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Explore the arithmetic structure of the Dwork family in this 54-minute lecture from the Hausdorff Center for Mathematics. Delve into joint work with Lambert A'Campo, examining the equation x50 +· · ·+x54 = 5tx0 . . . x4 in P4 and its rich mathematical properties. Learn about the potentially modular submotives Mt of H3 (Yt), as demonstrated by Harris-Shepherd-Barron-Taylor, and their association with automorphic forms for GSp4,K. Investigate ongoing research on Beilinson's conjecture for the L-value Ln (Mt , 0), focusing on the higher Chow group CH4 (Mt , 4) and its expected rank of two. Discover the progress made in constructing the desired classes in CH4 (Mt, 4) and computing their regulators, providing insights into the relationship between motivic L-functions and automorphic L-functions.
