Lecture 1
Date and time: 17 February 2026, 16:00-17:00
Title: The integrable system
Abstract: When the study of Higgs bundles on a Riemann surface began 40 years ago, what is now known as the Hitchin integrable system was a sideshow – an observation. The talk will follow the development of this over the years in a variety of contexts and in particular describe the more central role it now plays in the geometry of the moduli space.
Lecture 2
Date and time: 18 February 2026, 16:00-17:00
Title: A universal moduli space
Abstract: The moduli space of Higgs bundles has a natural hyperkähler metric which depends on the complex structure of the Riemann surface. On the other hand it may also be identified with a character variety of the fundamental group which just depends on the topology. These two aspects generate a differential-geometric structure on the universal bundle over Teichmüller space which is the subject of this talk.
Lecture 3
Date and time: 19 February 2026, 16:00-17:00
Title : The odd integrable system
Abstract: The definition of the integrable system involves the invariant symmetric polynomials on the Lie algebra of a simple group, but there is an analogous construction using invariant alternating forms. This leads to information about the Hochschild cohomology of the moduli space of stable bundles. The talk will review this construction and consider it in the special case of the intersection of two quadrics in any dimension, where explicit formulas have recently been revealed.
About the speaker: Nigel Hitchin studied mathematics in Oxford and gained a DPhil in 1972. After postdoctoral positions in the USA and Oxford he was appointed University Lecturer and Tutor at St Catherine’s College Oxford in 1979. From 1990 to 1997 he held chairs at Warwick and Cambridge before returning to Oxford as Savilian Professor of Geometry. He retired in 2016 and in that year was awarded the Shaw Prize in Mathematical Sciences. His work links together differential geometry, algebraic geometry and the equations of theoretical physics.
This lecture series is part of the program "Geometric Structures and Stability."