PDF, dvi and plain TeX files of papers and preprints by R. E. Borcherds

  1. tex dvi pdf A monster Lie algebra? (with J. H. Conway, L. Queen and N. J. A. Sloane .) Adv. Math. 53 (1984) 75-79.
  2. tex dvi pdf The Leech lattice and other lattices, Ph.D. thesis (Cambridge, 1985).
  3. tex dvi pdf The Leech lattice, Proc. Royal Soc. London A398 (1985) 365-376.
  4. tex dvi pdf Vertex algebras, Kac-Moody algebras and the monster, Proc.Nat. Acad. Sci. U.S.A. 83 (1986), 3068-3071.
  5. tex dvi pdf Automorphism groups of Lorentzian lattices, J.Alg. Vol 111, No. 1, Nov 1987, pp. 133-153.
  6. tex dvi pdf Generalized Kac-Moody algebras, J.Alg. Vol 115, No. 2, June 1988, p. 501-512.
  7. tex dvi pdf The 24-dimensional odd unimodular lattices. Sphere packings, lattices, and groups, by J.H. Conway and N. J. A. Sloane , chapter 17 (p. 421-430.) (This does not include the table of such lattices, which can be extracted from table -4 of "The Leech lattice and other lattices". )
  8. tex dvi pdf The cellular structure of the Leech lattice. (with J. H. Conway and L. Queen) Sphere packings, lattices, and groups, by J.H. Conway and N. J. A. Sloane , chapter 25 (p. 515-523.)
  9. tex dvi pdf Lattices like the Leech lattice, J.Alg. Vol 130, No. 1, April 1990, p.219-234.
  10. tex dvi pdf The monster Lie algebra, Adv. Math. Vol 83, No. 1, September 1990, p. 30-47.
  11. tex dvi pdf Central extensions of generalized Kac-Moody algebras, J. Algebra. Vol 140 No. 2, July 1991, 330-335.
  12. tex dvi pdf Introduction to the monster Lie algebra, (EXPOSITORY) ``Groups, combinatorics, and geometry, Durham 1990'', p. 99-107, L.M.S. lecture notes in mathematics 165, C.U.P. 1992, edited by M.W.Liebeck and J.Saxl.
  13. tex dvi pdf Monstrous moonshine and monstrous Lie superalgebras, Invent. Math. 109, 405-444 (1992).
  14. tex dvi pdf Sporadic groups and string theory, (EXPOSITORY) First E. C. M., Vol. I (Paris, 1992), 411-421, Progr. Math., 119, Birkhäuser, Basel, 1994.
  15. tex dvi pdf A characterization of generalized Kac-Moody algebras, J. Algebra 174, 1073-1079 (1995).
  16. tex dvi pdf Automorphic forms on Os+2,2(R) and infinite products, Invent. Math. 120, p. 161-213 (1995)
  17. tex dvi pdf Automorphic forms on Os+2,2(R)+ and generalized Kac-Moody algebras, (EXPOSITORY) Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), 744-752, Birkhäuser, Basel, 1995.
  18. tex dvi pdf The moduli space of Enriques surfaces and the fake monster Lie superalgebra, Topology vol. 35 no. 3, 699-710, 1996.
  19. tex dvi pdf Modular moonshine II (with A. J. E. Ryba) Duke Math. J. 83 (1996) no. 2, 435-459.
  20. tex dvi pdf Families of K3 surfaces (with L. Katzarkov, T. Pantev, N. I. Shepherd-Barron), J. Algebraic Geometry 7 (1998) 183-193.
  21. tex dvi pdf A Siegel cusp form of degree 12 and weight 12. (with E. Freitag, R. Weissauer), J. reine angew. Math. 494 (1998) 141-153. There are also some related tables.
  22. tex dvi pdf Modular moonshine III, Duke math. journal vol. 93 No. 1 (1998) 129-154.
  23. tex dvi pdf Automorphic forms with singularities on Grassmannians, Invent. Math. 132, 491-562 (1998)
  24. tex dvi pdf An automorphic form related to cubic surfaces, Unpublished note, 1998.
  25. tex dvi pdf Vertex algebras, Topological field theory, primitive forms and related topics (Kyoto, 1996), 35-77, Progr. Math., 160, Birkhäuser Boston, Boston, MA, 1998.
  26. tex dvi pdf The Gross-Kohnen-Zagier theorem in higher dimensions, Duke Math. J. 97 (1999), no. 2, 219-233, Correction Duke math journal vol 105 No. 1 p.183-184.
  27. tex dvi pdf The fake monster formal group, Duke Math J. Vol 100 No. 1 (1999), 139-165.
  28. tex dvi pdf Automorphic forms and Lie algebras, (EXPOSITORY) Current Developments in mathematics 1996, International Press 1998.
  29. tex dvi pdf What is a vertex algebra? (EXPOSITORY) Unpublished 1997 Arbeitstagung talk.
  30. tex dvi pdf What is moonshine? (EXPOSITORY) Proceedings of the I.C.M., Vol. I (Berlin, 1998). Doc. Math. 1998, Extra Vol. I, 607-615
  31. tex dvi pdf Coxeter groups, Lorentzian lattices, and K3 surfaces, IMRN 1998 No. 19, 1011-1031.
  32. tex dvi pdf Reflection groups of Lorentzian lattices. Duke Math. J. 104 (2000) no. 2, 319-366.
  33. tex dvi pdf Classification of positive definite lattices, Duke Math J. 105 (2000) no. 3, 525-567.
  34. tex dvi pdf Problems in moonshine. First International Congress of Chinese Mathematicians (Beijing, 1998), 3-10, AMS/IP Stud. Adv. Math., 20, Amer. Math. Soc., Providence, RI, 2001. Edited by Lo Yang and S.-T. Yau.
  35. tex dvi pdf Quantum vertex algebras. Taniguchi Conference on Mathematics Nara '98, 51-74, Adv. Stud. Pure Math., 31, Math. Soc. Japan, Tokyo, 2001.
  36. tex dvi pdf What is the monster? Notices of the A.M.S., vol 49, no. 9 Oct 2002, pages 1076-1077.
  37. ps Quantum field theory arXiv: math-ph/0204014 Notes by Alex Barnard from a lecture course.
  38. latex dvi pdf Renormalization and quantum field theory arXiv preprint http://arxiv.org/abs/1008.0129 Algebra & Number Theory 5-5 (2011), 627--658. DOI 10.2140/ant.2011.5.627