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Susan Montgomery

Professor of Mathematics

Contact Information
E-mail: smontgom@usc.edu
Phone: (213) 740-2419
Office: KAP 104

LINKS
Curriculum Vitae
Personal Website
 

Education

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

Academic Appointment, Affiliation, and Employment History

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  
 

Description of Research

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.
 

Funded Research

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., $2,500, 04/01/2013-11/30/2013  
 

Other Funded Research

National Science Foundations, Intercampus Workshop Program: Lie groups, Lie algebras, and their representations (PI: Geoffrey Mason at UC Santa Cruz; co-PIs Joseph Wolf at UC Berkeley and myself) , $50,000, 11/01/2013-10/31/2015  
National Science Foundation, Intercampus Workshop Program: Lie groups, Lie algebras, and their representations (PI: Geoffrey Mason at UC Santa Cruz; co-PIs Joseph Wolf at UC Berkeley, Milan Yakimov at UC Santa Barbara, and myself) , $50,000, 09/15/2011-08/31/2013  
National Science Foundation, Intercampus Workshop Program: Lie groups, Lie algebras, and their representations (PI: Geoffrey Mason at UC Santa Cruz; co-PIs Joseph Wolf at UC Berkeley, Milan Yakimov at UC Santa Barbara, and myself), $72,000, 06/01/2007-05/31/2011  
 

Conferences and Other Presentations

Conference Presentations

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

Other Presentations

"Modular representations of some Hopf algebras constructed from groups", Algebra Seminar, UC San Diego, La Jolla, CA, 05/14/2012  
"Orthogonal Representations of Hopf Algebras", Women in Science Distinguished Lecturer/Mathematics Department Colloquium, Iowa State University, Ames, Iowa, 09/02/2008-09/03/2008  
 

Publications

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.
 

Honors and Awards

American Association for the Advancement of Science Fellow, Fellow, 12/1/2012-  
Fellow (or Equivalent) of National Society in Discipline, Fellow of the American Mathematical Society, 10/1/2012-  
32nd Emmy Noether Lecturer, 1/7/2011  
USC Raubenheimer Outstanding Senior Faculty Award, 1987  
Guggenheim Fellowship Recipient, 1984-1985  
 

Service to the Profession

Administrative Appointments

Trustee of the American Mathematical Society, 1986-1996  
 

Committees

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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