Tropical Geometry
Abstract
This lecture is an introduction to tropical geometry with focus on its techniques and its applications. It is split in two parts. We begin with studying tropical varieties, how they arise and what structure they have. Along the way, we highlight important concepts and techniques that are useful beyond tropical geometry, like Gröbner bases and triangular decompositions. This serves as a theoretical foundation for the next part.
The second part is dedicated to applications of tropical geometry. It consists of a series of expository talks. Possible topics include but are not limited to:
- algebraic geometry: enumerative geometry.
- biology: phylogenetic trees
- economics: product-mix auctions, Ricardian economics.
- optimization: mean payoff games, multiobjective integer linear programming.
- physics: central configurations in the n-body problem.
Near the end of the first part, there will be a short overview of possible topics, for which suggestions are welcome. The topics will be selected based on the interests of the audience.
Date and time info
Monday, 09:00 - 10:30
Keywords
Tropical Geometry, Algebraic Geometry, Computer Algebra
Prerequisites
Basic knowledge about algebra and algebraic geometry is helpful, but not necessary.
Audience
MSc students, PhD students, Postdocs
Language
English
Remarks and notes
This lecture will feature some computer presentations. Bringing your laptop along is highly recommended.
