Caltech-Tsinghua Joint Colloquium

Spectral reciprocity reveals hidden connections between different automorphic spectra and has emerged as a powerful tool in the study of automorphic $L$-functions. In this talk, I will explain how recent spectral reciprocity formulas can be used to obtain explicit subconvexity bounds for $\mathrm{GL}_2$ over number fields, and I will highlight some arithmetic applications that follow from these ideas.