09. May 2016 to 13. May 2016
Lipschitz Hall, Endenicher Allee 60
Organizers: Ngoc Tran (Bonn University), Josephine Yu (Georgia Tech)
Description: Tropical geometry is the study of geometric and combinatorial structures arising from doing arithmetic where "addition" is taking maximum and "multiplication" is the usual addition. As tropical polynomials are convex piecewise linear functions, many combinatorial optimization problems have simple descriptions in terms of tropical polynomials. Methods from polyhedral geometry are well-suited for problems arising from tropical geometry and its applications.
Tropical mathematics provides a natural language for making connections between different mathematical areas and with applications. Recent advances in tropical geometry and tropical combinatorics make new progress possible for various application areas. In the last two years, tropical geometry has appeared in auction theory and trade theory in economics, linking it with developments in discrete convexity theory. This has led to new, exciting open problems in tropical geometry, economics and combinatorics.
This summer school aims to bring graduate students, postdocs, and researchers on this topic together for one intensive week. There will be three sets of lectures on economics, tropical geometry, and discrete convex analysis. Particular focus will be on open problems and interactions between participants with different interests and backgrounds.
Lecture Series by:
- Elizabeth Baldwin (London School of Economics)
- Tropical Hypersurfaces in Economics, and the Unimodularity Theorem (work joint with Paul Klemperer)
- The Extended Product-Mix Auction (work joint with Paul Klemperer and Paul Goldberg)
- Tropical Hypersurfaces in Economics, and the Unimodularity Theorem (work joint with Paul Klemperer)
- Michael Joswig (TU Berlin)
- Tropical Hypersurfaces
- Tropical Convexity
- Tropical Linear Programming
- Diane Maclagan (University of Warwick)
- Valuated matroids and tropical algebra
- Kazuo Murota (Tokyo Metropolitan University)
- Discrete Convex Analysis II: Properties of discrete convex functions
- Discrete Convex Analysis III: Algorithms for discrete convex functions
- John Weymark (Vanderbilt University)
- A geometric approach to dominant strategy implementation
- Yoshinori Shiozawa (Osaka City University)
- Some New Topics in International Trade Theory
Person |
Affiliation |
Period of stay |
Elie Alhajjar | George Mason University | |
Carlos Enrique Améndola Cerón | Technische Universitat, Berlin | |
Elizabeth Baldwin | London School of Economics | |
Marcel Celaya | Georgia Institute of Technology | |
Ozgur Ceyhan | University of Luxembourg | |
Robert Crowell | University of Bonn | |
Albin Erlanson | Bonn | |
Jean Bernard Eytard | CMAP/Ecole Polytechnique | |
Alexander Guterman | Moscow State University | |
Tim Haga | Universität Bremen | |
Simon Hampe | TU Berlin | |
Andreas Haupt | University of Bonn | |
Justin Hsu | University of Pennsylvania | |
Daniel Joo | Alfred Renyi Institute of Mathematics, Hungarian Academy of Sciences | |
Michael Joswig | TU Berlin | |
Bernhard Kasberger | Universität Wien | |
Gleb Koshevoy | CEMI RAS | |
Yun Liu | Copenhagen Business School | |
Georg Loho | Technische Universität Berlin | |
Bence Mélykúti | University of Freiburg | |
Diane Maclagan | University of Warwick | |
Christoph Lüders | University of Bonn | |
Henryk Michalewski | University of Warsaw | |
Kazuo Murota | Tokyo Metropolitan University | |
Christoph Pegel | Universität Bremen | |
Victoria Powers | Emory University | |
Satya Swarup Samal | University of Bonn | |
Benjamin Schröter | Technische Universität Berlin | |
Akiyoshi Shioura | Tokyo Institute of Technology | |
Yoshinori Shiozawa | Osaka City University | |
Simón Soto | Universidad de los Andes | |
Akihisa Tamura | Keio University | |
Ngoc Tran | Universität Bonn | |
Daniele Turchetti | MPIM | |
Martin Ulirsch | University of Bonn | |
Charles Wang | Georgia Institute of Technology | |
John Weymark | Vanderbilt University | |
Sonal Yadav | Department of Economics, University of Padua | |
Josephine Yu | Georgia Institute of Technology |