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Explore the intricacies of p-adic Eichler-Shimura theory and its arithmetic applications in this advanced mathematics lecture. Delve into the work of Pan and Rodriguez, examining the p-adic Eichler-Shimura decomposition of completed cohomology through the lens of higher Coleman theory. Gain insights into ongoing research on modularity, presented as a joint work in progress with G. Boxer, F. Calegari, and T. Gee. This 68-minute talk, delivered by Vincent Pilloni at the Hausdorff Center for Mathematics, offers a deep dive into cutting-edge mathematical concepts for those well-versed in advanced number theory and algebraic geometry.
