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 games
 Quantum error correction
 Quantum information theory
Research Description
My research interests are in operator space theory, operator system theory, and quantum information theory. In particular, I am interested in the local structure of operator spaces and operator systems, quantum games, and quantum error correction. Graduate students are welcome to email me if you are interested in any of these topics.
Courses Taught
 Spring '23:
 Math 595: Operator Space Theory
 Course Description. Updates and course information will be on our Canvas page. Email me for code.
 Course Outline
 Math 492: Quantum Channels and Error Correction II
 Math 415: Applied Linear Algebra
 Math 595: Operator Space Theory
 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 UrbanaChampaign
 Affiliate, Illinois Quantum Information Science and Technology Center, University of Illinois at UrbanaChampaign
 Scholarship Board Member, Sloan University Center of Exemplar Mentoring at Illinois, University of Illinois at UrbanaChampaign
News:
Along with Marius Junge, Felix Leditzky, and Thomas Sinclair, I am organizing the workshop ``QLA Meets QIT II'' to be held in Chicago 35 November. More information can be found here https://sites.google.com/view/qlameetsqitii/home and the poster is here /media/717
In the Spring term 2023 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, JuneJuly 2022
 Department of Mathematics, University of Virginia, April 2022
Research Visitors:
 Graeme Smith, University of Colorado Boulder, April 2023
 Nima Lashkari, Purdue University, March 2023
 Alexander MüllerHermes, University of Oslo, November 2022
Upcoming Lectures:

Lecture, Operator Algebras Seminar, Purdue University, April 2023, Title: TBD

Lecture, Quantum Information and Computing Seminar, University of Delaware, November 2022, Title: An Index for Inclusions of Operator Systems

Research Scholars Seminar, Discovery Partners Institute, Chicago, IL, September 2022, Title: Quantum Information Theory: an intro from the theoretical viewpoint

Lecture Series, KnOttawa Summer School, Kansas State University, July 2022, Topic: Quantum Information Theory

Lecture I: The Postulates of Quantum Mechanics Part I

Lecture II: The Postulates of Quantum Mechanics Part II

Lecture III: Quantum Operations and Quantum Noise Part I

Lecture IV: Quantum Operations and Quantum Noise Part II

Lecture V: Quantum Error Correction


Lecture, Kleines Seminar, WWU Münster, June 2022, Title: The Postulates of Quantum Mechanics and Further Observations

Lecture, Oberseminar C*algebren, WWU Münster, June 2022, Title: A Universal Representation for Quantum Commuting Correlations

Lecture, Operator Theory Seminar, University of Virginia, April 2022, Title: Matricial Archimedean Order Unit Spaces and Quantum Correlations

Plenary Lecture, Southeastern Analysis Meeting, University of Florida, March 2022, Title: Matricial Archimedean Order Unit Spaces and Quantum Correlations

Functional Analysis Seminar, University of California San Diego, February 2022, Title: Matricial Archimedean Order Unit Spaces and Quantum Correlations

Department of Mathematics & Statistics Colloquium, San José State University, September 2021, Title: From Correlation Sets to Tensor Products of C*algebras: The ConnesKirchberg Problem
Undergraduate Students:
 Jihong Cai (Mathematics)
 Abraham Holtermann (Physics)
 Chieh Hsu (Physics)
Recent Publications
 An index for inclusions of operator systems (with Colton Griffin and Thomas Sinclair) (2022). arXiv:2203.05710. Submitted

Approximating projections by quantum operations (with Colton Griffin, Aneesh Khilnani, and Thomas Sinclair) (2022) arXiv:2203.02627. To appear: Linear Algebra and Its Applications

Matricial Archimedean order unit spaces and quantum correlations (with Travis Russell and Mark Tomforde). (2021) arXiv:2109.11671. To appear: Indiana University Mathematics Journal

A universal representation for quantum commuting correlations (with Travis Russell and Mark Tomforde). (2021) arXiv:2102.05827. Published: Annales Henri Poincaré. DOI: 10.1007/s00023022011977.

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. 12161224.