The Department of Mathematics is honored to host the inaugural Shiing-Shen Chern Distinguished Lecture on February 5, 2026, to be given by Duke University Professor and former MSRI Director (2007-13), Prof. Robert Bryant(link is external). The inaugural lecture will take place at 4:10pm in Banatao Auditorium (310 Sutardja Dai Hall), followed by a reception in 1015 Evans Hall.
Lecture Title: Holonomy in Geometry: History and Current Developments
Abstract: The concept of ‘holonomy’ originally arose in the late 19th century in mechanics as a way to describe motion subject to constraints, such as a ball rolling on a table without slipping or twisting. However, its profound connection with the notion of curvature in differential geometry and generalizations of ‘conserved quantities’ under parallel translation was realized quite early in the 20th century, with fundamental contributions by É. Cartan, J. Schouten, E. Kähler and others in the decades 1910-30. A more systematic exploration in the 1950s by M. Berger and S.-s. Chern clarified its foundations and inspired conjectures such as Calabi’s conjecture about compact Kähler manifolds with trivial canonical bundle, famously solved by S.-T. Yau in the 1970s.
In the last 40 years, there have been many important advances in the so-called ‘exceptional’ cases, inspired by the desire to extend the ideas and results in Calabi–Yau geometry to these cases, with the ultimate goal of applying such results to physical theories going beyond string theory.
The current state of the subject still presents enormous challenges in geometric analysis, topology, and theoretical physics, and I hope to give the audience a sense of this rapidly developing frontier.
Slides from Prof. Bryant's February 5, 2026 Lecture (A link to a .pdf file is present).
Bio: Professor Robert Bryantreceived his PhD in 1979 from the University of North Carolina at Chapel Hill. He has served on the faculty at Rice University, UC-Berkeley, and Duke University, where he is currently the Phillip Griffiths Professor of Mathematics. His research spans a range of topics in the geometry of partial differential equations, including minimal surfaces and calibrations, Finsler and affine geometry, Riemannian and affine holonomy, and exterior differential systems. He is especially honored to be invited to deliver the inaugural Shing-Tung Yau and Yu-Yun Yau Endowed Lecture in Mathematics, dedicated to Shiing-Shen Chern, whose many beautiful and profound works have been a rich source of inspiration throughout Bryant’s career.