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 will be made available lecture by
lecture. They should be considered as incomplete drafts. I would
appreciate to receive comments, suggestions, and, of course, corrections.
- Tropical Arithmetic and Polynomials
- Puiseux Series and Tropicalization
- Graph Algorithms and the Tropical Determinant
- Tropical Polytopes
- Products of Simplices
- Tropical Halfspaces
Topics still to be transformed into lectures.
- Polytropes
- Cellular Resolutions
- 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