Applications of the GL(3) Kuznetsov trace formula

Kuznetsov trace formula, or trace formulas in general, has been very useful in many applications. It relates spectral sums over families of automorphic forms to geometric sums like Kloosterman sums. In the GL(2) setting, the typical applications of the GL(2) Kuznetsov trace formula are well understood. These include the evaluation of moments, studying sums of Kloosterman sums, and beyond endoscopic techniques. One natural question is whether similar applications can be found in higher rank settings, and not much is known even in GL(3). Addressing parts of the question, this talk will delve into three applications of the GL(3) Kuznetsov trace formula, analogous to the GL(2) applications mentioned above. In particular, we will discuss our ongoing work on the GL(3) converse theorem joint with Valentin Blomer, and the second moment of twisted GL(3) L-function joint with Junxian Li.