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Explore Eisenstein congruences at prime square level in this 58-minute conference talk delivered at the International Centre for Theoretical Sciences. Delve into advanced number theory concepts as part of the "Automorphic Forms and the Bloch–Kato Conjecture" program, which examines recent developments and connections between automorphic forms and arithmetic of special values of L-functions. Learn about the intricate mathematical relationships between Eisenstein series and congruences when considering prime square levels, a specialized topic within the broader context of understanding the arithmetic nature of special values of complex L-functions. Gain insights into how these congruences relate to the central problems in number theory, including connections to algebraic varieties, motives, and automorphic representations over global fields. Discover the mathematical foundations that contribute to progress on major conjectures such as the Birch and Swinnerton-Dyer conjecture and the far-reaching Bloch-Kato conjecture, while understanding the essential role automorphic forms play in studying L-values and their associated algebraic structures including Chow groups and Selmer groups.
