Contact Information
Research Areas
Research Interests
- Tensor theory of operator spaces
- Tensor theory of operator systems
- Local structure of operator spaces and 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 includes using techniques from operator algebras to give new characterizations of correlation sets which arise naturally in quantum information theory. I am also interested in the local structure of operator spaces and operator systems. Graduate students are welcome to email me if you are interested in any of these topics.
Courses Taught
- Fall '22:
- Math 492: Quantum Channels and error correction (8 students)
- Math 415: Applied Linear Algebra (280 students)
- Spring '22:
- Math 492: 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
News:
Along with Marius Junge, Felix Leditzky, and Thomas Sinclair, I am organizing the workshop ``QLA Meets QIT II'' to be held in Chicago 3-5 November. More information can be found here https://sites.google.com/view/qlameetsqitii/home
In the fall term 2022 I will be running an undergraduate research project on quantum channels and error correction.
Research Visits:
- Department of Computer Science, Columbia University, December 2022
- Mathematisches Institut, WWU Münster, June-July 2022
- Department of Mathematics, University of Virginia, April 2022
Upcoming Lectures:
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Lecture, Quantum Information and Computing Seminar, University of Delaware, November 2022, Title: TBD
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Lecture, Operator Algebras Seminar, Purdue University, October 2022, Title: TBD
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Research Scholars Seminar, Discovery Partners Institute, Chicago, IL, September 2022, Title: Quantum Information Theory: an intro from the theoretical viewpoint
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Lecture Series, KnOttawa Summer School, Kansas State University, July 2022, Topic: Quantum Information Theory
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Lecture I: The Postulates of Quantum Mechanics Part I
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Lecture II: The Postulates of Quantum Mechanics Part II
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Lecture III: Quantum Operations and Quantum Noise Part I
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Lecture IV: Quantum Operations and Quantum Noise Part II
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Lecture V: Quantum Error Correction
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Lecture, Kleines Seminar, WWU Münster, June 2022, Title: The Postulates of Quantum Mechanics and Further Observations
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Lecture, Oberseminar C*-algebren, WWU Münster, June 2022, Title: A Universal Representation for Quantum Commuting Correlations
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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
Undergraduate Students:
- Chieh Hsu (Physics)
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. Published: Annales Henri Poincaré. DOI: 10.1007/s00023-022-01197-7.
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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.