Universität Regensburg   IMPRESSUM   DATENSCHUTZ
Fakultät für Mathematik Universität Regensburg

Hinweis Bitte informieren Sie sich auf den jeweiligen GRIPS-Seiten über den digitalen Ablauf der Lehrveranstaltungen.

English Note For our digital courses all relevant information can be found on the appropriate GRIPS sites.

Seminar Tropical Geometry
Semester
SoSe 2021

Lecturer
Klaus Kuennemann and Jakob Werner

Type of course (Veranstaltungsart)
Seminar

Contents
Tropical geometry has its origins in Computer science, where certain linear optimization problems
were interpreted as solutions to polynomial equations with coefficients in the (min, +)-semiring.
The name “tropical” was coined by French mathematicians in honor of the Brazilian
computer scientist Imre Simon. In recent years, tropical geometry has found surprising
applications in algebraic geometry and non-archimedean analytic geometry, by associating to
algebro-geometric objects certain piecewise-linear (“tropical”) objects. In this seminar
we will not focus on these applications. Instead, we view tropical geometry as a geometry in its own
right, following the forthcoming book “Tropical Geometry” by Grigory Mikhalkin and
Johannes Rau. This has the advantage that in order to enter tropical geometry, only basic knowledge
in linear algebra and algebra is required. Therefore the first part of the seminar is addressed to
Bachelor and Lehramt students whereas the second part is intended for more advanced master students.
Our plan is to cover mainly Chapter 2 and Chapter 4 of Mikhalkin and Rau's book, first understanding
tropical hypersurfaces, and then tropical cycles and their stable intersection product.

Literature
Grigory Mikhalkin, Johannes Rau, Tropical Geometry. Available at:
http://math.uniandes.edu.co/~j.rau/downloads/main.pdf

Recommended previous knowledge
Linear Algebra and some algebra

Time/Date
Tuesday 16h15-17h45

Location
Zoom

Registration
  • Organisational meeting/distribution of topics: Tuesday February 9th 2021 at 16h15h in Zoom.
    Please contact Klaus Kuennemann or Jakob Werner by email to get access data for the Zoom
    meeting or if you have any further questions.
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Presentation: Giving a seminar talk of roughly 90 minutes
Examination (Prüfungsleistungen)
  • Detailed written report of the seminar talk
Regelungen bei Studienbeginn vor WS 2015 / 16
  • Benotet:
    • O. g. Studienleistung und o. g. Prüfungsleistung; die Note ergibt sich aus der Prüfungsleistung
  • Unbenotet:
    • O. g. Studienleistung
Modules
BSem, MSem, LA-GySem

ECTS
Siehe Modulkatalog. MV und Nebenfach: 4,5 LP bei Studienbeginn ab WS 15/16, 6 LP bei Studienbeginn
vor WS 15/16