For his remarkable contributions to the representation theory of Lie groups.

Binyong SUN

For his remarkable contributions to the representation theory of Lie groups.

Binyong Sun has made significant contributions to the representation theory of Lie groups, focusing particularly on the multiplicity one theorems for classical groups, the theory of theta correspondence, and the non-vanishing hypothesis in Rankin-Selberg convolutions.

The representation theory of Lie groups is foundational in modern mathematics. It originated from physics and is pivotal in the Langlands program, which has advanced numerous areas of number theory, including the proof of Fermat's last theorem.

Sun's first achievement lies in establishing the multiplicity one property for representations of classical Lie groups. Initially tackled by E. Cartan and H. Weyl in the compact case, Sun and his collaborator Chengbo Zhu extended this to the non-compact case. Their innovative approach solved this longstanding conjecture, laying the groundwork for relative representation theory and contributing to fundamental conjectures by Gan-Gross-Prasad.

His second major contribution is the theory of theta correspondences, a crucial method for studying automorphic forms across different groups. Sun and Zhu notably provided rigorous proof of Kudla and Rallis's conjecture regarding the non-vanishing of theta lifts in certain towers, significantly advancing the field.

Sun's third major achievement is the proof of the non-vanishing of period integrals for cohomological test vectors in Rankin-Selberg convolutions. This result, originally proposed by Kazhdan and Mazur in the 1970s, confirms their explicit computation and resolves a long-standing question in archimedean integrals.

Binyong Sun, born in 1976 in Zhoushan, Zhejiang Province, China and earned his Ph.D. from the Hong Kong University of Science and Technology in 2004. He worked for many years at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and is currently a professor at the Institute for Advanced Study in Mathematics, Zhejiang University.