Prof. Dr. Michael Joswig

Office hour: currently by appointment only.

Research areas: geometric combinatorics, mathematical software

News

• 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 new polymake release 2.12 appeared 19 March 2012.
• Upcoming polymake workshop in Darmstadt 22-23 March 2012.

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 Komei Fukuda, Joris van der Hoeven, and Nobuki Takayama, eds.): Mathematical Software - ICMS 2010, Proceedings, LNCS 6327, Springer 2010
• (with Thorsten Theobald): Algorithmic Geometry [German], Vieweg 2008
• (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

DFG Graduate School "Computational Engineering"

Engineering applications are becoming more and more complex. Consequently, the theory required to analyse corresponding systems becomes increasingly complicated as well. Experimental investigations are often too complex, too risky, or too costly. Computational Engineering (CE), including computer based modeling, analysis, simulation, and optimization, is a cost effective and efficient alternative to investigate engineering applications and to engineer new technical solutions.

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 2.10 (released June 9, 2011) is described on the polymake news page.
• We had our first polymake meeting in Darmstadt, 31 March - 1 April 2011. Tutorials and Examples from the presentations are still online.

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

• Tropical Geometry, ICMS, Edinburgh, UK, 2-6 April 2012
• "Triangulations", Oberwolfach, 29 April - 4 May 2012
• Minisymposium on Publicly Available Geometric/Topological Software, UNC Chapel Hill, 17 June 2012
• "Discrete Differential Geometry", Oberwolfach, 8-14 July 2012
• 21st International Symposium on Mathematical Programming, Berlin, 19-24 August 2012
• MEGA 2013, Frankfurt, 3-7 June 2013

Recent Talks

• "Highly Symmetric Integer Linear Programs", UC Davis, 2 September 2011
• "Splitting Polytopes", SFSU, 14 September 2011
• "Splitting Polytopes", UCLA, 6 October 2011
• "Totally Splittable Polytopes", ERC Workshop, FU Berlin, 24 October 2011
• "Dressians, Tropical Grassmannians, and Their Rays", CIEM, Castro Urdiales, 14 December 2011

Incoming Guests

• Arnau Padrol (UPC Barcelona), 18 April 2012
• Julian Pfeifle (UPC Barcelona), 27 April 2012
• Ben Burton (U Queensland), 7 May 2012
• Stephan Tillmann (U Sydney), 7 May 2012

Editorial Board Membership

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

Teaching and Seminars

• Discrete Mathematics [04-00-0137-vu], VL 4+2. [notes] [EVS]
• Algorithmic Discrete Mathematics [04-00-0208-se], SE 2

• Mathematics for Mechanical Engineering II [04-00-0076-vu], VL 4+2 (9CP). [notes] [EVS page]
• Linear Algorithmic Geometry [04-00-0287-vu], VL 2+1 (4.5CP).

Results for the written exam "Mathe I MB" (Friday, 14 Oct 2011).

Previous Terms

Previous Projects