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Notes from the lectures:

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(last edited 4-22-03)
langlands042203.pdf

Diagrams: diagrams.pdf

Robert P. Langlands
Institute for Advanced Study

Lecture Series (Tues & Thurs in April)
The search for general reciprocity laws

• Quadratic and quartic irrationalities in the later books of Euclid.
• Cyclotomic irrationalities in Gauss's Disquisitiones.
• Higher reciprocity laws.
• Analytic and algebraic proofs in class field theory.
• Reciprocity laws and automorphic forms.
• Past and future uses of the trace formula, especially for GL(2)
• Algebraic number theory and the trace formula.
• Analytic number theory and the trace formula.

Colloquium:
The renormalization fixed-point as a mathematical object.
Thursday, April 17 at 4 pm in MS 6627

Purpose:
This will be, by and large, an exhortatory lecture. Langlands will review the pertinent notions, argue that mathematicians have overlooked some fascinating and very difficult problems, and make some tentative suggestions about what might be done.

Background:
Robert P. Langlands is one of the greatest mathematicians of our times. His extraordinary vision has changed many areas of mathematics including number theory, automorphic forms, arithmetic algebraic geometry, mathematical physics, and probability. His remarkable and profound insights in the theory of automorphic forms have revolutionized that subject and placed it at the common meeting ground of some of the most fundamental questions in contemporary mathematics. His work waspart of the foundation on which Andrew Wiles built his proof of Fermat's Last Theorem.

Langlands was born in New Westminster, British Columbia in Canada in 1936. He received his Ph.D. from Yale University in 1960. He is currently the Hermann Weyl Professor in the School of Mathematics at the Institute for Advanced Study at Princeton. He received the Cole Prize of the American Mathematical Society in 1982, and the Wolf prize in 1995 which he shared with Andrew Wiles. He was awarded the Gold Medal of the Paris Academy of Sciences, the highest honor of the Academy, in 2000.

He is a Fellow of the Royal Society of London and has received numerous honorary degrees.

For additional details on Langlands and his work: Digital Math Archive on Langlands