It is a very natural question to generalize the concepts of trace and determinant of linear operators to infinite dimensional spaces. In this talk I will introduce the so-called trace class operators on complex separable Hilbert spaces for which the trace could be defined. We will also discuss a few basic properties of trace class operators and related concepts such as Hilbert-Schmidt operators. Time permitting I will also discuss the Fredholm determinants associate to trace class operators which is a natural generalization of usual determinants for operators on finite dimensional spaces. Speaker(s): Yuchen Liao (University of Michigan)