Roy Araiza | Mathematics at Illinois

Contact Information

257A Altgeld Hall (MC-382), Department of Mathematics, University of Illinois at Urbana- Champaign, 1409 West Green Street, Urbana, Illnois, 61801 USA

raraiza@illinois.edu

Research Areas

Analysis

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J.L. Doob Research Assistant Professor, Department of Mathematics

Affiliate, Illinois Quantum Information Science and Technology Center

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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:
1. Math 595: Operator Space Theory
  1. Course Description. Updates and course information will be on our Canvas page. Email me for code.
  2. Course Outline
2. Math 492: Quantum Channels and Error Correction II
3. Math 415: Applied Linear Algebra
Fall '22:
1. Math 492: Quantum Channels and Error Correction (8 students)
2. Math 415: Applied Linear Algebra (280 students)
Spring '22:
1. Math 492: Select Topics in Quantum Information Theory (16 students)
2. Math 415: Applied Linear Algebra (280 students)
Fall '21:
1. 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 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, June-July 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 Müller-Hermes, 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
1. Lecture I: The Postulates of Quantum Mechanics Part I
2. Lecture II: The Postulates of Quantum Mechanics Part II
3. Lecture III: Quantum Operations and Quantum Noise Part I
4. Lecture IV: Quantum Operations and Quantum Noise Part II
5. 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 Connes-Kirchberg 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/s00023-022-01197-7.
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.