The Narasimhan-Seshadri theorem (1965) is a profound correspondence between stable, degree zero, holomorphic vector bundles over a compact Riemann surface and unitary representations of the fundamental group. In 1983, Donaldson provided an alternate proof of this theorem by relating these vector bundles to flat smooth unitary connections. Unlike Narasimhanʼs and Seshadriʼs proof, his was more analytical in nature and relied on techniques from elliptic PDEs and calculus of variations.

Collectively, these results reveal a deep relationship between topological, smooth and holomorphic structures over a compact Riemann surface. In this talk, I hope to provide some insight into this relationship, as well as an outline of Donaldsonʼs proof

About Pure mathematics seminars

We present regular seminars on a range of pure mathematics interests. Students, staff and visitors to UQ are welcome to attend, and to suggest speakers and topics.

Seminars are held on Tuesdays from 3pm to 3.50pm in Room 67-442 of the Priestley Building (Building 67).

Talks comprise 45 minutes of speaking time plus five minutes for questions and discussion.

Information for speakers

Researchers in all pure mathematics fields attend our seminars, so please aim your presentation at a general mathematical audience.

Room 67-442 has a data projector and a whiteboard.

If you wish to use the data projector, contact us a few days in advance of your talk to avoid technical delays on the day - there's a tight turnaround with room bookings.

Contact us

To volunteer to talk or to suggest a speaker, email Ole Warnaar.


67 (Priestley Building)