Professor Nigel Hitchin of the University of Oxford speaks on "The Hyperkähler Geometry of Higgs Bundles"
On June 3, 2026, the inaugural Calabi Lecture, organized by the Institute of Geometry and Physics at the University of Science and Technology of China, was successfully held in the Lecture Hall on the third floor of Building 1, Section B, at the USTC Shanghai Institute for Advanced Studies. Professor Nigel Hitchin, Fellow of the Royal Society and Professor Emeritus at the University of Oxford, delivered a lecture entitled "The hyperkähler geometry of Higgs bundles." The lecture was chaired by Professor Xiuxiong Chen, Director of the Institute of Geometry and Physics, and was held in a hybrid format, attracting scholars and graduate students in geometry, mathematical physics, and related fields from China and abroad.
Vision of the Series |
The Calabi Lecture series is a major academic initiative of the Institute of Geometry and Physics. It is designed as a distinguished forum that brings leading mathematicians from around the world to present their most influential ideas, recent developments, and exemplary creative scholarship. Through this series, the Institute aims to promote intellectual exchange at the highest level and to inspire both established researchers and future generations of mathematicians.
The series pays tribute to the towering legacy of Professor Eugenio Calabi, whose profound vision transformed modern mathematics and influenced fields ranging from differential geometry and partial differential equations to algebraic geometry and mathematical physics. It also reflects the core values to which the Institute aspires: originality of thought, deep scholarship, relentless intellectual curiosity, and a lifelong dedication to education. By launching the Calabi Lecture series, the Institute seeks to celebrate, preserve, and continue this tradition of mathematical excellence and creativity.
A Moment of Heritage |
In his opening remarks, Professor Xiuxiong Chen, Professor Calabi's last doctoral student, described the inaugural lecture as both a high-level academic event and a meaningful act of mathematical inheritance. Inviting Professor Hitchin to deliver the first Calabi Lecture was a fitting tribute across generations, bringing into dialogue two remarkable intellectual traditions in differential and algebraic geometry.
Figure 1. Professor Xiuxiong Chen chairs the inaugural Calabi Lecture.
The Speaker |
Professor Hitchin received his D.Phil. from the University of Oxford in 1972 and has spent much of his distinguished career there. From 1990 to 1997, he held chair professorships at the Universities of Warwick and Cambridge before returning to Oxford, where he served as Savilian Professor of Geometry and is now Professor Emeritus. A Fellow of the Royal Society and recipient of numerous distinctions, including the Shaw Prize, the Sylvester Medal, and the Pólya Prize, Professor Hitchin is widely regarded as one of the central figures of modern differential geometry.
From his pioneering formulation of Higgs bundles and the Hitchin integrable system, which laid important foundations for major developments in algebraic geometry and the Langlands program, to his introduction of generalized complex structures, Professor Hitchin's work is marked by exceptional depth, elegance, and lasting influence. His research has also played a fundamental role in building deep connections between geometry and theoretical physics, making him an especially fitting speaker for the inaugural Calabi Lecture.
Lecture Highlights |
In the lecture, Professor Hitchin reviewed Calabi's foundational contributions to hyperkähler geometry. Calabi introduced the terminology of hyperkähler manifolds and constructed the first higher-dimensional complete example on the cotangent bundle of complex projective space, a landmark example in the subject. Professor Hitchin then explained that the moduli space of Higgs bundles on a Riemann surface carries a much-studied hyperkähler metric with structural features closely related to Calabi's construction.
Professor Hitchin focused on a real-valued function associated with a circle action, showing how the same idea applies both to Calabi's example and to the hyperkähler geometry of Higgs bundle moduli spaces. He further explained how this function can be used to describe the geometry of the Higgs bundle moduli space as the complex structure of the Riemann surface varies. The lecture offered a clear and insightful account of the deep interplay among hyperkähler geometry, algebraic geometry, and mathematical physics.
Figure 2. Professor Nigel Hitchin delivers "The hyperkähler geometry of Higgs bundles."
Following the lecture, participants on site and online engaged in discussion with Professor Hitchin on geometric structures, properties of moduli spaces, and possible extensions of the ideas presented in the talk. The event marked a strong beginning for the Calabi Lecture series and further strengthened the Institute's international academic exchange and collaboration in geometry and physics.
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