Lecture (webinar) from a special course
of the ChineseRussian Mathematical Center
«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 WisconsinMadison in 2001, and was the Moore Instructor of MIT during 20012004. 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 4manifolds and were developed by Donaldson in 80s based on the analysis of the moduli space of antiselfdual instantons. When reducing the instanton equation on the product of a surface with a 2dimensional torus, one gets the Hitchin equation. The study of the moduli space of the Hitchin equation initiated the study of the nonabelian Hodge theory, which involves the representation theory of the fundamental group and the harmonic Higgs bundle. The study of the nonabelian 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 KapustinWitten. 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 4manifolds.
It will cover the following topics:
 Moduli spaces of SU(2)instantons and the Donaldson theorem;
 A brief tour to the Donaldson invariants;
 Gluing techniques and its applications;
 The Floer’s homology groups.
The lecture will be held in English in the form of a webinar on the Zoom platform.
20:00  21:30 Beijing time（15:00  16:30 Moscow time)
Join Zoom Meeting:
https://zoom.us/j/84169649270?pwd=d3l5dzBqRXBYUHltV3JSajM5NkZvZz09
Meeting ID：841 6964 9270
Passcode：871999
(link may change closer to the event)
Lecture recording
https://rutube.ru/video/86207b5fa7a60631b3e462bdb98fde3b/