Speaker: John Voight (Dartmouth College)
Title: Modularity of K3 surfaces: explicit methods and computational questions
Abstract: The Langlands program predicts a deep connection between geometry and automorphic forms, encoded in their associated $L$-functions and Galois representations. For elliptic curves, this connection is summarized by the bijection between isogeny classes of elliptic curves over the rationals and classical newforms of weight 2 with rational Fourier expansion. In this talk, we discuss the predictions of Langlands for K3 surfaces, presenting some examples, open problems, and computational challenges.