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.
  1. Tropical Arithmetic and Polynomials
  2. Puiseux Series and Tropicalization
  3. Graph Algorithms and the Tropical Determinant
  4. Tropical Polytopes
  5. Products of Simplices
  6. Tropical Halfspaces
  7. Polytropes
  8. Matroid Subdivisions of Hypersimplices
  9. Bruhat-Tits Buildings

    10. References (selection)

    1. Develin, Mike; Sturmfels, Bernd: Tropical convexity. Doc. Math. 9 (2004), 1-27 (electronic); erratum ibid., pages 205-206.
    2. Miller, Ezra; Sturmfels, Bernd: Combinatorial commutative algebra. Graduate Texts in Mathematics, 227. Springer-Verlag, New York, 2005.
    3. Block, Florian; Yu, Josephine: Tropical convexity via cellular resolutions. J. Algebraic Combin. 24 (2006), no. 1, 103-114.
    4. Joswig, Michael; Sturmfels, Bernd; Yu, Josephine: Affine buildings and tropical convexity. Albanian J. Math. 1 (2007), no. 4, 187-211.
    5. Herrmann, Sven; Jensen, Anders; Joswig, Michael; Sturmfels, Bernd: How to Draw Tropical Planes, Preprint arXiv:0808.2383
    6. Abramenko, Peter; Brown, Ken: Buildings, Springer 2008.
    Michael Joswig

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