Date/Time
Date(s) - 02/03/2023
10:30 am - 11:30 am

Speaker:  Gagandeep Virk

Title:  Vector Valued Modular Forms of dimension 3

Abstract:  Vector Valued Modular Forms (VVMFs) are holomorphic functions on the complex upper half plane, that have many applications in analytic number theory. In this talk, I will present my current research on VVMFs of dimension 3. My PhD supervisor, Dr. Cameron Franc along with Dr. Geoffrey Mason in 2015 identified the connections between 3-dimensional VVMFs and hypergeometric series. I will show that this relationship can be further extended to polynomials. I will present formulae for families of 3-dimensional VVMFs on $Gamma_0(2)$, a subgroup in $SL_2(mathbb{Z})$. In the rest of the talk, we will explore connections of VVMFs with Fourier series. I will present Fourier series related to the 3-dimensional VVMFs and show that it behaves similar to Eisenstein series. 

Time:  10:30 – 11:30 am
Location:  Hamilton Hall, room 207