# Mathematics Colloquium - Christopher Marks

This event is in the past.

**Date:**October 28, 2019

**Time:**2:45 p.m. - 3:45 p.m.

**Category:**Lecture

Speaker: **Christopher Marks, California State Univeristy - Chico**

Title: **Free module theorems for modular subgroups**

Abstract: **One of the more fundamental results concerning vector-valued modular forms is the so-called free module theorem, which states that the space of vector-valued modular forms associated to a generic representation of the full modular group SL_2(Z) is free as a module over the ring of holomorphic modular forms for SL_2(Z). Although this result is now over ten years old, the method of proof provides a nice overview of vector-valued modular forms and I will spend a good portion of this talk explaining how the proof goes. In the last part of the talk, I will try to indicate how this theorem generally fails when one passes to proper subgroups of SL_2(Z), using recent (and ongoing) research on the index two subgroup of SL_2(Z) as a working example.**