Selected Topics in Algebraic Geometry I

Algebraic geometry provides conceptual framework for studying spaces cut out by polynomial equations, with deep applications across mathematics (for example in arithmetic and representations theory). The course is meant as a self-contained exposition to a chosen specialized topic in modern algebraic geometry, e.g. Tannakian formalism (alternative possibilities will be discussed in due time). Tannakian formalism deals with the problem of recovering algebraic groups (resp. other geometric objects) from the their categories of representations (resp. categories of quasi-coherent sheaves). The main part of the course will give a detailed introduction to this reconstruction principle, following the first three chapters of [Deligne-Milne: Tannakian categories]. In the remaining time, we discuss some applications in geometric representation theory, or cover other topics from this book, or outline further generalizations.