Research
I work in the area of operator theory and operator algebras. I have studied generalizations of the classical Nevanlinna-Pick Theorem to the context of W*-correspondences. More recently, I have become interested in Cartan subalgebras of groupoid C*-algebras, especially higher rank graph C*-algebras.
Publications
A. Duwenig, E. Gillaspy, R. Norton. Analyzing the Weyl construction for dynamical Cartan subalgebras, International Mathematics Research Notices (2021), rnab114, https://doi.org/10.1093/imrn/rnab114. (arxiv)
A. Duwenig, E. Gillaspy, R. Norton, S. Reznikoff, S. Wright. Cartan subalgebras for non-principal twisted groupoid C*-algebras,Journal of Functional Analysis 279(6) (2020). (arxiv)
R. Norton. Comparing Two Generalized Noncommutative Nevanlinna-Pick Theorems. Complex Analysis and Operator Theory 11(4) (2017), 875-894. (arxiv)
R. Norton. Pick interpolation, displacement equations, and W*-correspondences. PhD thesis, The University of Iowa (2017).
R. Angeles-Canul, R. Norton, M. Opperman, C. Paribello, M. Russell, and C. Tamon, Perfect State Transfer, Integral Circulants, and Join of Graphs, Quantum Information and Computation 10 (2010), 325-342. (arxiv)
A. Duwenig, E. Gillaspy, R. Norton, S. Reznikoff, S. Wright. Cartan subalgebras for non-principal twisted groupoid C*-algebras,Journal of Functional Analysis 279(6) (2020). (arxiv)
R. Norton. Comparing Two Generalized Noncommutative Nevanlinna-Pick Theorems. Complex Analysis and Operator Theory 11(4) (2017), 875-894. (arxiv)
R. Norton. Pick interpolation, displacement equations, and W*-correspondences. PhD thesis, The University of Iowa (2017).
R. Angeles-Canul, R. Norton, M. Opperman, C. Paribello, M. Russell, and C. Tamon, Perfect State Transfer, Integral Circulants, and Join of Graphs, Quantum Information and Computation 10 (2010), 325-342. (arxiv)
Presentations
Invited Talks
Contributed Talks
Invitation-only Workshops Attended
Conferences Attended
- Certain Cartan subalgebras of twisted groupoid C*-algebras, Special Session on Analysis and Differential Equations at Undergraduate Institutions, AMS Spring Eastern Sectional Meeting, online, April 2023
- Cartan subalgebras of twisted groupoid C*-algebras including higher rank graph C*-algebras, AMS Special Session on Advances in Operator Algebras, Joint Mathematics Meetings (JMM), Boston, MA, January 2023
- A gentle introduction to Cartan subalgebras of twisted groupoid C*-algebras, Faculty Seminar, St. Olaf College, December 2022
- A Mathematician's Guide to Designing a Roller Coaster, Colloquium, St. Olaf College, December 2022
- Cartan subalgebras of twisted groupoid C*-algebras including higher rank graph C*-algebras, Noncommutative Analysis at the Technion, Haifa, Israel, June 2022
- Cartan subalgebras of twisted groupoid C*-algebras and applications to higher rank graph C*-algebras, Subfactor Seminar, Vanderbilt University, April 2021
- Cartan subalgebras of non-principal twisted groupoid C*-algebras, Colloquium, University of Montana, March 2021
- Cartan subalgebras of twisted groupoid C*-algebras, AMS Special Session on Advances in Operator Algebras, Joint Mathematics Meetings (JMM), virtual meeting, January 2021
- Twisted groupoid C*-algebras and their Cartan subalgebras, Everytopic Seminar, Brandeis University, December 2020
- A Nevanlinna-Pick theorem in the context of the weighted Hardy algebra over a W*-correspondence, AMS Special Session on Recent Advances in Function and Operator Theory, JMM, Denver, CO, January 2020
- A guide to generalized Nevanlinna-Pick theorems, Midwest Women in Mathematics Symposium, University of Iowa, April 2019
- Interpolation: real world problems and the Nevanlinna-Pick theorem, Undergraduate Seminar, Fitchburg State University, February 2019
- Interpolation: real world problems and the Nevanlinna-Pick theorem, Undergraduate Math Society Seminar, Northwestern University, October 2018
- A Mathematician's Guide to Designing a Roller Coaster, Undergraduate Seminar, Southern New Hampshire University, September 2018
- A Mathematician's Guide to Designing a Roller Coaster, Undergraduate Seminar, Washington College, February 2018
- Investigating Pick interpolation in the setting of free noncommutative function theory, AMS Special Session on Free Convexity and Free Analysis, JMM, San Diego, CA, January 2018
- Pick interpolation and the displacement equation, Multivariable Operator Theory, Technion, Haifa, Israel, June 2017
- A Mathematician's Guide to Designing a Roller Coaster, Colloquium, Hampden-Sydney College, February 2017
- A Mathematician's Guide to Designing a Roller Coaster, Undergraduate Seminar, Lawrence University, February 2017
- Comparing Nevanlinna-Pick Theorems, Faculty Seminar, Salisbury University, February 2017
- A Mathematician's Guide to Designing a Roller Coaster, Colloquium, Santa Clara University, January 2017
- A Comparison of Nevanlinna-Pick Theorems, AMS Special Session on Advances in Operator Algebras, JMM, Atlanta, GA, January 2017
- Comparing Nevanlinna-Pick Theorems, Faculty Seminar, Bowdoin College, November 2016
- A Mathematician's Guide to Designing a Roller Coaster, Undergraduate Lunch Seminar, Bowdoin College, November 2016
- Comparing Nevanlinna-Pick Theorems, Operator Algebras Seminar, Purdue University, September 2016
- Comparing Two Generalized Nevanlinna-Pick Theorems, Iowa-Nebraska Functional Analysis Seminar (INFAS), Des Moines, IA, April 2016
- Displacement Theory and W*-correspondences, JMM, Seattle, WA, January 2016
Contributed Talks
- Pick interpolation in the context of W*-correspondences, Great Plains Operator Theory Symposium (GPOTS), Texas Christian University, May 2017
- Comparing Nevanlinna-Pick Theorems, Operator Theory Seminar, University of Iowa, August 2016
- A Comparison of Generalized Nevanlinna-Pick Theorems, GPOTS, University of Illinois at Urbana-Champaign, May 2016
- A New Nevanlinna-Pick Type Theorem, Operator Theory Seminar, University of Iowa, April 2016
- A Comparison of Two Generalized Nevanlinna-Pick Theorems, Jakobsen Memorial Conference, University of Iowa, March 2016
- Displacement Theory in the Context of W*-correspondences, GPOTS, Purdue University, May 2015
Invitation-only Workshops Attended
- Women in Operator Algebras III, Banff International Research Station, June 2023
- Multivariable Operator Theory and Function Spaces in Several Variables, (virtually hosted by) Casa Matematica Oaxaca, August 2021
- Summer Research for Women in Mathematics, Mathematical Sciences Research Institute, July 2019
- Women in Operator Algebras, Banff International Research Station, November 2018
Conferences Attended
- AMS Spring Eastern Sectional Meeting, online, April 2023
- JMM, Boston, MA, January 2023
- Noncommutative Analysis at the Technion, Haifa, Israel, June 2022
- GPOTS, virtual meeting, May 2021
- JMM, virtual meeting, January 2021
- Operator Theory with its Applications, virtual meeting, August 2020
- Canadian Operator Symposium (COSy), virtual meeting, May 2020
- JMM, Denver, CO, January 2020
- GPOTS, Texas A&M, May 2019
- Midwest Women in Mathematics Symposium, University of Iowa, April 2019
- Groupoidfest, University of Illinois at Chicago, November 2018
- GPOTS, Miami University, May 2018
- JMM, San Diego, CA, January 2018
- MathFest, Chicago, IL, July 2017
- Multivariable Operator Theory, Technion, June 2017
- GPOTS, Texas Christian University, May 2017
- JMM, Atlanta, GA, January 2017
- INFAS, Des Moines, IA, November 2016
- East Coast Operator Algebras Symposium (ECOAS), Loyola University, October 2016
- Workshop in Noncommutative Analysis, University of Iowa, June 2016
- GPOTS, University of Illinois at Urbana-Champaign, May 2016
- INFAS, Des Moines, IA, April 2016
- Jakobsen Memorial Conference, University of Iowa, March 2016
- JMM, Seattle, WA, January 2016
- ECOAS, University of Iowa, October 2015
- GPOTS, Purdue University, May 2015
- Kansas-Iowa-Nebraska Functional Analysis Seminar, Creighton University, March 2015
- Midwest Women in Mathematics Symposium, Dominican University, March 2015
- INFAS, Des Moines, IA, April 2014
- INFAS, Des Moines, IA, November 2013
- AMS Central Sectional Meeting, Washington University, October 2013
- AMS Central Sectional Meeting, Iowa State University, April 2013
- INFAS, Des Moines, IA, November 2012