# BMS Advanced Course: Tropical Convexity

Time/Location: Summer 2009, each Monday at 10-12 in MA 742 (TU
Berlin). It is an advanced course of the Berlin Mathematical School,
which will be held in English upon request.

## Requirements

Linear algebra and a basic knowledge in polytope theory and/or
discrete optimization and/or commutative algebra and/or algebraic
geometry.

## Contents

The Lecture Notes for this course were the initial seed for my forthcoming book Essentials of Tropical Combinatorics.
- Tropical Arithmetic and Polynomials
- Puiseux Series and Tropicalization
- Graph Algorithms and the Tropical Determinant
- Tropical Polytopes
- Products of Simplices
- Tropical Halfspaces
- Polytropes
- Matroid Subdivisions of Hypersimplices
- Bruhat-Tits Buildings
- Develin, Mike; Sturmfels, Bernd: Tropical convexity. Doc. Math. 9 (2004), 1-27 (electronic); erratum ibid., pages 205-206.
- Miller, Ezra; Sturmfels, Bernd: Combinatorial commutative algebra. Graduate Texts in Mathematics, 227. Springer-Verlag, New York, 2005.
- Block, Florian; Yu, Josephine: Tropical convexity via cellular resolutions. J. Algebraic Combin. 24 (2006), no. 1, 103-114.
- Joswig, Michael; Sturmfels, Bernd; Yu, Josephine: Affine buildings and tropical convexity. Albanian J. Math. 1 (2007), no. 4, 187-211.
- Herrmann, Sven; Jensen, Anders; Joswig, Michael; Sturmfels, Bernd: How to Draw Tropical Planes, Preprint arXiv:0808.2383
- Abramenko, Peter; Brown, Ken: Buildings, Springer 2008.

Michael Joswig

Last modified: Tue Jun 2 15:09:46 CEST 2009