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

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

20.05. Initials and Gröbner Bases

Initials and Groebner Bases.png

10.06. Tropical Linear Algebra

Linear Algebra.png

24.06. Graph Theory in Tropical Linear Algebra

Graph Theory in Tropical Linear Algebra.png

Questions which will be discussed:

TropicalSemiring.pdf

TropicalPolynomials.pdf

Valuations.pdf

Varieties.pdf

ConvexGeometry.pdf

InitialsAndGroebnerBases.pdf

LinearAlgebra.pdf

LinearAlgebra2.pdf

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