Complex geometry

lmat2265  2019-2020  Louvain-la-Neuve

Complex geometry
Note from June 29, 2020
Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
5 credits
30.0 h + 15.0 h
Q2
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.
Aims

At the end of this learning unit, the student is able to :

1
 

The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.
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.
Faculty or entity


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

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

Master [60] in Mathematics

Master [60] in Physics

Master [120] in Physics