Speaker:  Kenta Suzuki (MIT)

Title:  The explicit Local Langlands Correspondence for G2 and GSp4, character formulas and stability

Abstract:  I will talk about my recent joint work with Yujie Xu, where we prove the Local Langlands Conjecture explicitly for G2 (combined with previous work of Aubert-Xu) and GSp(4). I will discuss Aubert-Moussaoui-Solleveld’s construction of the cuspidal support map using the generalized Springer correspondence, which serves as a key property of our correspondence. I will also discuss character formulas in terms of generalized Green functions to pin down the ”mixed packets,” i.e., L-packets with multiple cuspidal supports. In the case of GSp(4), we classify the stable distributions on GSp(4), extending the methods of DeBacker-Kazhdan, using the homogeneity result of DeBacker and Waldspurger.