Prof. Dr. Michael Joswig

Next Office Hours:
Wednesday, 15 May, 9:30 - 12:30 (for seminar)
Tuesday, 21 May, 14:00 - 15:00
Tuesday, 28 May, 15:00 - 16:00

Research areas: geometric combinatorics, mathematical software

News

• Fall School "Tropical and Polyhedral Combinatorics"
• I am working on a forthcoming book "Essentials of Tropical Combinatorics". Take a look at the web page with a first draft and send comments.
• The polymake release 2.12 appeared in March 2012. Next version 2.13 due in early 2013.

Publications

• complete list of publications
• publications according to Mathematical Reviews
• publications according to Zentralblatt MATH
• Preprints via UC Davis front end to the arXiv

Books

• (with Thorsten Theobald): Polyhedral and Algebraic Methods in Computational Geometry, Springer 2013, translated and revised from Algorithmische Geometrie [German], Vieweg 2008.
• (with Komei Fukuda, Joris van der Hoeven, and Nobuki Takayama, eds.): Mathematical Software - ICMS 2010, Proceedings, LNCS 6327, Springer 2010
• (with Nobuki Takayama, eds.): Algebra, Geometry, and Software Systems, Springer 2003

Projects

Click on an icon for more detailed information about a project.

Decompositions of Lattice Polytopes

Lattice polytopes are objects at a junction between combinatorics and algebraic geometry. The study of their triangulations, coarsest subdivisions, mixed subdivisions, and other decompositions is motivated by the mutual interaction between these fields as well as by applications in number theory, optimization, statistics, mathematical physics, and algorithmic biology.

Project in the DFG Priority Program SPP 1489. Research assistant: Andreas Paffenholz.

Related:

• Tight Spans of Finite Metric Spaces
• Defect Polytopes and Counter-Examples With polymake

Mathematical Software

Specialized software is the key tool to help the mind doing research in mathematics. At the same time mathematical software bridges the gap between the diverse fields of mathematics and their application areas.

polymake

polymake is a software system for convex polytopes, simplicial complexes, and more. Co-authored with Ewgenij Gawrilow (now TomTom) and actively supported by many people [BibTeX-Entry]. If you are interested to see how polymake can be used, see the documentation or this extra page with references.

• The most recent version 2.12 (released March 25, 2012) is described on the polymake news page.
• Get an idea of how to use the system from the polymake Miscellanea.

Electronic Geometry Models

This is an Electronic Journal for discrete and differential (and other) geometry. Joint work with Konrad Polthier.

RealLie

This is a small program which computes real representations of quasi-simple Lie groups. It is quite old but still functional and occasionally useful. Joint work with Richard Bödi.

Upcoming Events

• MEGA 2013, Frankfurt, 3-7 June 2013
• FPSAC 2013, Paris, France, 24-28 June 2013
• Mathematical Congress of the Americas, Guanajuato, Mexico, 5-9 Aug 2013
• 18th ÖMG Congress and Annual DMV Meeting, Innsbruck, Austria, 23-27 Sep 2013
• Delaunay Geometry: Polytopes, Triangulations and Spheres, FU Berlin, 7-9 Oct 2013

Recent Talks

• "Tropical Combinatorics", U Sydney, Australia, 30 November 2012
• "polymake for High-Dimensional Computational Geometry", CGL Review Meeting, Berlin, 13 December 2012
• "Lattice Polygons and Real Roots", U Saarbrücken, 1 February 2013

Editorial Work

• Mitteilungen der DMV, Editor-in-Chief

• Advances in Geometry
• Beiträge zur Algebra und Geometrie
• Electronic Geometry Models

Teaching and Seminars

• Discrete Optimization, VL 4+2.
• Discrete Mathematics, SE 2.

Previous Terms

Previous Projects