Markus Lange-Hegermann

Email: markus at momo.math.rwth-aachen.de

I am a PhD student at the Lehrstuhl B für Mathematik. My research interests are in commutative algebra, differential algebra and homological algebra, especially computational aspects. My advisor is Wilhelm Plesken.

Publications

• Algorithmic Thomas Decomposition of Algebraic and Differential Systems (accepted, preprint). (together with Thomas Bächler, Vladimir Gerdt and, Daniel Robertz)
• Thomas Decomposition of Algebraic and Differential Systems, CASC 2010 Proceedings, Tsakhkadzor, Armenia. (arXiv) (together with Thomas Bächler, Vladimir Gerdt and, Daniel Robertz)
• An Axiomatic Setup for Algorithmic Homological Algebra and an Alternative Approach to Localization (Journal of Algebra and its Applications 10,2 (2011), 269-293). (arXiv, doi) (together with Mohamed Barakat)

Conferences, Talks, Poster and Workshops

• Invited talk at the Oberseminar Computational Mathematics at the University of Kassel about "Thomas Decomposition of Differential Systems", 10.1.2012
• Workshop Variation of Cohomology: D-Modules, Monodromy and Arithmetic
• FELIM 2011; [talk about Thomas Decomposition]
• Schwerpunkttagung Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory
• Constructive homological algebra methods, implementations and applications, CIRM, Luminy; [talk "The Cohomology of Coherent Sheaves"]
• Nikolaus Conference 2010
• CASC 2010; [talk about Thomas Decomposition]
• ISSAC 2010; [software presentation about LocalizeRingForHomalg], [ACM SIGSAM Bulletin for the software presentation], [poster about Thomas decomposition], [ACM SIGSAM Bulletin for the poster]
• Sage Days 23.5; [talk about LocalizeRingForHomalg]
• Nikolaus Conference 2009; [talk about LocalizeRingForHomalg and GAP]
• Nikolaus Conference 2008

Software

DifferentialThomas

I am implementing the differential case of the Thomas decomposition of (partial) differential systems in Maple. The package can be found here: [homepage]

homalg-project

I am taking part in the homalg-project. I have worked on many of the core pcakges, but am mostly responsible for the packages GradedModules and LocalizeRingForHomalg.

PrimDecomp

PrimDecomp is a little piece of code for computing primary decomposition used in Anna Fabianska's PSL package

Simulation of a Pendulum

A little simulation of a pendulum I wrote together with Thomas Bächler and Marcel Wallraff during our diploma studies.

Teaching

• Winter term 2011/2012: Computer practica for math students
• Summer term 2011: Computer practica for math students
• Winter term 2010/2011: Exercises for cohomology of coherent sheaves (Kohomologie kohärenter Garben)
• Winter term 2010/2011: Computer practica for math students
• Summer term 2010: Computer practica for math students
• Winter term 2009/2010: Computer practica for math students
• Summer term 2009: Computer practica for math students
• Winter term 2008/2009: Computer practica for math students
• Summer term 2008: Student assistent for linear algebra
• Winter term 2007/2008: Student assistent for computer practica for math students
• Summer term 2007: Student assistent for computer practica for math students
• Winter term 2006/2007: Student assistent for computer practica for math students
• Winter term 2005/2006: Student assistent for linear algebra

I am also taking part in offering courses for pupils from nearby schools