Unpublished Manuscripts

In different branches of mathematics, there are influential manuscripts whose existence is known to the experts, there references to them in various papers -- but which are not published (usually because they are unfinished and thus not suitable for publication). In the old days, the only way to get such a manuscript would be to ask someone for a copy (this explains why virtually all known copies of G. Segal's preprint on mathematical definition of conformal field theory bear the same inscripiton "Do not copy" -- they all can be traced to the copy of D. Freed). Nowadays, many of such manuscripts are avaliable on the internet and can be found using Google.

On this page, I tried to collect links to such manuscripts in my field (representation theory/math physics). In most cases, these are just links to other locations on the web. The exception is the manuscript of Beilinson, Feigin, and Mazur, which is posted here with the author's permission.

G. Segal, The definition of conformal field theory
This text was circulating as a preprint for many years. It has finally been published in the book Topology, geometry and quantum field theory, London Math. Soc. Lecture Note Ser., 308, Cambridge Univ. Press, Cambridge, 2004.
J. Bernstein, Course on D-modules
One of the best introductions to the theory of D-modules. It was never published; however, a copy is available from the web page of Langlands seminar at Univ. of Chicago, which also cotains a number of other remarkable texts.
A. Beilinson, B. Feigin, B. Mazur, Notes on Conformal Field Theory: TeX, DVI, PDF
This text was written in 1991 and never published. It is posted here with the author's permission. It is incomplete and many details are missing. By now there are several published books which contain exposition of some parts of this text: for example, D. Gaitsgory's Notes on 2D conformal field theory and string theory in Quantum fields and strings: a course for mathematicians, Amer. Math. Soc., 1999; B. Bakalov, A. Kirillov, Lectures on Tensor Categories and Modular Functors, AMS, 2001. However, some of the ideas of the text have never been fully developed.
A scanned PDF version of this text is also available from Barry Mazur's web page.
K. Walker, On Witten's 3-manifold invariants.
This text was also written in 1991 and never published. It contains an introduction to the invariants of knots and 3-manifolds arising from conformal field theory.
A. Beilinson, D. Kazhdan, Flat Projective Connections
Unpublished. Here is a PDF file, provided by Bezrukavnikov.

Back to Alexander Kirillov's web page.

Valid HTML 4.01!