University of Karlsruhe), 2005
Seminar on Modern Software Development (University of Karlsruhe), 2005
Notes on a course given by Markus Grassl (University of Karlsruhe), 2005
Notes on a course given by Rainer Steinwandt (University of Karlsruhe), 2005
Seminar on Bioinformatics (University of Karlsruhe), 2001