COURSE UNIT TITLE

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSISTANT PROFESSOR CELAL CEM SARIOĞLU

Offered to

Mathematics
Mathematics

Course Objective

Riemann surfaces can be defined in several different, equivalent ways, for example as one-dimensional complex manifolds, or as oriented two-dimensional real manifolds. In addition, any compact Riemann surface can be embedded in projective space, thus giving it the structure of an algebraic curve. Riemann surfaces therefore appear in many areas of mathematics, from complex analysis, algebraic and differential geometry, to algebraic topology and number theory.

The course will introduce some of the classical results on Riemann surfaces, emphasizing the interplay between topology, complex analysis and geometry. So, we will start with the topological setup and then pass via analysis to algebraic geometry.

Learning Outcomes of the Course Unit

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Recomended or Required Reading

Textbook:
1. Hershel M. Farkas, Irwin Kra, Riemann Surfaces, Springer, 1980.
2. Otto Forster, Lectures on Riemann Surfaces, Springer, 1981.
3. Alan F. Beardon, A Primer on Riemann Surfaces, Cambridge University Press, 1984.
4. Simon Donaldson, Riemann Surfaces, Oxford University Press, 2011.
Supplementary Books:
5. Rick Miranda, Algebraic Curves and Riemann Surfaces, American Mathematical Society, 1995.
6. Lars V. Ahlfors, Leo Sario, Riemann Surfaces, Princeton University Press, 2015.
7. Hershel M. Farkas and Irwin Kra, Theta Constants, Riemann Surfaces and the Modular Group, American Mathematical Society, 2001.
References:
8. Wilhelm Schlag, A course in Complex Analysis and Riemann Surfaces, American Mathematical Society, 2014 .
9. Raghavan Narasimhan, Compact Riemann Surfaces, Birkhauser, 1992.
10. Eberhard Freitag, Complex Analysis 2: Riemann Surfaces, Several Complex Variables, Abelian Functions, Hihger Modular Functions, Springer, 2010.
11. Jürgen Jost, Compact Riemann Surfaces, 3rd edition, Springer, 2006.
12. Ernesto Girondo, Gabino Gonzalez-Diez, Introduction to Compact Riemann Surfaces and Dessin d Enfants, Cambridge University Press, 2012.
13. Henri Paul de Saint-Gervais, Uniformisation des surfaces de Riemann retour sur un théoreme centenaire, ENS editiıns, 2010.
14. Lars V. Ahlfors, Complex Analysis, 3rd edition, McGraw-Hill, 1979.
15. Hermann Weyl, The concept of a Riemann Surface, 3rd edition, Dover Books, 2009.

Planned Learning Activities and Teaching Methods

Lecture notes, Presentation, Problem solving, Homework Assignments

Assessment Methods

Further Notes About Assessment Methods

Midterm exam, Homework Assignments, Final exam

Assessment Criteria

To be succesful, at the end of the term, the relative grade must be 75 or greater.

Language of Instruction

English

Course Policies and Rules

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

Asst. Prof. Dr. Celal Cem Sarıoğlu
E-mail: celalcem.sarioglu@deu.edu.tr
Office: +90 232 301 8607

Office Hours

TBA

Work Placement(s)

None

Workload Calculation

Contribution of Learning Outcomes to Programme Outcomes