In recent decades the advances in our knowledge of the physical world have been closely connected to the progressions in mathematics. I will begin the talk by reviewing some of the most important such examples, in both the physics of fundamental particles and the physics of electrons in solid materials; along the way I will introduce some background mindsets and motivations of working physicists. Then I will talk about our recent studies on physics theories in which the topological aspects have non-trivial interplay with the non-topological aspects, including topological quantum field theories (with or without symmetry protection) that are not fully extended and thus have non-topological physics on boundary, as well as some fascinating dualities between Chern-Simons-matter theories.

Jing-Yuan Chen is a Member at the Institute for Advanced Study at Tsinghua University. He received PhD in Physics from the University of Chicago, and was a postdoc fellow at Stanford Institute for Theoretical Physics before the current appointment. He works on 1) theoretical condensed matter physics, including both formal developments and experimental phenomenologies, 2) formal aspects of quantum field theory, and more recently, 3) the connection between quantum information and gravity.