Due to the COVID-19 crisis, the information below is subject to change,
in particular that concerning the teaching mode (presential, distance or in a comodal or hybrid format).

5 credits

30.0 h + 15.0 h

Q2

This biannual learning unit __is not being organized__ in 2020-2021 !

Teacher(s)

Haine Luc;

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

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

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

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

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**