On 27July 2022，Nanhua Xi, an academician of the Chinese Academy of Sciences, inaugurated the Calabi Lecture of the Institute of Mathematical Sciences. The Calabi Lecture is the institute’s distinguished lecture series which is intended as a forum to feature acclaimed mathematicians, the current state of mathematics, exemplary research and creative work.

The institute’s founding director, Professor Xiuxiong Chen, chaired the inauguration of the Calabi Lecture. He explained that the lecture is so named because Calabi embodies what the institute aspires to be known for: original thinkers and erudite educators.

Calabi has made a number of contributions to mathematics. He is perhaps best known for his pioneering work in Kaehler Geometry; his Laplacian comparison theorem and maximum principle for continuous functions have become an indispensable tool in geometric analysis; his work on minimal and maximal surfaces, on harmonic isometric embeddings, on affine geometry have all been highly influential. He has published less than 50 research papers, but large proportion of them have been a major part of research literature in the last 70 years.

Professor Xiuxong Chen studied with Calabi as a Ph.D student.“Calabi has greatly influenced me as a mathematician and as a person.” He told the audience.

Professor Chen then introduced Academician Nanhua Xi. Professor Xi has made fundamental and profound contributions to our understanding of algebraic groups and quantum groups. He is renowned for his work on Lusztig's conjecture, on Deligne-Langlands conjecture, on Hecke algebra, on finite dimensional representations of quantum groups, and a host of other influential works. Professor Xi received Shiing-Shen Chern Prize in 2005 and a National Natural Sciences Award in 2007. He was elected an academician of the Chinese Academy of Sciences in 2009.

“It is fitting that Profesor Xi inaugurates the Calabi Lecture, because he, like Calabi, is an original thinker and erudite educator, and he has been a patron of our institute.” Professor Chen remarked.

Before he started his lecture, Professor Xi recalled an anecdote about Calabi and commented: “Calabi resides on a different plane than the rest of us”. Professor Xi’s lecture is titled “The based ring of affine Weyl group”. The affine Weyl group is a special class of Coxeter group. Its Hecke algebra is closely related to the representations of p-adic groups. The latter plays an important role in the Langlands program. The affine Weyl group and its Hecke algebra are also closely associated with geometric representation theory. In this talk, he focused on a conjecture of Lusztig about the based ring of an affine Weyl group. He discussed the cases for which the conjecture has been confirmed and those where counterexamples exist. The lecture ended with a question-and-answer session.

The lecture took place in hybrid form with fully online participation and offline attendance. It was well attended by scholars from IMS, Fudan, USTC, Tongji, CAS, and overseas institutions as well.