Arithmetic Study Group: Modular Invariant Partition Functions in String Theory
24 January 2017 14:00 in CM103
String theory is a physical theory which aims to unify quantum field theory with general relativity. As well as being a promising theory of quantum gravity, string theory has also led to developments in pure mathematics. In this, the first of two consecutive talks, we will recap some historical developments in physics and see how they suggest the need for string theory. A basic description of string theory will be presented, and we will see that a quantity known as the partition function of the theory is invariant under modular transformations. A particular string theory will be presented, whose partition function demonstrates a surprising link between modular forms and group theory. This is the first of numerous interesting connections between string theory and the theory of modular forms, which the second talk will discuss in further detail.