In-Person and Online Talk 

Zoom Link: https://theias.zoom.us/j/88393312988?pwd=emtLbTJ5ZnMvS3hBVmNmYjhIUEFIdz09

I will discuss recent work with Maksym Radziwill in which we show that for any fixed tempered cuspidal representation $\pi$ of $\mathrm{GL}(4)$ over the rationals, there exist infinitely many primitive characters $\chi$ such that the twisted $L$-function $L(s,\pi\times\chi)$ is non-vanishing at the central point $s=1/2$. I will focus on the proof, which involves a mix of ideas.