Professor of Mathematics
University of Toronto
will deliver the
Leonidas Alaoglu Memorial Lecture
"Weighted Orbital Integrals
and the Langlands Program"
Abstract: Weighted orbital integrals are the terms on the geometric side of the trace formula. A deeper understanding of their properties is becoming an increasingly important ingredient for progress in the Langlands program.
We shall begin with a brief and informal description of the general goals of the Langlands program. We shall then describe in elementary terms how weighted orbital integrals arise. Finally, we shall outline the solution of a comparison problem for weighted orbital integrals on different real groups. The problem is a local version of the kind of reciprocity laws predicted by the Langlands program. Its solution goes back to traditional concerns of classical analysis, namely, linear differential equations with boundary values.
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 of Toronto and the mathematics community.
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.
The Leonidas Alaoglu Memorial
Lecture was established by friends and family of the late Leonidas Alaoglu in recognition
of his great talents, distinguished contributions to mathematics, and long friendship with
Caltech. The Institute is privileged to honor his memory with a lecture each year by an