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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, and 2019 Clay Research Award. In 2018, he gave an invited address at ICM 18 in Rio de Janeiro. He was named a Fellow of the AMS in 2019.
2023 Fellow of the American Academy of Arts and Sciences
2023 Fellow of the American Academy of Arts and Sciences
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arXiv (Cornell University) (2023)
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Inventiones mathematicaeno. 2 (2023): 1-100
arXiv (Cornell University) (2023)
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