Topology has become an important principle in modern physics. For example, the flux quantization of magnetic monopole, the source of magnetic field proposed by P. A. M. Dirac, is a topological property of the electromagnetic gauge field. Topological properties of the space-time and gauge fields also determine the structure of various quantum anomalies. 

More recently, the principle of topology has been applied to condensed matter physics in the study of topological states of matter. Topological states of matter are new quantum states which are distinguished by their topological properties. The first topological states of matter ever discovered are the integer and fractional quantum Hall states. In recent years, new topological states of matter known as topological insulators and topological superconductors have been theoretically predicted and experimentally discovered. Topological states of matter are described by topological field theories which characterize their topological properties. For example, three-dimensional topological insulators are associated with a `` $\Theta$ vacuum” term related to the second Chern invariants of the electromagnetic field, which describes a topological magneto-electric effect. The surface state of a topological superconductor is a Majorana fermion, a fermion studied extensively in high energy physics which is its own anti-particle. In certain topological superconductors, point defects, such as vortices or ends of nanowires, carry a single Majorana zero mode which means a qubit is stored non-locally in a pair of such defects. Such a nonlocal degree of freedom makes the topological superconductor a promising candidate of topological quantum computation.

In the research of topological states of matter, new mathematical tools, such as Chern-Simons theory, K-theory, tensor category and group cohomology, etc., have been introduced and played an essential role. Therefore it is important to bring mathematicians and physicists together, to improve the understanding to mathematical tools and to address the needs in physics. Therefore we have this one day meeting aimed for exchanging ideas and inspiring interactions between mathematicians and physicists in the field of topological physics.