5.00 credits
30.0 h + 15.0 h
Q2
This learning unit is not being organized during year 2021-2022.
Language
French
Prerequisites
- LMAT1222, Analyse complexe 1 (or equivalent)
- Basics in differential geometry, LMAT1241 ou LMAT1342 (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
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.
Teaching materials
- syllabus en français
Faculty or entity
MATH
