M. Susan Montgomery

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, 2012-2016
• Representations and actions of finite-dimensional Hopf algebras, (National Science Foundation), Susan Montgomery $159,612, 2009-2013
• Semisimple Hopf algebras: their representations and actions, (National Science Foundation), M Susan Montgomery $211,336, 2006-2010

USC Funding

• WiSE Supplemental Faculty Support. None $2,500, 2012-2014

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.

Proceedings

• 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.

• Fellow, 2012/12/01
• 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

Conferences Organized

• Co-organizer of Special Session on Non-commutative Algebras, Mathematical Congress of the Americas”, 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”, 06/27/2013-06/30/2013
• Co-organizer , Lie Groups, LIe Algebras, and their Representations (NSF sponsored Workshop) “,
• Member of Scientific Committee, Hopf Algebras and Tensor Categories”,
• Co-organizer of Special Session on Hopf Algebras and their Representations, AMS Annual Meeting”, 01/06/2011-01/09/2011
• Organizer, Lie Groups, LIe Algebras, and their Representations (NSF sponsored Workshop) “,

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”, 2013-2017