Richard E. Borcherds의 정보

수상나이 39
출생년도 1959
사망년도
출생지 Cape Town(South Africa)
현재소속 Cambridge University
연구실적 [자세히 보기]
관련출판물 1.James Lepowsky, Joram Lindenstrauss, Yuri I. Manin, John Milnor, The mathematical work of the 1998 Fields medalists. Notices Amer. Math. Soc. 46 (1999), no. 1, 17--26

2. Atsushi Matsuo, The achievements of Fields medalist R. E. Borcherds. II. (Japanese) S\=ugaku 51 (1999), no. 1, 57--61

3. K\=oichir\=o Harada, The achievements of Fields medalist R. E. Borcherds. I. (Japanese) S\=ugaku 51 (1999), no. 1, 56--57
4. Adolfo Quir?s, The Fields Medals [of 1998]. (Spanish) Gac. R. Soc. Mat. Esp. 1 (1998), no. 3, 439--446

5. C. S. Rajan, Bhatia Rajendra, T. R. Ramadas, Nimish A. Shah, The work of the Fields medalists:1998. Current Sci. 75 (1998), no. 12, 1290--1295

6. Peter Goddard, The work of [Fields medalist] Richard Ewen Borcherds. Mitt. Dtsch. Math.-Ver. 1998, no. 3, 33--38

시상내역 Received a medal for his work in the fields of algebra and geometry, in particular for his proof of the so-called Moonshine conjecture.
Other Award
연구단행본 [1] Borcherds, Richard E. Quantum vertex algebras. Taniguchi Conference on Mathematics Nara '98, 51--74, Adv. Stud. Pure Math., 31, Math. Soc. Japan, Tokyo, 2001. 17B69 (81R10)
[2] Borcherds, Richard E. 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. 20D08 (11F22 17B67 17B69 20F55)
[3] Borcherds, Richard E. Automorphic forms and Lie algebras. Current developments in mathematics, 1996 (Cambridge, MA), 1--36, Int. Press, Boston, MA, 1997. 11F22 (17B67 17B69)
[4] Conway, J. H.; Sloane, N. J. A. Sphere packings, lattices and groups. Third edition. With additional contributions by E. Bannai, R. E. Borcherds, J. Leech, S. P. Norton, A. M. Odlyzko, R. A. Parker, L. Queen and B. B. Venkov. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 290. Springer-Verlag, New York, 1999. lxxiv+703 pp. ISBN: 0-387-98585-9 11H31 (05B40 11H06 20D08 52C07 52C17 94B75 94C30)
[5] Borcherds, Richard E. Vertex algebras. Topological field theory, primitive forms and related topics (Kyoto, 1996), 35--77, Progr. Math., 160, Birkhäuser Boston, Boston, MA, 1998. 17B69
[6] Borcherds, Richard E. Automorphic forms on ${\rm O}\sb {s+2,2}(\bold R)\sp {+}$ and generalized Kac-Moody algebras. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), 744--752, Birkhäuser, Basel, 1995. 11F55 (11F22 17B67)
[7] Borcherds, Richard E. Sporadic groups and string theory. First European Congress of Mathematics, Vol. I (Paris, 1992), 411--421, Progr. Math., 119, Birkhäuser, Basel, 1994. 11F22 (17B67 20D08 81T30)
[8] Borcherds, Richard E. Introduction to the Monster Lie algebra. Groups, combinatorics & geometry (Durham, 1990), 99--107, London Math. Soc. Lecture Note Ser., 165, Cambridge Univ. Press, Cambridge, 1992. 11F22 (17A70 17B10 17B67 20D08)
[9] Conway, J. H.; Sloane, N. J. A. Sphere packings, lattices and groups. Second edition. With additional contributions by E. Bannai, R. E. Borcherds, J. Leech, S. P. Norton, A. M. Odlyzko, R. A. Parker, L. Queen and B. B. Venkov. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 290. Springer-Verlag, New York, 1993. xliv+679 pp. ISBN: 0-387-97912-3 11H31 (05B40 11H06 20D08 52C07 52C17 94B75)
[10] Konve\u\i, Dzh.; Sloèn, N. {\cyr Upakovki sharov, reshetki i gruppy. Tom} {\rm II}. (Russian) [Sphere packings, lattices and groups. Vol. II] With contributions by E. Bannai, R. Borcherds, J. Leech, S. P. Norton, A. M. Odlyzko, R. A. Parker, L. Queen and B. B. Venkov. Translated from the English by S. G. Vlèduts [Sergei G. Vl\u adu\c t], S. N. Litsyn, M. A. Tsfasman and N. N. Yakovlev. ``Mir'', Moscow, 1990. pp. 417--792. ISBN: 5-03-002369-0 11H31 (05B40 11H06 20E32 52C07)
[11] Konve\u\i, Dzh.; Sloèn, N. {\cyr Upakovki sharov, reshetki i gruppy. Tom} {\rm I}. (Russian) [Sphere packings, lattices and groups. Vol. I] With contributions by E. Bannai, R. Borcherds, J. Leech, S. P. Norton, A. M. Odlyzko, R. A. Parker, L. Queen and B. B. Venkov. Translated from the English by S. N. Litsyn, M. A. Tsfasman and G. B. Shabat. With a preface by Yu. I. Manin and Tsfasman. ``Mir'', Moscow, 1990. 415 pp. ISBN: 5-03-002368-2 11H31 (05B40 11H06 20E32 52C07)
연구논문
  • Borcherds, Richard E.   "Correction to: ""The Gross-Kohnen-Zagier theorem in higher dimensions"""   Duke Math. J.   105   1   (2000)   183-184   11F55, 11F30, 11F50, 11G18
  • Borcherds, Richard E.   Classification of positive definite lattices   Duke Math. J.   105   3   (2000)   525-567   11E12, 11E41, 11H06, 11H55
  • Borcherds, Richard E.   Reflection groups of Lorentzian lattices   Duke Math. J.   104   2   (2000)   319-366   11H56, 11F11, 11F27, 11M36, 51F15
  • Borcherds, Richard E.   The fake Monster formal group   Duke Math. J.   100   1   (1999)   139-165   17B69, 11F22, 17B35, 17B67, 20D08
  • Borcherds, Richard E.   The Gross-Kohnen-Zagier theorem in higher dimensions   Duke Math. J.   97   2   (1999)   219-223   11F55, 11F30, 11F50, 11G18
  • Borcherds, Richard E.   Coxeter groups, Lorentzian lattices, and $K3$ surfaces   Internat. Math. Res. Noteices     19   (1998)   1011-1031   20F55, 11H56, 14J28
  • Borcherds, Richard E.   What is Moonshine?   Doc. Math.   Extra vol.I     (1998)   607-615   17-02, 11F22, 17B67, 17B69, 20D08
  • Borcherds, Richard E.   Modular moonshine. III   Duke Math. J.   93   1   (1998)   129-154   17B69, 11F22, 20D08
  • Borcherds, Richard E.;Katzarkov, Ludmil;Pantev, Tony;Shepherd-Barron, N. I.   Families of $K3$ surfaces   J. Algebraic Geom.   7   1   (1998)   183-193   14J28, 11F55, 14J05
  • Borcherds, Richard E.;Freitag, E.;Weissauer, R.   A Siegel cusp form of degree 12 and weight 12   J. Reine Angew. Math.   494     (1998)   141-153   11F46, 11F45, 11F27
  • Borcherds, Richard E.   Automorphic forms with singularities on Grassmannians   Invent. Math.   132   3   (1998)   491-562   11F37, 11F22, 14J28, 17B67, 57R57
  • Borcherds, Richard E.;Ryba, Alex J. E.   Modular Moonshine. II   Duke Math. J.   83   2   (1996)   435-459   17B69, 11F22, 20D08
  • Borcherds, Richard E.   The moduli space of Enriques surfaces and the fake Monster Lie superalgebra   Topology   35   3   (1996)   699-710   14J28, 11F55, 17B67, 32N10, 32N15
  • Borcherds, Richard E.   Automorphic forms on ${rm O}sb {s+2,2}(R)$ and infinite products   Invent. Math.   120   1   (1995)   161-213   11F55, 11F11, 11F22, 17B67, 20G20
  • Borcherds, Richard E.   A characterization of generalized Kac-Moody algebras   J. Algebra   174   3   (1995)   1073-1079   17B67
  • Borcherds, Richard E.   Monstrous moonshine and monstrous Lie superalgebras   Invent. Math.   109   2   (1992)   405-444   11F22, 17A70, 17B67, 20D08
  • Borcherds, Richard E.   Central extensions of generalized Kac-Moody algebras   J. Algebra   140   2   (1991)   330-335   17B67, 17B05
  • Borcherds, Richard E.   The monster Lie algebra   Adv. Math.   83   1   (1990)   30-47   17B67, 11F22, 11H06, 20D08
  • Borcherds, Richard E.   Lattices like the Leech lattice   J. Algebra   130   1   (1990)   219-234   11H06, 17B67, 20H15
  • Borcherds, Richard E.   Generalized Kac-Moody algebras   J. Algebra   115   2   (1988)   501-512   17B05, 17B10, 17B67
  • Borcherds, Richard E.   Automorphism groups of Lorentzian lattices   J. Algebra   111   1   (1987)   133-153   20B27, 51F15
  • Borcherds, Richard E.   Vertex algebras, Kac-Moody algebras, and the Monster   Proc. Nat. Acad. Sci. U.S.A.   83   10   (1986)   3068-3071   17B67, 17B10, 20D08
  • Borcherds, R. E.   The Leech lattice   Proc. Roy. Soc. London Ser. A   398   1815   (1985)   365-376   11H06
  • Borcherds, R. E.;Conway, J. H.;Queen, L.;Sloane, N. J. A.   A monster Lie algebra?   Adv. in Math.   53   1   (1984)   75-79   17B67, 11H06, 20D08