Skip navigation
Please use this identifier to cite or link to this item:
Title: Derived Structures in the Duality of Automorphic Periods
Authors: Chen, Eric Y.
Advisors: Venkatesh, Akshay
Contributors: Mathematics Department
Subjects: Mathematics
Issue Date: 2023
Publisher: Princeton, NJ : Princeton University
Abstract: Built on top of the global Langlands correspondence – a matching of automorphic forms on a reductive group G and Galois representations into its Langlands dual group Gˇ – is the question of functoriality, i.e., the construction and detection of natural transfers of automorphic forms between varying G, predicted by maps between varying Gˇ. Traditionally, this involved understanding natural numerical invariants attached to both sides of the correspondence: computing automorphic periods on the one hand, and understanding analytic properties of various Langlands L-functions on the other. Recently, Ben-Zvi–Sakellaridis–Venkatesh proposed a duality framework that extends Langlands duality to these numerical invariants, in which automorphic periods and L-functions are extracted from Hamiltonian actions of G and Gˇ, respectively. We expand on this perspective by computing new automorphic periods and by recasting old computations in the context of this emergent duality. In the process, we encounter and introduce the notion of nonabelian L-functions as the Galois-side counterpart to our new automorphic computations, and we suggest that they may be understood as reflecting the presence of singularities or derived structures, on the Hamiltonian Gˇ-action.
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

Files in This Item:
File Description SizeFormat 
Chen_princeton_0181D_14539.pdf571.1 kBAdobe PDFView/Download

Items in Dataspace are protected by copyright, with all rights reserved, unless otherwise indicated.