Fall School Tropical and Polyhedral Combinatorics
The RG Algorithmic Discrete Mathematics organizes a fall
school on tropical and polyhedral combinatorics as part
of the priority program Algorithmic
and Experimental Methods. The school will be held from October
9 to 12 at TU Darmstadt.
The lectures are targeted at advanced students (usually having
completed their BSc degree) and beginning PhD students that want
to learn more about Combinatorics, Discrete Geometry, and their
applications. As prerequisites, some knowledge in polyhedral
theory is useful.
The fall school is part of the class Tropical Combinatorics of Prof Joswig.
We will meet at Dolivostr. 15, Room 142 (first floor, left, at the end of the aisle). Prospective participants are asked to contact Ms Röder (roeder at mathematik.tu-darmstadt.de) until beginning of October.
|Michael Joswig (MJ):||Tropical Combinatorics|
Tropical polynomials and tropical hypersurfaces,
Principles of combinatorial optimization from a geometric viewpoint,
Connection to polytope theory,
|Andreas Paffenholz (AP):||Lattice Polytopes and Triangulations|
Ehrhart Theory: lattice polytopes, generating functions,
Ehrhart and h*-Polynomials, Reciprocity and der
Theorem of Brion
Geometry of Numbers, Flatness
Lecture Notes and Slides
|9-11||MJ: Tropical Arithmetic and Polynomials||AP: Ehrhart Theory: Reciprocity||MJ: Tropical Polytopes||AP: Geometry of Numbers|
|12-14||lunch break||lunch break||lunch break||lunch break|
|14-16||AP: Ehrhart Theory: basics||MJ: Graph algorithms and the tropical determinant||AP: Theorem of Brion||MJ: Products of simplices, mixed subdivisions and the Cayley trick|
Ziegler, Lectures on Polytopes
Schrijver, Linear and Integer Programming
Beck, Robbins, Counting the continuous discretely
Richter-Gebert, Jürgen; Sturmfels, Bernd; Theobald, Thorsten
First steps in tropical geometry. (English summary) Idempotent mathematics
and mathematical physics, 289-317,
Contemp. Math., 377, Amer. Math. Soc., Providence, RI, 2005.
- Joswig, Michael; Theobald, Thorsten Algorithmische Geometrie. (German) [Algorithmic geometry] Polyedrische und algebraische Methoden. [Polyhedral and algebraic methods] Vieweg Studium: Aufbaukurs Mathematik. [Vieweg Studies: Mathematics Course] Vieweg, Wiesbaden, 2008.