M. Susan Montgomery

Professor of Mathematics
Email smontgom@usc.edu Office KAP 104 Office Phone (213) 740-2419


  • Ph.D. Mathematics, University of Chicago, 8/1969
  • S.M. Mathematics, University of Chicago, 6/1966
  • B.A. Mathematics, University of Michigan, 5/1965
  • Tenure Track Appointments

    • Professor, University of Southern California, 09/01/1982 –
    • Associate Professor, University of Southern California, 09/01/1975 – 09/01/1982
    • Assistant Professor, University of Southern California, 09/01/1970 – 09/01/1975

    Visiting and Temporary Appointments

    • Member, Mittag-Leffler Institute, Stockholm, Sweden, 03/01/2004-04/30/2004
    • Co-Organizer and Member, Math Sciences Research Institute, Berkeley, 08/15/1999-06/15/2000
    • Gastprofessor, Mathematisches Institut, University of Munich, Germany, 01/01/1996-06/01/1996
  • Summary Statement of Research Interests

    Professor Montgomery studies non-commutative algebras: Hopf algebras and their actions on rings, including automorphism groups of algebras, and quantum groups.

  • Contracts and Grants Awarded

    • Finite-dimensional Hopf Algbras and their Representations, (National Science Foundation), M Susan Montgomery, $179,827, 06/01/2013 – 06/01/2016
    • Representations and actions of finite-dimensional Hopf algebras, (National Science Foundation), Susan Montgomery, $159,612, 06/01/2010 – 05/31/2013
    • Semisimple Hopf algebras: their representations and actions, (National Science Foundation), M Susan Montgomery, $211,336, 07/01/2007 – 06/30/2010

    USC Funding

    • WiSE Supplemental Faculty Support. None: This grant supported two visitors to USC;
      one was Sarah Witherspoon of Texas A&M.

      It also provided funding to send two of my graduate students to France for an important meeting in our area., $2500, 04/01/2013 – 11/30/2013

  • Conference Presentations

    • Brauer characters for representations of bismash products , Session on Hopf Algebras and Tensor CategoriesTalk/Oral Presentation, Canadian Math Society, Invited, Halifax, Nova Scotia, Canada, 06/04/2013 – 06/06/2013
    • Computing Frobenius-Schur indicators for doubles of groups , AMS Special Session on Quantum Groups and Noncommutative Algebraic GeometryTalk/Oral Presentation, American Math Society, Invited, Tulane University, New Orleans. LA, 10/13/2012 – 10/14/2012
    • Modular representations of bismash products , Noncommutative Invariant TheoryTalk/Oral Presentation, University of Washington and the NSF, Invited, University of Washington, Seattle, 05/26/2012 – 05/27/2012
    • Brauer characters and Frobenius-Schur indicators for bismash products. , AMS Special Session on Tensor Categories and Representation TheoryTalk/Oral Presentation, American Math Society, Invited, Boston, MA, 01/04/2012 – 01/07/2012
    • Values of Frobenius-Schur indicators for Hopf algebras , AMS Special Session on Noncommutative Geometry and AlgebraTalk/Oral Presentation, American Math Society, Invited, University of Utah, Salt Lake City, 10/22/2011 – 10/23/2011
    • Recent results on Frobenius-Schur indicators for Hopf algebras , Hopf Algebras and Tensor CategoriesKeynote Lecture, Ministerio de Ciencia e Innovacion, Spain, Invited, Almeria, Spain, 07/04/2011 – 07/08/2011
    • Orthogonal representations: from groups to Hopf algebras , Noether Lecture: AMS annual meetingKeynote Lecture, Association for Women in Mathematics, Invited, New Orleans, 01/06/2011 – 01/09/2011
    • Invariants for Representations of Semisimple Hopf algebras , New Trends in Noncommutative AlgebraLecture/Seminar, NSF, NSA, PIMS, Invited, University of Washington, Seattle, 08/09/2010 – 08/13/2010
    • Frobenius-Schur indicators of representations of Hopf algebras and the trace of the antipode , Conference in Hopf Algebras and Noncommutative AlgebraKeynote Lecture, Israel Science Foundation, Invited, Ben Gurion University, Israel, 05/24/2010 – 05/28/2010
    • Orthogonal Representations of Hopf algebras , Canadian Math Society National MeetingKeynote Lecture, Canadian Math Society, Invited, St Johns, Newfoundland, Canada, 06/03/2009 – 06/07/2009

    Other Presentations

    • Modular representations of some Hopf algebras constructed from groups, Algebra Seminar, La Jolla, CA, 2011-2012
    • Orthogonal Representations of Hopf Algebras, Women in Science Distinguished Lecturer/Mathematics Department Colloquium, Ames, Iowa, 2008-2009
  • Journal Article

    • Jedwab, A., Montgomery, S. (2013). Modular Representations and Indicators for Bismash Products. Journal of Algebra/Academic Press. Vol. 377, pp. 281-297.
    • Kashina, Y., Montgomery, S., Ng, S. (2012). On the trace of the antipode and higher indicators. Israel Journal of Mathematics. Vol. 188, pp. 57-90.
    • Jedwab, A., Montgomery, S. (2011). A q-Identity Related to a Comodule. Communications in Algebra. Vol. 39, pp. 4669-4678.
    • Guralnick, R., Montgomery, S. (2009). Frobenius-Schur indicators for subgroups and Drinfel’d doubles of the Weyl groups. Transactions of the American Mathematical Society/American Mathematical Society. Vol. 361 (7), pp. 3611-3632.
    • Bahturin, Y., Kotchetov, M., Montgomery, S. (2009). Group gradings on simple Lie algebras in positive characteristic. Proceedings of the American Mathematical Society. Vol. 137 (4), pp. 1245-1254.
    • Montgomery, S., Jedwab, A. (2009). Representations of some Hopf algebras associated to the symmetric group Sn. Algebras and Representation Theory. Vol. 12, pp. 1-17.


    • Montgomery, S. (2009). Hopf Galois theory: a survey, in New Topological Contexts for Galois Theory and Algebraic Geometry. In A. Baker and B. Richter (Ed.), pp. 367-400. Coventry. Geometry and Topology Monographs.
    • American Association for the Advancement of Science Fellow, Fellow, 2012/12/01
    • Fellow (or Equivalent) of National Society in Discipline, Fellow of the American Mathematical Society, 2012/10/01
    • 32nd Emmy Noether Lecturer, 2011/01/07
    • USC Raubenheimer Outstanding Senior Faculty Award, 1987
    • Guggenheim Fellowship Recipient, 1984-1985
  • Administative Appointment

    • Trustee of the American Mathematical Society, 1986 – 1996


    • Member, AMS Nominating Committee (elected)

      I served as acting chair in 2007, 2005 – 2008

    Conferences Organized

    • Co-organizer of Special Session on Non-commutative Algebras, Mathematical Congress of the Americas, Guanajuato. Mexico, 08/05/2013
    • Co-organizer of Special Session on Hopf algebras, Coalgebras, and their Categories of Representations, Joint Meeting of the American Math Society and the Romanian Math Society, Alba Iulia, Romania, 06/27/2013 – 06/30/2013
    • Co-organizer , Lie Groups, LIe Algebras, and their Representations (NSF sponsored Workshop) , USC Math Dept, Spring 2012
    • Member of Scientific Committee, Hopf Algebras and Tensor Categories, Almeria, Spain, 2010-2011
    • Co-organizer of Special Session on Hopf Algebras and their Representations, AMS Annual Meeting, New Orleans , 01/06/2011 – 01/09/2011
    • Organizer, Lie Groups, LIe Algebras, and their Representations (NSF sponsored Workshop) , USC Math Dept, Spring 2010

    Editorships and Editorial Boards

    • Editorial Board Member, Algebra and Number Theory, 2007 – 2013
    • Editorial Board Member, Algebras and Representation Theory, 1998 – 2013
    • Co-editor, Special Issue of Communications in Algebra in honor of Miriam Cohen, 07/2010 – 11/2011
    • Editorial Board Member, Journal of Algebra, 1987 – 2008

    Professional Offices

    • Vice-President, American Math Society, 02/01/2014 – 01/31/2017
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