John Quigg’s research is in the area of C*-algebras. This is the mathematics that grew out of quantum mechanics in the first half of the 20th century. The states of a quantum system can be modeled as unit vectors in a Hilbert space, and the observables can be modeled as operators on the Hilbert space. Combining the operators algebraically and closing under limits gives a concrete C*-algebra. The study of C*-algebras makes connections with many parts of mathematics, including analysis, algebra, topology, geometry, and discrete math. The area of C*-algebras has has been applied to such diverse areas as dynamical systems, quantum field theory, wavelets, and number theory. In addition to many papers on the subject of C*-algebras, John Quigg has co-authored an American Mathematical Society Memoir connecting C*-dynamical systems to category theory.
S. Kaliszewski, T. Omland, and J. Quigg. Cuntz-Li algebras from a-adic numbers. Revue Roumaine de Math Pures et Appliques (2014).
S. Kaliszewski and J. Quigg. Coactions and skew products for topological graphs. Integral Equations and Operator Theory (2013).
S. Kaliszewski, J. Quigg, and D. Robertson. Functoriality of Cuntz-Pimsner correspondence maps. Journal of Mathematical Analysis and Applications (2013).
S. Kaliszewski, M. B. Landstad, and J. Quigg. Exotic group C*-algebras in noncommutative duality. New York Journal of Mathematics (2013).
S. Kaliszewski, N. Patani, and J. Quigg. Obstructions to a general characterization of graph correspondences. Journal of the Australian Mathematical Society (2013).
S. Kaliszewski, P. S. Muhly, J. Quigg, and D. P. Williams. Fell bundles and imprimitivity theorems. Münster Journal of Mathematics (2013).
S. Kaliszewski, P. S. Muhly, J. Quigg, and D. P. Williams. Fell bundles and imprimitivity theorems: Mansfield's and Fell's theorems. Journal of the Australian Mathematical Society (2013).
S. Kaliszewski, M. Landstad, and J. Quigg. A crossed-product approach to the Cuntz-Li algebras. Proceedings of the Edinburgh Mathematical Society (2012).
S. Kaliszewski, N. Larsen, and J. Quigg. Inner coactions, Fell bundles, and abstract uniqueness theorems. Münster Journal of Mathematics (2012).
S. Kaliszewski, N. Patani, and J. Quigg. Characterizing Graph C*-Correspondences. Houston J. Math (2012).
V. Deaconu, A. Kumjian, and J. Quigg. Group actions on topological graphs. Ergodic Theory and Dynamical Systems (2012).
A. an Huef, J. Quigg, I. Raeburn, and D. P. Williams. Full and reduced coactions of locally compact groups on C*-algebras. Expositiones Mathematicae (2011).
E. B ´edos, S. Kaliszewski, and J. Quigg. On reflective-coreflective equivalence and associated pairs. Theory and Applications of Categories (2011).
E. B ´edos, S. Kaliszewski, and J. Quigg. Reflective-coreflective equivalence. Theory and Applications of Categories (2011).
S. Kaliszewski, P. S. Muhly, J. Quigg, and D. P. Williams. Coactions and Fell bundles. New York J. Math (2010).
D. Pask, John Quigg, A. Sims. Coverings of skew products and crossed products by coactions. J. Australian Math. Soc (2009).
S. Kaliszewski, John Quigg. Categorical Landstad duality for actions. Indiana Univ. Math. J (2009).
S. Kaliszewski, M. B. Landstad, J. Quigg. Hecke C*-algebras and semidirect products. Proc. Edinburgh Math. Soc (2009).
S. Kaliszewski, John Quigg, I. Raeburn. Proper actions, fixed-point algebras and naturality in nonabelian duality. J. Funct. Anal (2008).
S. Kaliszewski, M. B. Landstad, and J. Quigg. Hecke C*-algebras, Schlichting completions, and Morita equivalence. Proc. Edinburgh Math. Soc (2008).
S Kaliszewski, John Quigg. Landstad's characterization for full crossed products. New York J. Math (2007).
John Quigg. Bundles of C*-correspondences over directed graphs and a theorem of Ionescu. Proc. Amer. Math. Soc (2006).
Echterhoff, S., Kaliszewski, S., Quigg, J., Raeburn, I. A Categorical Approach to Imprimitivity Theorems for C*-Dynamical Systems. (2006).
D Pask, John Quigg, I Raeburn. Coverings of k-graphs. J. Algebra (2005).
Steven Kaliszewski, John Quigg. Mansfield's Imprimitivity Theorem for Full Crossed Products. Trans. Amer. Math. Soc (2005).
D Pask, John Quigg, I Raeburn. Fundamental groupoids of k-graphs. New York J. Math (2004).
John Quigg, R Exel, M Laca. Partial dynamical systems and C*-algebras generated by partial isometries. J. Operator Theory (2002).
John Quigg, S Echterhoff. Full duality for coactions of discrete groups. Math. Scand (2002).
John Quigg, S Kaliszewski. Three bimodules for Mansfield's imprimitivity theorem. J. Austral. Math. Soc (2001).
Steven Kaliszewski, John Quigg, I Raeburn. Skew products and crossed products by coactions. J. Operator Theory (2001).
S Echterhoff, S Kaliszewski, John Quigg, I Raeburn. Naturality and induced representations. Bull. Austral. Math. Soc (2000).
S Kaliszewski, John Quigg. Equivariance and imprimitivity for discrete Hopf C*-coactions. Bull. Austral. Math. Soc (2000).
John Quigg. Proper actions and coactions. ASU C*-Seminar (Oct 2014).
John Quigg. The nondegenerate, the enchilada, and the outer. seminar at University of Otago, New Zealand (Aug 2014).
John Quigg. The nondegenerate, the enchilada, and the outer. seminar at University of Wollongong, Australia (Jul 2014).
John Quigg. Trouble in CP-Land. Great Plains Operator Theory Symposium, Manhattan, KS (May 2014).
John Quigg. Trouble in CP-Land. seminar at Dartmouth College (May 2014).
John Quigg. Exact and exotic crossed products. ASU C*-Seminar (Oct 2013).
John Quigg. Exotic coactions. seminar at Norwegian University of Science and Technology (Aug 2013).
John Quigg. Exotic coactions. Workshop on groups, dynamical systems, and C*-algebras (Aug 2013).
John Quigg. Exotic coactions. Great Plains Operator Theory Symposium, Berkeley, CA (May 2013).
John Quigg. K-theory for C*-algebras. ASU C*-Seminar (Feb 2013).
John Quigg. Fell bundles and imprimitivity theorems: towards a universal generalized fixed point algebra. seminar at Norwegian University of Science and Technology (Nov 2012).
John Quigg. Functoriality and Cuntz-Pimsner algebras. seminar at Norwegian University of Science and Technology (Oct 2012).
John Quigg. Exotic group C*-algebras. seminar at University of Oslo (Aug 2012).
John Quigg. Functoriality of Cuntz-Pimsner algebras. Great Plains Operator Theory Symposium, Houston, TX, (Jun 2012).
John Quigg. Fell bundles over groupoids, and imprimitivity. Groupoid Fest, Reno, NV (Jan 2012).
John Quigg. Intro to Hilbert modules. ASU C*-Seminar (Sep 2011).
John Quigg. A crossed-product approach to the Cuntz-Li algebras. seminar at University of Otago (Jul 2011).
John Quigg. Functoriality of Cuntz-Pimsner algebras. seminar at University of Wollongong (Jul 2011).
John Quigg. Fields, bundles and Hilbert modules, wrap-up. ASU C*-Seminar (Apr 2011).
John Quigg. Organizational meeting - C*-bundles. ASU C*-Seminar (Jan 2011).
John Quigg. Topological graphs and principal bundles. Oslo-Trondheim operator algebra seminar (1-day conference), Oslo, Norway (Dec 2010).
John Quigg. Introduction to graph algebras and Cuntz-Pimsner algebras. ASU C*-Seminar (Nov 2010).
John Quigg. Introduction to Hilbert modules. ASU C*-Seminar (Sep 2010).
Steve Kaliszewski and John Quigg. Categorical Perspectives in noncommutative duality. Summer school on C*-algebras and their interplay with dy- namical systems, Sophus Lie Conference Cen (Jun 2010).
John Quigg. Multiplier bimodules and Cuntz-Pimsner algebras. Great Plains Operator Theory Symposium, Denver, CO (Jun 2010).
John Quigg. Topological graphs and principal bundles. seminar at Norwegian University of Science and Technology (May 2010).
John Quigg. Topological graphs and principal bundles. colloquium at Dartmouth College, Hanover, NH (Apr 2010).
Quigg, John. Skew Products of Topological Graphs and Noncommutative Duality. Special Session on Operator Algebras, Regional AMS Meeting, Riverside, CA (Nov 2009).
John Quigg. Skew products of topological graphs and noncommutative duality. C*-Seminar (Nov 2009).
John Quigg. Skew products of topological graphs and noncommutative duality. Fields Institute (Toronto, Canada) (Jul 2009).
John Quigg. Application of coactions to direct integrals. Great Plains Operator Theory Symposium, Boulder, CO (Jun 2009).
John Quigg. Topological graphs. C*-Seminar (Apr 2009).
John Quigg. C*-Coactions and Fell Bundles - the Discrete Case. Noncommutative Duality Week, Dartmouth College (Feb 2009).
John Quigg. The spectral theorem, and Fell bundles over groupoids, III. C*-Seminar (Dec 2008).
John Quigg. The spectral theorem, and Fell bundles over groupoids, II. C*-Seminar (Nov 2008).
John Quigg. Application of coactions to direct integrals. Groupoid Fest, Riverside, CA (Nov 2008).
John Quigg. The spectral theorem, and Fell bundles over groupoids. C*-Seminar (Oct 2008).
John Quigg. Applications of non-abelian duality to higher-rank graph C*-algebras. University of Wollongong (Australia) (Aug 2008).
John Quigg. Applications of non-abelian duality to higher-rank graph C*-algebras. University of New South Wales (Sydney, Australia) (Aug 2008).
John Quigg. Applications of non-abelian duality to higher-rank graph algebras. University of Guelph (Canada) (Jul 2008).
John Quigg. Coverings of skew-products and crossed products by coactions. Fields Institute (Toronto, Canada) (Jul 2008).
John Quigg. Coverings of skew-products and crossed products by coactions. Great Plains Operator Theory Symposium, Cincinnati, OH (Jun 2008).
John Quigg. Proper actions, fixed-point algebras, and naturality in nonabelian duality. C*-Algebras Associated to Discrete and Dynamical Systems, BIRS, Banff (Canada) (Jan 2008).
Kaliszewski, S, Quigg, John. Landstad's characterization for full crossed products. University of Newcastle, Newcastle, Australia (Aug 2006).
Kaliszewski, S, Quigg, John. A groupoid approach to imprimitivity theorems. Norwegian University of Science and Technology, Trondheim, Norway (Jun 2006).
Kaliszewski, S, Quigg, John. A groupoid approach to imprimitivity theorems. University of Oslo, Oslo, Norway (Jun 2006).
Kaliszewski, S, Quigg, John. Landstad's characterization for full crossed products. Great Plains Operator Theory Symposium (May 2006).
Kaliszewski, S, Muhly, P, Quigg, John. Groupoid bundles and imprimitivity. Groupoid Fest, Ames, IA (Nov 2005).
Quigg, John. C*-Completions of Hecke Algebras. Operator Algebras and Applications (Jun 2005).
Kaliszewski, S, Lansdtad, M, Quigg, John. C*-Completions of Hecke Algebras. Operator Algebras and Applications, National University of Ireland, Cork, Ireland (Jun 2005).
Quigg, John. Fundamental Groupoids of Categories. Groupoid Fest (Nov 2004).
Quigg, John. k-graphs, coverings, and coactions. NSF-CBMS Regional Research Conference on Graph Algebras (Jun 2004).
Quigg, John. k-graphs, coverings, and coactions. Great Plains Operator Theory Symposium (May 2004).
Quigg, John. k-Graphs, Coverings, and Coactions. Special Session on Groupoids in Analysis and Geometry, Regional AMS Meeting (Oct 2003).
Quigg, John. The full Mansfield, Special Session on operator algebras and noncommutative geometry. Annual Meeting of the Australian Mathematical Society (Oct 2002).
Quigg, John. The full Mansfield. Great Plains Operator Theory Symposium (May 2002).
Quigg, John. Maximal coactions. Centre for Advanced Study (Dec 2001).
Quigg, John. Maximal coactions, Special Session on C*-algebras and crossed products. Regional AMS Meeting (Mar 2001).
Quigg, John. A groupoid approach to imprimitivity theorems. Groupoid Fest (Nov 2000).
Quigg, John. Categorical Landstad duality. C*-Algebras and Their Invariants
Quigg, John. Categorical Landstad duality. Great Plains Operator Theory Symposium
Quigg, John. Categorical Landstad duality. Norwegian University of Science and Technology
Quigg, John. Coactions: a curious category. University of Wollongong
Quigg, John. Using groupoids to restrict coactions to homogeneous spaces. Groupoid Fest
Service
Theoretical Math Seminar Committee, member (2013 - Present)
Graduate Committee, member (head of MAT PhD program) (2010 - Present)
Ad hoc committee to revise analysis qualifier sequence, member (2008 - Present)
