James Arthur (mathematician)

James Arthur (born May 22, 1944) is a Canadian mathematician renowned for his significant contributions to the field of automorphic forms and representation theory. He is particularly known for his work on the trace formula, a powerful tool used to study the distribution of automorphic representations.

Arthur received his B.Sc. from the University of Toronto in 1966 and his Ph.D. from Yale University in 1970 under the supervision of Robert Langlands. After holding positions at the Institute for Advanced Study and the University of Toronto, he joined the faculty of the University of Toronto in 1977, where he remained until his retirement.

Arthur's work has had a profound impact on number theory and related areas. His most significant achievement is the development of the Arthur-Selberg trace formula, a generalization of the Selberg trace formula. This formula relates geometric data, such as the volumes of locally symmetric spaces, to spectral data, such as the eigenvalues of the Laplacian operator. It is a fundamental tool in the study of automorphic forms and has been used to prove many important results.

He has received numerous awards and honors for his work, including the Wolf Prize in Mathematics in 2015 and the Abel Prize in 2021. He is a Fellow of the Royal Society of Canada and a Foreign Associate of the National Academy of Sciences. Arthur has also held visiting positions at several prestigious institutions, including the Institute for Advanced Study and the École Normale Supérieure.

Arthur's contributions have solidified his place as one of the leading mathematicians of his generation. His work continues to inspire and influence researchers in number theory, representation theory, and related fields.