时间：2026年11月4日（周三）16:00-17:00
地点：E14-215
主持人： 理论科学研究院 陈华一
主讲人: 麻省理工学院 张伟
主讲人简介: Wei Zhang received a BS from Peking University in 2004 and a PhD from Columbia University in 2009. Following a postdoctoral fellowship and a Benjamin Peirce Fellowship at Harvard, he joined the mathematics faculty at Columbia University in 2011, and in 2017 MIT mathematics faculty as a full professor. Zhang works in number theory, automorphic forms, and arithmetic geometry. His research program involves fundamental objects such as L-functions, which appear in the Riemann hypothesis and its generalizations, and are central to the Langlands program. He has been developing the theory of relative trace formula to connect L-functions with algebro-geometric objects, notably the discovery of "arithmetic fundamental lemmas." In the function field case, he and Zhiwei Yun have discovered geometric interpretations for the higher derivatives of L-functions. In another direction, Zhang and his collaborators have made significant advances on conjectures subsequent to the Gross--Zagier theorem on elliptic curves, including a proof of the Birch and Swinnerton-Dyer conjecture for approximately 66% of elliptic curves. Zhang received the 2010 SASTRA Ramanujan Prize, the Sloan Research Fellowship in 2013, Morningside Gold Medal of Mathematics at ICCM 2016, the 2018 New Horizon prize in mathematics, 2019 Clay Research Award, and the 2025 Alexanderson Award. In 2018, he gave an invited address at ICM 18 in Rio de Janeiro. He was named a Fellow of the AMS (2019), a Simons Investigator (2022), and a Fellow of the American Academy of Arts and Sciences (2023).
讲座主题：Arithmetic Diagonal Cycles and L-Functions
讲座摘要：The zeta function (or L-function) of an algebraic variety over a number field is conjectured to encode deep information about its algebraic cycles. We illustrate this paradigm by studying two types of "arithmetic diagonal cycles" on products of Shimura varieties: the diagonal cycle on the self-product of a Shimura variety and the graph cycle associated with the embedding of a Shimura subvariety of codimension one. In both cases, we present conjectures and theorems relating suitable arithmetic intersection numbers to the first derivatives of the relevant L-functions. We also discuss applications to the conjectures of Beilinson, Bloch, and Kato, which generalize the Birch and Swinnerton-Dyer conjecture for elliptic curves to higher-dimensional varieties.
