Professor Henri Darmon (McGill) has been appointed as a Clay Senior Scholar to participate in this program. After being trained by the Bernoullis in mathematics, Euler followed. On the occasion of the 300th anniversary (on April 15, 2007) of Eulers birth, an attempt is made to bring Eulers genius to the attention of a broad. The goal of this semester is to bring together researchers working on different aspects of this young but fast-developing subject, and to make progress on understanding the mysterious relations between L-functions, Euler systems, and algebraic cycles. Leonhard Euler was born in Basel, Switzerland, in 1707, the son of a Calvinist pastor. The cohomology classes of special cycles (and related constructions such as Eisenstein classes) form the foundation of the theory of Euler systems, providing one of the most powerful methods known to prove vanishing or finiteness results for Selmer groups of Galois representations. Sminaire Lotharingien de Combinatoire electronic only 44 (2000): B44d, 71 p. The arithmetic intersection numbers and the p-adic regulators of special cycles are directly related to the values and derivatives of L-functions, as shown in the pioneering theorem of Gross-Zagier and its p-adic avatars for Heegner points on modular curves. The study of special algebraic cycles on Shimura varieties has led to progress in our understanding of these conjectures. This article is about a mathematician who in 1775, while France was mired in revolution, was in St Petersburg researching both mathematics and science. Each of these was assigned a number, from E1 to E866, which is now referred to as the 'Enestrm number. He enumerated 866 distinct works, including books, journal articles, and some letters he deemed to be especially important. Leonhard Euler derived equations of motion for both (in modern terminology) point mass mechanics and analytic mechanics. It resides at the heart of a collection of important conjectures (due especially to Deligne, Beilinson, Bloch and Kato) that connect values of L-functions and their leading terms to cycles and Galois cohomology groups. So opens Charles Dickenss book A Tale of Two Cities, a story set in revolutionary France of 1775. In 1913, Swedish mathematician Gustaf Enestrm completed a comprehensive survey of Euler's works. Website: The fundamental conjecture of Birch and Swinnerton-Dyer relating the Mordell–Weil ranks of elliptic curves to their L-functions is one of the most important and motivating problems in number theory.
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