Abstract

Classifications of mathematical objects are very often the most important problems in various branches of mathematics. Intuitively, some classification problems are simple, and others are complicated. In this talk we will give some examples of classification problems and introduce a mathematical theory that studies the relative complexity of classification problems in mathematics. The theory is also known as invariant descriptive set theory, or the descriptive set theory of equivalence relations. We will demonstrate how to apply the theory to the study of classification problems in mathematics.

Biography

Su Gao is a Chair Professor of Nankai University. He graduated from Peking University and the Chern Institute of Mathematics, and obtained his PhD from UCLA. He worked as a postdoc at Caltech. From 2001 to 2021 he was a faculty member at the University of North Texas, and he served as Regents Professor, Chair of the Mathematics Department, and the Founding Dean of the College of Science. His main research interests are in mathematical logic and foundations of mathematics, and he has done work in topological groups, symbolic and topological dynamical systems, and ergodic theory. He solved some major open problems in descriptive set theory, and has published in top mathematical journals such as Inventiones Mathematicae and prestigious specialized journals such as the Journal of Symbolic Logic. Su Gao serves as an Editor for Science China Mathematics and some other journals in logic and mathematics, and he is the Managing Editor of the Perspectives in Logic series. He is a lifetime member of the Chinese Mathematical Society, a Council member of the Association for Symbolic Logic, and the Chair of the Committee on Mathematical Logic of the Chinese Mathematical Society.