Discrete Geometry, WS 04/05
Michael Joswig, Fachbereich Mathematik, TU Darmstadt.
VL 2+1: Tuesday, 16:1517:55, S3 06/052. Exercise (irregularly,
as announced in the lecture): Wednesday, 8:009:40, S2 15/301.
Some General References
 Martin Aigner and Günter M. Ziegler: Proofs from the
Book, 3rd edition, Springer, 2003.
 Branko Grünbaum: Convex Polytopes, (2nd edition with
comments by Volker Kaibel, Victor Klee, and Günter
M. Ziegler), Springer, 2003.
 Michael Joswig and Nobuki Takayama (eds.): Algebra,
Geometry, and Software Systems, Springer, 2002.
 Jiri Matousek: Lectures on Discrete Geometry, Springer, 2002.
 Günter M. Ziegler: Lectures on Polytopes, Springer, 1995.
Selected Tropical Geometry References
 Mike Develin, Francisco Santos, and Bernd Sturmfels: On the rank of a tropical matrix, arxiv.org/math.CO/0312114, MSRI Proceedings, to appear.
 Mike Develin and Bernd Sturmfels: Tropical Convexity, Documenta Math. 9 (2004), 127.
 Michael Joswig: Tropical Halfspaces, arxiv.org/math.CO/0312068, MSRI Proceedings, to appear.
 Ki Hang Kim and Fred W. Roush: Factorization of polynomials in one variable over the tropical semiring, arxiv.org/math.CO/0501167.
 Grigory Mikhalkin: Enumerative tropical algebraic geometry in R2, arxiv.org/math.AG/0312530, J. AMS, to appear.
 Jürgen RichterGebert, Bernd Sturmfels, and Thorsten Theobald: First steps in tropical geometry, arxiv.org/math.AG/0306366, Contemp. Math., AMS, to appear.
 Lior Pachter and Bernd Sturmfels: Tropical Geometry of Statistical Models, arxiv.org/qbio.QM/0311009.
 Frank Sottile: Tropical Geometry, arxiv.org/math.AG/0501146.
 David Speyer: Tropical Linear Spaces, arxiv.org/math.CO/0410455.
 David Speyer and Bernd Sturmfels: Tropical Mathematics, arxiv.org/math.CO/0408099.
 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 3dimensional
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:

Add
/home/polymake/bin
to your
PATH
environment variable, i.e., if you are using
bash
, e.g., then do:
PATH=/home/polymake/bin:$PATH

Make the shared libraries of the proper
gcc
version 3.4.3 available:
export LD_LIBRARY_PATH=/opt/gnu/lib

For your convenience it is recommended that you add both the
above command lines to your
.bashrc
(or
equivalent) file.

Please, do
polymake reconfigure
once (even if
you did it before).

External packages installed: geomview, JavaView, nauty.

Documentation in HTML locally available at
this local link.
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.tudarmstadt.de
Last modified: Tue Feb 1 19:04:43 CET 2005