Laurent Bartholdi

I'm a Professor at the Mathematical Institute of the Georg-August University of Göttingen.

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Address:: Laurent Bartholdi; Office 202, Mathematical Institute; Bunsenstraße 3-5; D-37073 Göttingen; Germany; Telephone: +49 551 39 7826; Secretary: +49 551 39 7752; Facsimile: +49 551 39 22674; E-Mail: laurent.bartholdi@gmail.com; Web: http://goo.gl/JJaZo or http://www.uni-math.gwdg.de/laurent

$LB in Abisko, March 2012$

News:: Groups in Action in Vercors (France), 26-31.8.2012

Publications (HTML), Google Scholar and arXiv

Curriculum vitae:: In HTML, TeX or PDF format .

I am currently interested in understanding fractal behaviour in group theory and algebra, and its use for holomorphic dynamical systems.

Self-similar, or fractal, objects abound in mathematics; depending on context, they mean a space containing several almost disjoint copies of itself as subspaces; a group containing the direct product of copies of itself as a subgroup; or an algebra containing a matrix algebra over itself as a subalgebra. The fractalness is algebraically encoded via the collection of inclusion maps of these subobjects in their common parent.

A self-similar group may be associated with any complex dynamical system, and yields an extremely potent algebraic invariant of that dynamical system up to isotopy and conjugation. I currently explore more deeply the connection between complex dynamics and fractal groups, and use it to extend the classification of degree-two polynomials (described by points in the Mandelbrot set) to arbitrary-degree rational functions.

Seminars:: Mathematical events; Department colloquium; GK colloquium

Courses:: Self-similar Lie algebras stud-ip access), Wed 12:15-14:00, Sitzungszimmer.; Lie Groups (in German; requires stud-ip access), Wed 14:15-16:00, Thu 10:15-12:00, Sitzungszimmer.

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Links:

The FR GAP-package, for manipulation of groups and semigroups generated by automata.
The Float GAP-package, for manipulation of real, complex, interval etc. floating-point numbers.
Göttingen collection of mathematical models
Slides I received from speakers in the conference "Trends and Directions in Conformal Dynamics" in Oberwolfach, October 17-21, 2008
Windows crashes in everyday life -- a commented photo gallery
Movies Movies illustrating the "twisted rabbit" paper in progress with V. Nekrashevych.
How I Rank in Hell
My Images
A movie I made (hi-rez) of the Schreier graph of the Gupta-Sidki group, in avi and MPEG-1 format.
Bibliography (BibTeX) of papers I'm interested in, in zip and tar.gz format.
LaTeX2e style file for sending notes in LaTeX to the CRAS (Comptes Rendus de l'Académie des Sciences de Paris), in zip and tar.gz format (contains G. Perec's article "Experimental... Cantatrix sopranica L." as a sample).