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Explore a 58-minute lecture from the ZhengTong Chern-Weil Symposium Spring 2025 featuring Jacob Tsimerman from the University of Toronto, presented by the University of Chicago Department of Mathematics. Delve into "Diophantine Results for Shimura Varieties," where Tsimerman examines these higher-dimensional analogues of modular curves that are fundamental to modern number theory. Learn about the challenges in the exceptional setting for Shimura varieties where the lack of moduli interpretation creates difficulties. Discover how Tsimerman and his collaborators Ben Bakker and Ananth Shankar approach analogues of important results like finiteness of S-rational points, the Tate conjecture, the Shafarevich conjecture, and semisimplicity of Galois representations. Understand the crucial role of constructing canonical integral models at almost all primes in advancing these mathematical concepts.
