Informal material
Istanbul lectures on the history of mathematics
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.
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Istanbul konferans dizisi (Robert P. Langlands)
Yıldız Technical University
June 2003
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 Jean-Pierre Labesse ran a seminar Friday mornings on the twisted trace formula. Almost all of the lectures were written up. What I've posted here are scans of the originals, made by Alice Garber at the IAS.
There was at one time thoughts of turning the scans to \(\TeX\), but that is no longer under discussion. There are several errors in the Friday morning lectures, although none crippling. Corrected versions were later incorporated into the book La Formule des Traces Tordue d’après le Friday Morning Seminar by Jean-Pierre Labesse and Jean-Loup Waldspurger.
Thursday afternoon
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The structure of trace formulas and their comparison (Robert Langlands)
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Orbital integrals of spherical functions (Jonathan Rogawski)[ Sem10.pdf ]
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Preliminary facts about unitary groups in three variables (Jonathan Rogawski)[ rogawski-1.pdf ]
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Stable conjugacy, stable trace formula (Jonathan Rogawski)[ rogawski-2.pdf ]
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Division algebras I (Robert Langlands)[ Sem11.pdf ]
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On the global correspondence between \(\mathrm{GL}(n)\) and division algebras (Marie-France Vigneras)[ Sem12.pdf ]
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Division algebras III (Robert Langlands)[ Sem13.pdf ]
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The hyperbolic terms for \(\mathrm{SL}(3)\) and \(\mathrm{SU}(3)\) (Robert Langlands)
Friday morning
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Introduction (Robert Langlands)[ Lecture_1.pdf ]
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The basic identity proved (Robert Langlands)[ Lecture_2.pdf ]
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The coarse \(O\)-expansion (Jean-Pierre Labesse)[ Lecture_3.pdf ]
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Absolute convergence of the coarse \(O\)-expansion (Jean-Pierre Labesse)[ Lecture_4.pdf ]
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\(O\)-expansion and weighted orbital integrals (Jean-Pierre Labesse)[ Lecture_5.pdf ]
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Properties of the truncation operator (Robert Langlands)[ Lecture_6.pdf ]
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Preparation for the coarse \(\chi\)-expansion I. Statement of Lemmas (Robert Langlands)[ Lecture_7.pdf ]
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Preparation for the coarse \(\chi\)-expansion. Proof of the Lemmas (Robert Langlands)[ Lecture_8.pdf ]
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The modified basic identity and weighted orbital integrals (Jean-Pierre Labesse)[ Lecture_9.pdf ]
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The inner product formula (Jean-Pierre Labesse)[ Lecture_12.pdf ]
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Some formal properties of the terms in the trace formula (Jean-Pierre Labesse)[ Lecture_13.pdf ]
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The fine \(\chi\)-expansion (Robert Langlands)[ Lecture_15.pdf ]