Optimization and Tropical Geometry

This is a BMS Advanced Course which is part of the Thematic Einstein Semester Network Games, Tropical Geometry and Quantum Communication. The course takes place on Mondays, 10-12, in MA 041 at TU Berlin.

Teaching assistant: Robert Löwe

Contents

  1. Shortest Paths and the Hungarian Method [15 April]; Exercises and problems 1
  2. Tropical Hypersurfaces [29 April]
  3. Tropical Linear Programming, MEAN-PAYOFF and Semi-Algebraic Sets [06 May]
  4. Product-Mix Auctions [13 May]
  5. Multicriteria Optimization and Alexander Duality of Monomial Ideals [20 May]
  6. Divisors on Curves, Riemann-Roch and Chip Firing Games [27 May]

This course will be followed by an international conference (hosted at ZIB in June) and subsequent project work. For each lecture I will provide a set of problems that the participants are expected to work on, on their own. The jours fixes on Friday provide an opportunity for exchange on those problems and to ask questions. The first jour fix will take place on Friday, 12 April, at 10:00 in the BMS seminar room MA212 at TU.

Participants of the TES are expected to work on projects to be presented at the final workshop on 1 July (hosted at ZIB).

You are very welcome to join us for the Kickoff Meeting on 09 April, 18:00 at Mathematische Fachbibliothek, TU Berlin.

References

  1. Marianne Akian, Stéphane Gaubert, Alexander Guterman: Tropical polyhedra are equivalent to mean payoff games. Internat. J. Algebra Comput. 22 (2012), no. 1, 1250001
  2. Daniele Alessandrini: Logarithmic limit sets of real semi-algebraic sets, Adv. Geom. 13/1 (2013), 155-190.
  3. Matthew Baker, Serguei Norine: Riemann-Roch and Abel-Jacobi theory on a finite graph, Adv. Math. 215 (2007), 766-788.
  4. Elizabth Baldwin, Paul Klemperer: Understanding Preferences: ``Demand Types'', and the Existence of Equilibrium with Indivisibilities, preprint (2015)
  5. Michael Joswig: Essentials of tropical combinatorics, draft of a book, to appear
  6. Michael Joswig, Georg Loho: Monomial tropical cones for multicriteria optimization, arXiv:1707.09305v2 (2017)
  7. Michael Joswig, Benjamin Schröter: The tropical geometry of shortest paths, arXiv:1904.01082 (2019)
  8. Ngoc Mai Tran, Josephine Yu: Product-mix auctions and tropical geometry, arXiv:1505.05737v4 (2017)
  9. Diana Maclagan, Bernd Sturmfels: Introduction to tropical geometry, Springer 2015
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Last modified: Mon Apr 15 07:54:34 UTC 2019 by joswig