# Associate Professor of Mathematics Zhouli Xu is 2022 ICM Lecturer

**September 13, 2022 | By Michelle Franklin**

The International Congresses of Mathematicians (ICM) is one of the largest mathematical conferences in the world. Outstanding mathematicians from around the world present their best work covering all areas of mathematics. The first ICM took place in Switzerland in 1897. It is now held once every four years, thus being an invited lecturer is quite prestigious. In 2022, Associate Professor of Mathematics Zhouli Xu was invited to speak in the topology section of ICM, although with two other UC San Diego mathematicians: Professor Amir Mohammadi and Professor Tianyi Zheng.

Zhouli Xu is a Chinese mathematician specializing in the subject of topology. He earned his B.S. and M.S. in Mathematics from Peking University and his Ph.D. from the University of Chicago in 2017. He was a C.L.E. Moore Instructor at MIT before joining UC San Diego in 2020. He has been an associate professor of Mathematics since July 2022.

He is a recipient of the Plotnick Fellowship (2015) and the William Rainey Harper Dissertation Fellowship (2016), both from the University of Chicago. In 2022, he was awarded the K-Theory Foundation Prize, which is given to outstanding mathematicians under 35 years of age once every four years.

Xu works in the area of topology, which is the study of the geometric properties of an object that are preserved despite continuous deformations (essentially the transformation of an object without tearing). These geometric objects could exist in any dimension — for example, one could imagine a sphere in dimension “n” sitting inside the Euclidean space in dimension “n plus 1.”

One could consider mapping spheres in different dimensions and trying to classify them up to continuous deformation. This classification problem is called the computation of the homotopy groups of spheres, which describes how spheres of various dimensions can wrap around each other. This problem has been around for over 100 years, but much is still unknown.

In his ICM lecture, Xu discussed a recent breakthrough on this problem, which he achieved alongside his collaborators. They introduced a new methodology via motivic homotopy theory. It is worth noting that motivic homotopy theory was designed to study problems in algebraic geometry, but surprisingly Xu's work has shown that it can be also used to study problems in classical topology.

**Further Reading:**

*Proceedings of the National Academy of Science*: Stable Homotopy Group of Spheres (2020)*The Annals of Mathematics*: The triviality of the 61-stem in the stable homotopy groups of spheres (2017)