The Shaw Prize Lecture in Mathematical Sciences 2025 - From Shape to Space

Abstract

Many ancient cultures studied geometric objects and shapes, discovering various facts about them. When people started systematically describing theorems in geometry by using 'proofs', in ancient Greeks, the major focus of study in geometry changed from individual shapes to the 'space' into which those shapes are placed. The discovery of non-Euclidean geometry showed that there are many possible 'spaces'. Nowadays, the basic question asked by geometers, in light of modern scientific developments, is: What is the space we are in? In the 19th century, Bernhard RIEMANN invented the theory of manifolds, which describes spaces of arbitrary higher dimensions. This has been a foundation for various mathematics in the 19th and 20th centuries. However, various phenomena have now been discovered that we need to change it for the next development. Thus, a basic question in geometry now becomes: How can we describe and understand the spaces? Modern mathematics are very abstract and the spaces in modern mathematics are much far away from the geometric objects we can directly experience. Therefore, what we mean by spaces is a highly non-trivial question. In this talk, the speaker would like to explain a possible way to describe a space by systematically studying the shapes which the space contains.


About the Speaker

Prof. Kenji FUKAYA was born in 1959 in Yokohama, Japan and is currently a Professor of the Beijing Institute of Mathematical Sciences and Applications (BIMSA) and the Yau Mathematical Sciences Center (YMSC) at Tsinghua University, PRC. He received his Bachelor’s degree and PhD from the University of Tokyo, Japan in 1981 and 1986 respectively. He was a Research Assistant (1983–1986) and was appointed as an Associate Professor (1987–1993) at the University of Tokyo. He then moved to Kyoto University, Japan as a Professor (1994–2013) and became a permanent member of the Simons Center for Geometry and Physics at the State University of New York at Stony Brook, USA in 2013. He has been appointed as a Professor at BIMSA and YMSC since 2024. He is a member of the Japan Academy.


Registration

This lecture is free and open to the public, but prior registration is required.

• Seating will be on a first-come, first-served basis.

• Attendees should register only for themselves. Both name and email address are required for registration.

• Successful registrants will receive a confirmation email, which must be presented at the reception on the day of the event.

Please click here for registration.