## Conference on automorphic forms and the trace formula,

in honour of James Arthur on the occasion of his 60th birthday

## Professor James G. Arthur, Department of Mathematics

Professor
James Arthur has published 56 research papers, comprising over two thousand
pages in mathematical journals of the highest reputation. He is regarded
as one of two or three leading mathematicians in the world in the central
fields of representation theory and automorphic forms. In addition to
being an outstanding scientist, Professor Arthur is an excellent teacher
and has a distinguished record of service to both the University and the
mathematics community.

Representation theory is the study of the deeper aspects of symmetry.
The notion of symmetry plays a prominent role in mathematics, and indeed
throughout much of science. It is a fundamental unifying force. Representation
theory probes the hidden mathematical properties of symmetry in much
the same way that spectroscopy analyzes hidden physical properties of
light and matter. Automorphic forms is the branch of representation
theory that relates symmetry with arithmetic and number theory. According
to a general philosophy of R. Langlands of Princeton, automorphic forms
hold the key to unifying vast areas of mathematics, some of which date
back several centuries. The Langlands programme is a stunning blueprint
for relating arithmetic and algebra on the one hand, with analysis and
spectral theory on the other.

Over the past thirty years, Professor Arthur has been a leader in the
quest to take the Langlands programme from the realm of conjecture to
actual mathematical realization. In so doing, he made many fundamental
discoveries, which have had a tremendous impact on mathematical research.
In a series of papers that spanned two decades, he was able to construct
the general trace formula, a mathematical equation of enormous power
that had been sought by mathematicians since the 1950s. His joint work
with L. Clozel, which appeared in Annals of Mathematics Studies, solved
a critical comparison problem for trace formulae on different groups.
He has introduced a remarkable conjectural classification of automorphic
representations, in terms of what are now known as Arthur packets. In
the early 1990s, he found a local version of the trace formula that
had been conjectured by D. Kazhdan.

Professor Arthur is highly sought after as a lecturer on the international
scene. His oral and written exposition of mathematics is clear and inspiring.
He is a dedicated mentor of young faculty and graduate students. His
active role in the International Mathematical Union, which organizes
the International Congress of Mathematicians every four years, has brought
Canada to greater prominence on the world mathematical stage.

Professor Arthur has achieved many distinctions in his career. Elected
as a Fellow of the Royal Society of Canada in 1980 and the Royal Society
of London in 1992, he became the first recipient of the Synge Award
of the Royal Society of Canada in 1987. He was awarded the CRM/Fields
Institute Prize and the Henry Marshall Tory Medal in 1997. In 1999 he
received the Canada Gold Medal for Science and Engineering from NSERC,
making him the only mathematician to have won Canada's top award in
science. Professor Arthur has twice been an invited lecturer for the
International Congress of Mathematicians. He was awarded the Wilbur
Lucius Cross Medal from the Graduate School of Yale University and a
Guggenheim Fellowship in 2000. In 2002, he received an honorary doctorate
from the University of Ottawa in recognition of his achievements in
mathematics.

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