Contact Information
Research Areas
Research Interests
- Tensor theory of operator spaces
- Tensor theory of operator systems
- Quantum information theory
- Operator algebras
Research Description
My research interests are in operator space theory, operator system theory, and quantum information theory. My recent work has been in using techniques from operator algebras to give new characterizations of correlation sets which arise naturally in quantum information theory. Graduate students are welcome to email me if you are interested in any of these topics.
Courses Taught
- Spring '22:
- Math 598: Select Topics in Quantum Information Theory (16 students)
- Math 415: Applied Linear Algebra (280 students)
- Fall '21:
- Math 125: Elementary Linear Algebra (80 students)
Additional Campus Affiliations
- Seminar Committee Member, Illinois Quantum Information Science and Technology Center, University of Illinois at Urbana-Champaign
- Affiliate, Illinois Quantum Information Science and Technology Center, University of Illinois at Urbana-Champaign
- Scholarship Board Member, Sloan University Center of Exemplar Mentoring at Illinois, University of Illinois at Urbana-Champaign
Research Visits:
- Mathematisches Institut, WWU Munster, June-July 2022
- Department of Mathematics, University of Virginia, April 2022
Upcoming Lectures:
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Lecture Series, KnOttawa Summer School 2022, Topic: Quantum Information Theory
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There will be five lectures with focuses TBD
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Lecture, Oberseminar C*-algebren, WWU Münster June 2022, Title TBD
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Lecture, Operator Theory Seminar, University of Virginia, April 2022, Title: Matricial Archimedean Order Unit Spaces and Quantum Correlations
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Plenary Lecture, Southeastern Analysis Meeting, University of Florida, March 2022, Title: Matricial Archimedean Order Unit Spaces and Quantum Correlations
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Functional Analysis Seminar, University of California San Diego, February 2022, Title: Matricial Archimedean Order Unit Spaces and Quantum Correlations
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Department of Mathematics & Statistics Colloquium, San José State University, September 2021, Title: From Correlation Sets to Tensor Products of C*-algebras: The Connes-Kirchberg Problem
News:
Recent Publications
- An index for inclusions of operator systems (with Colton Griffin and Thomas Sinclair) (2022). arXiv:2203.05710. Submitted
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Approximating projections by quantum operations (with Colton Griffin, Aneesh Khilnani, and Thomas Sinclair) (2022) arXiv:2203.02627. Submitted
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Matricial Archimedean order unit spaces and quantum correlations (with Travis Russell and Mark Tomforde). (2021) arXiv:2109.11671. To appear: Indiana University Mathematics Journal
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A universal representation for quantum commuting correlations (with Travis Russell and Mark Tomforde). (2021) arXiv:2102.05827. To appear: Annales Henri Poincaré.
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An abstract characterization for projections in operator systems (with Travis Russell). (2020) arXiv:2006.03094. To appear: Journal of Operator Theory
- R we living in the matrix? (with Rolando de Santiago). Notices of the American Mathematical Society. Volume 66, Number 8, (2019), Pgs. 1216-1224.