Hodge Theory and Periods of Varieties

Starting from 19th century, elliptic and hyperelliptic integrals captivated the imagination of almost every mathematician. The initial observations provided the intuition for much of the development of modern complex geometry. At our present day, one starts learning the subject from these modern abstractions. However, in this lecture, we will work with concrete examples to see for ourselves what the ancients have seen in order to develop our intuition. This is intended so that we can anticipate what the abstract technical framework must look like, without doing anything technically demanding. We will end the first block by looking ahead and studying projective hypersurfaces, their Hodge decomposition and their periods.

Date and time info
Block course: May 6 - 10, time tba

Keywords
Curves, surfaces, periods, cohomology

Prerequisites
Linear algebra, calculus, visualization skills

Audience
MSc students, PhD students, Postdocs

Language
English

Remarks and notes
This is a block course, consisting of two blocks with each block lasting a week. There will be 4 hours of lectures per day with an additional 2 hours for working on exercises in groups. The second block will be late in summer.