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# «Donaldson Invariants and Hitchin Moduli Space. Part I. An introduction to the Donaldson theory»

 Lecturer Bohui Chen Professor, Sichuan University Bio: Bohui Chen got his Ph.D. from the University of Wisconsin-Madison in 2001, and was the Moore Instructor of MIT during 2001-2004. He became a full professor of Sichuan University and the vice dean of the School of Mathematics since 2004. His main research interests include the geometric and topological invariants from various types of moduli spaces.

Donaldson invariants are important invariants to classify the smooth structures of 4-manifolds and were developed by Donaldson in 80s based on the analysis of the moduli space of anti-self-dual instantons. When reducing the instanton equation on the product of a surface with a 2-dimensional torus, one gets the Hitchin equation. The study of the moduli space of the Hitchin equation initiated the study of the non-abelian Hodge theory, which involves the representation theory of the fundamental group and the harmonic Higgs bundle. The study of the non-abelian Hodge theory has been studied for a long time since the middle of 1980s. At the beginning of this century, Hitchin moduli space became a key object in the geometrical Langlands program proposed by Kapustin-Witten. The geometrical Langlands duality conjecture says the brane category of a Hitchin moduli space related to a group G is equivalent to the Hitchin moduli space associated to the dual group GT. This course will provide a quick review of the above important theories and conjectures. This is an advanced course for senior undergraduate students, graduate students or researchers who have interests in these fields. This course is separated into three parts and each part will be taught by an experienced researcher in this field.

The course consists of four lectures, which is designed to be a brief introduction to the Donaldson theory on smooth 4-manifolds.

It will cover the following topics:

1. Moduli spaces of SU(2)-instantons and the Donaldson theorem;
2. A brief tour to the Donaldson invariants;
3. Gluing techniques and its applications;
4. The Floer’s homology groups.

Лекция пройдет на английском языке в форме вебинара на платформе Zoom.

20:00 - 21:30 Beijing time（15:00 - 16:30 Moscow time)

Join Zoom Meeting:

Meeting ID：841 6964 9270

Passcode：871999

(ссылка может быть изменена ближе к мероприятию)

## Запись лекции

https://rutube.ru/video/f483f8c340b6abbec3e4c29e32df89b8/