Summer Course for 2010:

The Summer Course will meet for seven weeks, five days per week, 60 minutes per day.

The topic will be:

• Complex Algebraic Curves - June 21 - August 6

The theory of complex algebraic curves is one of the most beautiful areas of mathematics. Initially developed in 19th century, it still attracts a lot of interest and has important applications in areas ranging from number theory to theoretical physics. In this minicourse, after reviewing necessary concepts from basic algebra, topology and complex analysis, we will then start from basic properties and examples of algebraic curves and proceed towards the Riemann-Roch theorem and Abel's theorem. If time permits, some applications will also be considered.

Our main refernces will be

Complex Algebraic Curves by F. Kirwan (London Math. Soc. Student Texts 23, Cambridge University Press). Required Text

and

Introduction to Algebraic Curves by P. A. Griffiths (Translations of Mathematical Monographs 76, AMS), Recommended Text.