Skip to content Skip to navigation

Academic Events

Dynamical Systems and Descriptive Set Theory

At the invitation of the Institute of Mathematics, Nanjing Normal University, Professor Su Gao,Chair Professor at Nankai University, delivered a report titled "Dynamical Systems and Descriptive Set Theory" at 9:30 AM on May 22, 2026, in Room 526 of Xingjian Building. Faculty and students from the School of Mathematical Sciences attended the event.In his report, Professor Gao began by reviewing the problem of Borel reducibility amongBorel equivalence relations, using it to classify the complexity of problems across different areas of mathematics. Starting from the most basic equivalence relation—equality of real numbers—he introduced five standard equivalence relations commonly used for comparison with others. He then elaborated on the application of this theory in symbolic dynamics, focusing on the complexity of conjugacy equivalence and bifactor equivalence. Furthermore, Professor Gao introduced Toeplitz subshifts as a special class of minimal Cantor systems and discussed the complexity issues associated with them. In presenting joint work with his collaborators, he noted that they introduced the concept of "topological rank," successfully computed the complexity of the conjugacy relation for Toeplitz subshifts of topological rank 2, and fully characterized the complexity of the bifactor relation for all Toeplitz subshifts.After the report, faculty and graduate students engaged in in-depth and lively discussions with Professor Gao, covering topics such as the Tukey order under the factorpreorder of Cantor systems and automorphism groups.Professor Su Gao is an internationally leading scholar in the field of descriptive set theory. He currently holds the position of Chair Professor at Nankai University. He previously served at the University of North Texas, where he held positions as Assistant Professor, Associate Professor, Professor, and Regents Professor, during which he also served as Department Chair of Mathematics and Founding Dean of the College of Science.His research focuses on mathematical logic and the foundations of mathematics, with fruitful contributions to topological groups, symbolic and topological dynamics, and ergodic theory. Professor Gao has achieved a series of breakthrough results in descriptive set theory, successfully solving several core open problems in the field. His work has appeared in leading mathematics journals such as Inventiones Mathematicae, Advances in Mathematics, Memoirsof the American Mathematical Society, and Transactions of the American MathematicalSociety, as well as top logic journals including the Journal of Symbolic Logic, Bulletin of Symbolic Logic, and Annals of Pure and Applied Logic.(By Dekui Peng)