Recently, Atobe determined the intersection of all non-Archimedean local Arthur packets for symplectic and split odd orthogonal groups. Independently, in joint work with Alexander Hazeltine and Baiying Liu, we arrived at the same results using different methods. Furthermore, we gave 4 applications of our results. In this talk, I will discuss the complexities of non-Archimedean local Arthur packets with a focus on their intersections. I will first introduce the background of the theory of Arthur packets, and review Moeglin's explicit construction of local Arthur packets and Atobe's refinement. Next, I will state our main results about intersection of local Arthur packets, and then focus on two of our applications. As the first application, we characterize when a representation is in an L-packet of Arthur type in terms of its construction data. As the second application, we introduce our conjectural definition of "the" local Arthur parameter of a representation of Arthur type. If time permits, I will talk about the other 2 applications and some work in progress.

Meeting number (access code): 2514 465 6785

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