Robert P. Langlands

The renormalization fixed point as a mathematical object

Author: 
Robert P. Langlands
Abstract: 

Journal
Journal: 

Appeared in Twenty years of Bialowieza: A Mahtematical anthology, World Scientific Monograph Series in Mathematics

Volume: 
8
Type: 
article
Keywords: 
Mathematical Physics

Author's comments: This paper was prepared for a meeting in Bialowieza that I was unable at the last minute to attend. It has appeared in the proceedings of that conference, Twenty years of Bialowieza: A mathematical anthology. The paper was intended as a beginning.

School of Mathematics: 

Aspects combinatoires des équations de Bethe

Author: 
Robert P. Langlands
Yvan Saint-Aubin
Journal
Journal: 

Advances in Mathematical Sciences: CRM's 25 Years

Year: 
1991
Type: 
article
Keywords: 
Mathematical Physics
MathReview: 
95d:60161

Author's comments: There are two papers on the Bethe Ansatz, but the work is far from complete. I have always wanted to return not only to the algebraic geometrical arguments initiated in the second paper, which seem to me of considerable intrinsic mathematical interest as algebraic geometry, but also to the notion of Wellenkomplex and the Puiseux expansions introduced briefly at the end of the first paper. So far, I have not found the time.

School of Mathematics: 

Shimuravarietäten und Gerben

Author: 
Robert P. Langlands
Journal
Journal: 

Journal für die reine und angewandte Mathematik

Volume: 
378
Year: 
1987
Type: 
article
Keywords: 
Shimura
MathReview: 
88i:11036

Author's comments: It has been pointed out by J. Milne, by M. Pfau and by H. Reimann that there is a blunder in this paper in the treatment of gerbes. For a description of the error, for necessary corrections, and for further references, see the notes of Reimann, The semi-simple zeta function of quaternionic Shimura varieties, Lect. Notes Math. 1657.

School of Mathematics: 

Sur la mauvaise réduction d'une variété de Shimura

Author: 
Robert P. Langlands
Journal
Journal: 

Journées de Géométrie Algébrique de Rennes, Astérisques

Volume: 
65
Year: 
1979
Type: 
article
Keywords: 
Shimura
MathReview: 
82c:10039

Author's comments: Although this paper has some merit, it also leaves a lot to be desired, and suffers from the author's inexperience with the material. For a better treatment of more general questions and corrections to the assertions of this paper, the reader is advised to consult a paper of Thomas Zink, Über die schlechte Reduktion einiger Shimuramannigfaltigkeiten, Comp. Math. 45 (1981).

School of Mathematics: 

A prologue to functoriality and reciprocity: Part 1

Author: 
Robert Langlands
Abstract: 

Journal
Year: 
Finished in late 2012
Type: 
article
Keywords: 
Beyond Endoscopy

Author's comments: There is as yet no text with the title Functoriality and Reciprocity. Begun as preparations for a lecture, the text appearing here was, and remains, a first attempt to come to terms with the two topics of the title, an attempt that is perhaps doomed by its nature and by my years to remain provisional.

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