| Abstract: |
In the first part of this talk, we will give a basic introduction to the theory of modular forms, both scalar and vector-valued, which should be sufficient background to understand what follows. In the second part of the talk, we will discuss a conjecture regarding the Fourier coefficients of vector-valued modular forms for noncongruence subgroups of the modular group, including a brief discussion of how this conjecture connects to rational conformal field theory in mathematical physics. We will conclude the talk by explaining some results we have obtained in support of this conjecture. |
