Dr. Andreas Paffenholz

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,
Algorithmic aspects
Lecture Notes
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

Voraussichtlicher Zeitplan

Tue Wed Thu Fri
9-11 MJ: Tropical Arithmetic and Polynomials AP: Ehrhart Theory: Reciprocity MJ: Tropical Polytopes AP: Geometry of Numbers
11-12 exercises exercises exercises exercises
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
16-17 exercises exercises exercises exercises

Introductory Reading