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Generalized Moonshine

Research Project

Project/Area Number 24740005
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Algebra
Research InstitutionUniversity of Tsukuba

Principal Investigator

CARNAHAN Scott  筑波大学, 数理物質系, 助教 (10600538)

Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords代数 / ムーンシャイン
Outline of Final Research Achievements

I have developed the theory of conformal blocks on twisted nodal algebraic curves using logarithmic geometry, and applied this to the discovery of fusion rules and higher associativity data for twisted modules of the monster vertex algebra. For this purpose, I have also introduced general theories of higher frames for smooth morphisms, and infinite dimensional crystalline descent theorems. I gave a method for constructing vertex algebras and abelian intertwining algebras, given a family of modules, intertwining operators, and higher associativity data. I applied this construction to twisted modules of the monster vertex algebra, and produced a family of infinite dimensional Lie algebras with actions of large finite groups. By the results of this research, I have proved many cases of the generalized moonshine conjecture, in particular for the classes pA in the monster for all primes p.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (16 results)

All 2014 2013 2012 Other

All Journal Article (2 results) (of which Peer Reviewed: 1 results) Presentation (9 results) (of which Invited: 9 results) Remarks (5 results)

  • [Journal Article] Monstrous Lie Algebras2014

    • Author(s)
      Scott Carnahan
    • Journal Title

      RIMS講究録

      Volume: 1872 Pages: 83-93

    • Related Report
      2013 Research-status Report
  • [Journal Article] Generalized Moonshine II: Borcherds Products2012

    • Author(s)
      Scott Carnahan
    • Journal Title

      Duke Mathematical Journal

      Volume: 161 Issue: 5 Pages: 893-950

    • DOI

      10.1215/00127094-1548416

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Dong-Li-Mason plus Weil2014

    • Author(s)
      Scott Carnahan
    • Organizer
      Workshop on finite groups and their representations, vertex operator algebras, and algebraic combinatorics
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2014-12-16
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Introduction to Mathieu Moonshine2014

    • Author(s)
      Scott Carnahan
    • Organizer
      Workshop on Mathieu Moonshine
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2014-08-25
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Dong-Li-Mason plus Weil2014

    • Author(s)
      Scott Carnahan
    • Organizer
      Algebras, Groups and Geometries 2014
    • Place of Presentation
      東京大学
    • Year and Date
      2014-06-27
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Dong-Li-Mason plus Weil2014

    • Author(s)
      Scott Carnahan
    • Organizer
      Hualien Workshop on Finite Groups, VOA, Algebraic Combinatorics, and Related Topics
    • Place of Presentation
      國立東華大学(台湾)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Monstrous Lie Algebras2013

    • Author(s)
      Scott Carnahan
    • Organizer
      Moonshine and Beyond
    • Place of Presentation
      仙台
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Monstrous Lie Algebras2013

    • Author(s)
      Scott Carnahan
    • Organizer
      Conference on Moonshine, Mock modular forms, and String theory
    • Place of Presentation
      Simons Center for Geometry and Physics (アメリカ)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Monstrous Lie Algebras2013

    • Author(s)
      Scott Carnahan
    • Organizer
      Workshop on finite groups and their representations, vertex operator algebras, and algebraic combinatorics
    • Place of Presentation
      RIMS, Kyoto University
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Monstrous Lie Algebras2013

    • Author(s)
      Scott Carnahan
    • Organizer
      Taitung workshop on group theory, VOA and algebraic combinatorics
    • Place of Presentation
      Taitung University, Taiwan
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Generalized Moonshine mini-course2012

    • Author(s)
      Scott Carnahan
    • Organizer
      Generalized Moonshine mini-course
    • Place of Presentation
      Tokyo Women's Christian University
    • Related Report
      2012 Research-status Report
    • Invited
  • [Remarks] Scott Carnahan

    • URL

      http://www.math.tsukuba.ac.jp/~carnahan/

    • Related Report
      2014 Annual Research Report
  • [Remarks] テニュアトラック普及・定着事業

    • URL

      http://ttweb.sec.tsukuba.ac.jp/e_scott.html

    • Related Report
      2014 Annual Research Report
  • [Remarks] Scott Carnahan

    • URL

      http://www.math.tsukuba.ac.jp/~carnahan/

    • Related Report
      2013 Research-status Report
  • [Remarks] テニュアトラック普及・定着事業

    • URL

      http://ttweb.sec.tsukuba.ac.jp/e_scott.html

    • Related Report
      2013 Research-status Report
  • [Remarks] Scott Carnahan

    • URL

      http://www.math.tsukuba.ac.jp/~carnahan/

    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2021-04-07  

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