# Tropical Geometry

**Lecturer:**Yue Ren**Date:**Monday, 09:00 - 10:30**no lecture on Monday, May 22****Room:**MPI MiS A3 02**Language:**English**Target audience:**MSc students, PhD students, Postdocs**Keywords:**Tropical Geometry, Algebraic Geometry, Computer Algebra**Prerequisites:**Basic knowledge about algebra and algebraic geometry is helpful, but not necessary.**Remarks:**This lecture will feature some computer presentations. Bringing your laptop along is highly recommended.

## 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.

## Regular Lectures (Summer 2017)

**Basic Notions in (Geometric) Group Theory**- Karim Adiprasito
- Monday, 11:00 - 13:00, University A-314

**Information Theory II**- Nihat Ay
- Tuesday, 11:00 - 12:30, MPI MiS A3 02

**The variational approach to stochastic PDE**- Benjamin Gess
- Wednesday, 11:00 - 12:30, MPI MiS A3 01

**Mathematical methods in the neurosciences**- Jürgen Jost
- Friday, 13:30 - 15:00, MPI MiS A3 01

**Moduli spaces, stability conditions and birational geometry**- Christian Lehn
- Friday, 10:00 - 12:00, MPI MiS G3 10

**Tropical Probability**- Rostislav Matveev
- Thursday, 11.00 - 12:30, MPI MiS A3 02

**Partial Differential Equations**- Felix Otto
- Wednesday, 9:15 - 11:00, MPI MiS A3 01

**Tropical Geometry**- Yue Ren
- Monday, 9:00 - 10:30, MPI MiS A3 02

**Interpolation Spaces**- Jonas Sauer
- Tuesday, 9:00 - 10:30, MPI MiS A3 01

**Navier-Stokes Equations**- László Székelyhidi:
- Thursday, 9:00 - 11:00 and Friday, 9:00 - 11:00, University SG 3-11

**IMPRS-Ringvorlesung: Geometry and Dynamical Systems**- Tanja Eisner, Hans-Bert-Rademacher, Matthias Schwarz
- Tuesday, 13:15 - 14:45, MPI MiS E1 05 (Leibniz-Saal)

**Seminar on Ergodic theory of group actions**- Tanja Eisner, Tobias Finis, Artem Sapozhnikov
- Tuesday, 09:15 - 11:45, University SG 3-11