RISC JKU

Tropical Geometry
VL: 326.133
Summer semester 2021
DI. Dr. Sebastian Falkensteiner

 

Time and location:   Thu 15:30 – 17:00 (two-week), S3 047 (or via Zoom)

First meeting: 11 March

Lecture: A theoretical introduction into the area of Tropical Geometry will be presented. Tropical Geometry can be understand as a piecewise linear version of Algebraic Geometry. The applications reach to well-known problems in Algebra, Geometry, Combinatorics and Differential Algebra.
Video records will be of about 1 hour length and should be watched in advance to the corresponding meeting. The questions related to the content will be discussed in the meeting. For a (positive) grade these questions have to be worked out and submitted.

The course will mainly follow

D. Maclagan, B. Sturmfels: Introduction to Tropical Geometry,
American Mathematical Society, 2015.

Participants are expected to be acquainted with the basic notions in Computer Algebra (Commutative Algebra and Algebra are beneficial but not necessary).

Video recordings:

11.03. Tropical Semiring
11.03. Tropical Polynomials
25.03. Valuations
22.04. Algebraic Varieties
22.04. Tropical Varieties
06.05. Convex Geometry

Questions which will be discussed:

TropicalSemiring.pdf
TropicalPolynomials.pdf
Valuations.pdf
Varieties.pdf
ConvexGeometry.pdf

Website: www.risc.jku.at/education/courses/ss2021/tropical