Complex geometry

lmat2265  2020-2021  Louvain-la-Neuve

Complex geometry
The version you’re consulting is not final. This course description may change. The final version will be published on 1st June.
5 credits
30.0 h + 15.0 h
Q2

  This biannual learning unit is not being organized in 2020-2021 !

Teacher(s)
Language
French
Prerequisites
- LMAT1222, Analyse complexe 1 (or equivalent)
- Basics in differential geometry, LMAT1241 ou LMAT1342 (or equivalent)
Main themes
Compact Riemann surface theory and its applications to integrable systems.
Content
In 2019-2020, the course will address the main theorems of compact Riemann surfaces with applications to integrable systems.
1. Compact Riemann surfaces:
- Riemann-Roch theorem
- Abel's theorem
- Jacobi varieties, Jacobi inversion problem and theta functions
2. Applcations to integrable systems (theory of solitons):
- Baker-Akhiezer functions
- Equations of the theory of solitons
Teaching methods
During the classes, students are invited to actively participate, by asking questions based on their previous knowledge of basic complex analysis and basic differential geometry.
Evaluation methods
Assessment is made on the basis of an oral presentation during the teaching sessions and an oral examination at the end of the class. The oral presentation during the teaching sessions consists in presenting a chapter in a book, or a research article offering new perspectives. The oral examination at the end of the semester tests the knowlege and the hability to use the concepts and the theorems viewed during the class.
Online resources
Syllabus and references on the moodle website of LMAT2265
Bibliography
O. Forster, Lectures on Riemann Surfaces, Graduate Texts in Mathematics 81, Springer-Verlag.
Teaching materials
  • syllabus en français
Faculty or entity


Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Aims
Master [120] in Mathematics
5

Master [120] in Physics
5

Master [60] in Physics

Master [60] in Mathematics