Discrete Geometry, WS 04/05

Michael Joswig, Fachbereich Mathematik, TU Darmstadt.

VL 2+1: Tuesday, 16:15-17:55, S3 06/052. Exercise (irregularly, as announced in the lecture): Wednesday, 8:00-9:40, S2 15/301.

Some General References

  1. Martin Aigner and Günter M. Ziegler: Proofs from the Book, 3rd edition, Springer, 2003.
  2. Branko Grünbaum: Convex Polytopes, (2nd edition with comments by Volker Kaibel, Victor Klee, and Günter M. Ziegler), Springer, 2003.
  3. Michael Joswig and Nobuki Takayama (eds.): Algebra, Geometry, and Software Systems, Springer, 2002.
  4. Jiri Matousek: Lectures on Discrete Geometry, Springer, 2002.
  5. Günter M. Ziegler: Lectures on Polytopes, Springer, 1995.

Selected Tropical Geometry References

  1. Mike Develin, Francisco Santos, and Bernd Sturmfels: On the rank of a tropical matrix, arxiv.org/math.CO/0312114, MSRI Proceedings, to appear.
  2. Mike Develin and Bernd Sturmfels: Tropical Convexity, Documenta Math. 9 (2004), 1-27.
  3. Michael Joswig: Tropical Halfspaces, arxiv.org/math.CO/0312068, MSRI Proceedings, to appear.
  4. Ki Hang Kim and Fred W. Roush: Factorization of polynomials in one variable over the tropical semiring, arxiv.org/math.CO/0501167.
  5. Grigory Mikhalkin: Enumerative tropical algebraic geometry in R2, arxiv.org/math.AG/0312530, J. AMS, to appear.
  6. Jürgen Richter-Gebert, Bernd Sturmfels, and Thorsten Theobald: First steps in tropical geometry, arxiv.org/math.AG/0306366, Contemp. Math., AMS, to appear.
  7. Lior Pachter and Bernd Sturmfels: Tropical Geometry of Statistical Models, arxiv.org/q-bio.QM/0311009.
  8. Frank Sottile: Tropical Geometry, arxiv.org/math.AG/0501146.
  9. David Speyer: Tropical Linear Spaces, arxiv.org/math.CO/0410455.
  10. David Speyer and Bernd Sturmfels: Tropical Mathematics, arxiv.org/math.CO/0408099.
  11. Thorsten Theobald: On the frontiers of polynomial computations in tropical geometry, arxiv.org/math.CO/0411012

... and a list of open problems maintained by Mike Develin.

Additional Remarks

  • Cauchy's Rigidity Theorem says that 3-dimensional convex polytopes are not flexible. For a proof see "Proofs from the Book", Chapter 12.
  • polymake

    polymake, version 2.1.0, is installed on the machines in the pool. In order to be able to use it you should follow these instructions:

    Visit polymake's homepage for updates etc.

    Polytope examples and more to be found on the Electronic Geometry Models server.

    Michael Joswig, email: lastname at mathematik.tu-darmstadt.de
    Last modified: Tue Feb 1 19:04:43 CET 2005