Informal material
Author's comments: These notes are a very first draft of the very first part of a continuing series of lectures that will be held at the Yildiz Teknik Universitesi in Istanbul and may ultimately become an informal essay on various simple aspects of mathematical history and related matters. As they now stand, they are no more than a tentative beginning both linguistically and conceptually. They are posted primarily for use by the audience at the lectures. I apologize in advance for all their failings, grammatical and mathematical. All being well, these will be corrected with time.
The Thursday afternoon and Friday morning seminars
In the fall of 1983 Langlands and others held a seminar at the Institute for Advanced Study (Princeton) on Thursday afternoons, and Langlands and JeanPierre Labesse ran a seminar Friday mornings on the twisted trace formula. The notes from the lectures are in the process of being put to \(\TeX\), but in the meantime I post scans of the originals (done by Alice Garber at the Institute in Princeton). Not all lectures were written up for distribution.
Thursday afternoon

Orbital integrals of spherical functions (Jonathan Rogawski)[ Sem10.pdf ]

Division algebras I (Robert Langlands)[ Sem11.pdf ]

On the global correspondence between \(\mathrm{GL}(n)\) and division algebras (MarieFrance Vigneras)[ Sem12.pdf ]

Division algebras III (Robert Langlands)[ Sem13.pdf ]
Friday morning

Introduction (Robert Langlands)[ Lecture_1.pdf ]

The basic identity proved (Robert Langlands)[ Lecture_2.pdf ]

The coarse \(O\)expansion (JeanPierre Labesse)[ Lecture_3.pdf ]

Absolute convergence of the coarse \(O\)expansion (JeanPierre Labesse)[ Lecture_4.pdf ]

\(O\)expansion and weighted orbital integrals (JeanPierre Labesse)[ Lecture_5.pdf ]

Properties of the truncation operator (Robert Langlands)[ Lecture_6.pdf ]

Preparation for the coarse \(\chi\)expansion I. Statement of Lemmas (Robert Langlands)[ Lecture_7.pdf ]

Preparation for the coarse \(\chi\)expansion. Proof of the Lemmas (Robert Langlands)[ Lecture_8.pdf ]

The modified basic identity and weighted orbital integrals (JeanPierre Labesse)[ Lecture_9.pdf ]

The inner product formula (JeanPierre Labesse)[ Lecture_12.pdf ]

Some formal properties of the terms in the trace formula (JeanPierre Labesse)[ Lecture_13.pdf ]

The fine \(\chi\)expansion (Robert Langlands)[ Lecture_15.pdf ]