Siddharth Mahendraker (BC)

The relative trace formula plays a fundamental role in understanding distinguished automorphic representations. In this talk, I introduce a new regularized relative trace formula for the Galois period on SL(2). I will give an overview of the proof of convergence of the geometric side, and then discuss the fine geometric expansion, with a special focus on the contribution from relative unipotent orbital integrals. It turns out that these can be understood geometrically in terms of the Springer resolution of the nilpotent cone for Lie(SL(2)). This clarifies and generalizes formulas first written down by Labesse and Langlands in the setting of the usual trace formula.