From Microstructures to Image Analysis: Professor Sir John Ball Returns to CityUHK for Two HKIAS Distinguished Lectures
Professor Sir John Ball, an HKIAS Senior Fellow and one of the world's most distinguished mathematicians, continued his regular visits to City University of Hong Kong (CityUHK). He delivered two HKIAS Distinguished Lectures in June and July, 2026, bringing his characteristic depth and clarity to both talks, which were well attended by faculty members, researchers, and students. During his visit, he also engaged in academic exchanges with scholars at CityUHK.
On 24 June 2026, Sir John delivered the first of his two lectures, titled “Highly Irregular Microstructures and T_N Configurations” and chaired by Professor Pierre Nolin of CityUHK's Department of Mathematics. In the lecture, Sir John explored the remarkable martensitic microstructures observed in the alloy Ti76Nb22Al2, which undergoes a cubic-to-orthorhombic transformation with six martensitic variants having middle eigenvalue 1 — a property that permits exact interfaces between the high-temperature cubic austenite phase and the low-temperature orthorhombic martensite phase. Sir John explained the underlying theory, showing how the unusual microstructure arises because the twelve energy-well matrices compatible with the undistorted austenite are pairwise incompatible, and described efforts to understand the observed microstructures through gradient Young measures, exact gradients, and T_N-configurations. Through the lens of gradient Young measures and T_N-configurations, the lecture offered a rare window into how abstract mathematical principles can govern the behaviour of real-world materials.
Professor Sir John Ball delivering the first of his two lectures, titled “Highly Irregular Microstructures and T_N Configurations” on 24 June 2026.
【From left】 Professor Sir John Ball with Professor Pierre Nolin, Department of Mathematics, CityUHK
On 2 July, his second lecture “Image Comparison and Scaling via Nonlinear Elasticity” was chaired by Professor Wei Xiang, Associate Professor in the Department of Mathematics at CityUHK. Sir John shifted focus from the microscopic to the visual, presenting a novel approach to image comparison grounded in nonlinear elasticity. Rather than treating images as mere arrays of pixels, the model seeks optimal geometric transformations between them — a fresh perspective that bridges pure mathematics and computer vision. He further discussed whether, for linearly related images, the minimization algorithm delivers the linear transformation as the unique minimizer — a question of both theoretical and practical significance for image analysis.
Professor Sir John Ball delivering his second HKIAS Distinguished Lecture, titled “Image Comparison and Scaling via Nonlinear Elasticity” on 2 July 2026.
During his visit, Sir John also met with Professor Kenneth Leung, Vice-President (Research) of CityUHK, Professor Shuk Han Cheng, former Executive Director of HKIAS, and Professor Denver Danfeng Li, current Executive Director of HKIAS, as well as faculty members from the Department of Mathematics, including Professor Pierre Nolin, Associate Professor Wei Xiang, Assistant Professor Lina Zhao, and Assistant Professor Fushuai Jiang. The exchanges spanned a range of mathematical topics and offered valuable opportunities for CityUHK researchers to connect with Sir John's broad expertise.
About Professor Sir John Ball
Professor Sir John Ball is Professor of Mathematics at Heriot-Watt University and served as Sedleian Professor of Natural Philosophy at the University of Oxford from 1996 to 2018. Knighted in 2006, he is a Fellow of the Royal Society, a former President of Royal Society of Edinburgh, and a recipient of the Sylvester Medal (2009) and the King Faisal Prize for Science (2018).