# MA8108 Advanced complex analysis

# Fall 2017

Yurii Lyubarskii, yurii [dot] lyubarskii [at] ntnu [dot] no, room 954, SB2

##### Schedule:

Tuesdays, 13:15-15:00, room KJL 22 Wednesdays, 12:15-14:00, room 734, SB2

First lecture - Tuesday, 29.08

**Welcome to MA8108 !**

This PhD course is given every second year, and usually 4th and 5th year (Master) students take it along with PhD students.

This year the topic of the course is * Riemann surfaces*.

We will mainly follow Chapter 2 in B.Dubrovin "Integrable Systems and Riemann Surfaces". This book deals with integrable systems and non-linear equations, but the second chapter contains a proper introduction to the theory of Riemann surfaces. The presentation is pretty compressed, additional materials will be provided during the lectures. If time permit we will discuss application to non-linear equations.

The information/organization meeting will take place on Thursday August 24, 14:15, room 734 SB2

- The course fits students at 4-5th year Master or PhD level.
- Prerequisites: TMA4175, Complex analysis - recommended, TMA4120 Mathematics 4K or similar - must.
- It can be taken as a regular course (MA8108) or a 'fordypningsemne' (TMA4505).

### Messages

05.09. In the next lectures we cover some material which is assumed already known in our textbook. This is about fundamental group of Riemann surface, and simplest differential forms. We will follow mainly Chapter 1, Sections 3, 9, and 10 of the book

Otto Forster, "*Lectures on Riemann surfaces*", Graduate Texts in Mathematics, 81. Springer-Verlag, New York, 1991.

Lecture 19.09 is moved to Kjl 24