Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-42-15-M-7

Tropical Geometry (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-42-15-M-7 Tropical Geometry 4.5 CP (135 h)

Basedata

CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-AGCA] Algebra, Geometry and Computer Algebra
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V MAT-42-15-K-7
Tropical Geometry
P 28 h 107 h - - PL1 4.5 irreg.
  • About [MAT-42-15-K-7]: Title: "Tropical Geometry"; Presence-Time: 28 h; Self-Study: 107 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86418 ("Tropical Geometry")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

  • Puiseux field,
  • convex geometry,
  • tropicalisation and tropical varieties,
  • tropical moduli spaces and intersection theory,
  • selected results from tropical enumerative geometry.

Competencies / intended learning achievements

Based on the example of tropical varieties, the students have gained practical knowledge of how to deal with particular types of varieties. They have learnt to use numerous techniques from algebraic geometry, which enable them to acquire in-depth knowledge in this area and its applications.

They are able to name the essential propositions of the lecture as well as to classify and to explain the connections. They understand the proofs presented in the lecture and are able to comprehend and explain them. In particular, they are able to outline the conditions and assumptions that are necessary for the validity of statements.

Literature

  • A. Gathmann, Tropical Algebraic Geometry,
  • D. Maclagan, B. Sturmfels: Introduction to Tropical Geometry.

Requirements for attendance (informal)

Modules:

Courses

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-42-15-M-7]

Module-Pool Name
[MAT-41-MPOOL-7] Specialisation Algebraic Geometry and Computer Algebra (M.Sc.)
[MAT-RM-MPOOL-7] Pure Mathematics (Advanced Modules M.Sc.)