On June 28th, 2024, Professor Jack Koolen from the University of Science and Technology of China was invited by our institute to give a lecture on "Recent Progress in Distance-Regular Graphs" at Room 414 in the North District Integrated Building. The conference was hosted by our institute's President, Ping Weiying, and faculty and students from the School of Statistics and Data Science attended the lecture.

The lecture focused on distance-regular graphs (DRGs). First, Professor Jack Koolen introduced the definition and basic theory of DRGs. Then, he gave examples of the sources of infinite families of DRGs and the four known DRGs with infinite families of vertices that have vertex transitivity but not distance transitivity.

Next, Professor Jack Koolen explained distance-regular graphs with classical parameters. He began by defining the concept, then introduced the principles of Grassmann graphs and bilinear forms. He then gave a detailed explanation of his own research on distance-regular graphs with classical parameters.

Finally, Professor Jack Koolen introduced 1-homogeneous graphs, noting that graphs with 1-homogeneous properties are simply called 1-homogeneous graphs and that 1-homogeneous graphs are always distance-regular graphs.

Additionally, Professor Jack Koolen's student shared his research on tree similarity for sparse grid point sets based on this concept. He began by introducing compatible partition systems and splitting systems in graphical form.

In the interactive session, teachers and students consulted professor about the lecture content. Professor Jack Koolen gave a patient answer, which triggered a discussion between teachers and students.

The whole lecture had a strong academic atmosphere. Professor Jack Koolen’s explanation provided valuable thinking for everyone, which greatly enhanced teachers and students’ understanding of the academic frontier.

(By Zhang Xinyue, Hu Yuneng, Wang Yuke, Lin Yang, Tao Chunhai)