Roy M. Araiza

Roy M. Araiza
Department of Mathematics
Purdue University

I received my PhD in mathematics from Purdue University in April 2021 under the direction of Thomas Sinclair. My thesis was titled "On the abstract structure of operator systems and applications to quantum information theory." Beginning the 2021 academic year I will be joining the Department of Mathematics at the University of Illinois at Urbana-Champaign as a J.L. Doob Research Assistant Professor. Originally I am from the Silicon Valley in California and obtained my Bachelor of Arts in mathematics from San Jose State University. Here is a family photo taken at IPAM in May 2018 (from left-to-right: Dan-Virgil Voiculescu, Sorin Popa, Jesse Peterson, Thomas Sinclair, Myself).

Here is a copy of my CV.

Check out the Purdue Operator Algebras Seminar. For schedules of previous semesters click here.

I was a TA for the Groundwork in Operator Algebras Lecture Series GOALS.

Thomas Sinclair and I are organized the workshop QLA Meets QIT which was held at Purdue November '19.

During the spring semester of 2018 I was a visiting researcher in the semester long program Quantitative Linear Algebra held at IPAM at UCLA. The report on the program can be found here.

When I am not working on mathematics I enjoy playing chess and reading. In particular, my favorite topics to read about include science, history, and philosophy.
Some quotes and speeches.

Contact Information

Purdue University
Department of Mathematics

Email: raraiza [at] purdue [dot] edu

Office:
MATH 1030
150 North University Street
West Lafayette, Indiana
47907

Research Interests

• Tensor theory of operator spaces
• Tensor theory of operator systems
• Quantum information theory
• Operator algebras

Publications & Preprints

1. A Universal Representation for Quantum Commuting Correlations (with Travis Russell and Mark Tomforde). Submitted. arXiv:2102.05827
2. An Abstract Characterization for Projections in Operator Systems (with Travis Russell). Submitted. arXiv:2006.03094.
3. $\mathcal{R}$ we living in the matrix? (with Rolando de Santiago) Notices of the American Mathematical Society (2019) Volume 66, Number 8, Pgs. 1216-1224 pdf.

Expository Papers

• The Column and Row Hilbert Operator Spaces pdf
• Pisier's Self-Dual Operator Hilbert Space pdf

Travel Schedule 2020:

• 24-28 February, West Point
• 12-16 March, AMS Sectional Meeting, Advances in Operator Algebras, University of Virginia
• 16 April, Mathematical Physics and Operator Algebras Seminar, Michigan State University
• 1-7 May, Noncommutative Geometry and Operator Algebras Spring Institute, Vanderbilt
• 28 June-19 July, Groundwork for Operator Algebras Lecture Series (GOALS), Michigan State University
• 17-18 October, East Coast Operator Algebras Symposium, University of Virginia

Travel Schedule 2021:

Link to Grad Rep website.

Purdue Department of Mathematics website

The proscription of Cicero, however, caused most strife in their debates, Antony consenting to no terms unless Cicero should be the first man to be put to death, Lepidus siding with Antony, and Caesar holding out against them both. They held secret meetings by themselves near the city of Bononia for three days, coming together in a place at some distance from the camps and surrounded by a river. It is said that for the first two days Caesar kept up his struggle to save Cicero, but yielded on the third and gave him up. The terms of their mutual concessions were as follows. Caesar was to abandon Cicero, Lepidus his brother Paulus, and Antony Lucius Caesar, who was his uncle on the mother's side. So far did anger and fury lead them to renounce their human sentiments, or rather, they showed that no wild beast is more savage than man when his passion is supplemented by power. -Plutarch's Life of Cicero

In the course of 13 October, Napoleon rode out on a reconnaissance and entered Jena. The German philosopher Georg Wilhelm Friedrich Hegel, then a professor at the university there and in no way sympathetic to revolutionary France, wrote to a friend on seeing him: "I saw the Emperor-this world spirit-riding out of the city...It is indeed a wonderful sensation to see such an individual, who, concentrated here at a single point, astride a horse, reaches out over the world and masters it...The spirit of the age, who commands history."

"The pursuit of truth and beauty is a sphere of activity in which we are permitted to remain children all our lives." -Albert Einstein

"It may happen to me to lose battles, but no one shall ever see me lose minutes either by over-confidence or by sloth.
-Napoleon Bonaparte

"Each day we go to our work in the hope of discovering." -Nikola Tesla

"For myself, I have but one requirement, that of success." -Napoleon Bonaparte

When the Duke of Wellington was asked who is the greatest captain of the age, he responded with, "in past ages, in this age, in any age, Napoleon."

"Intellectual passion drives out sensuality." -Leonardo da Vinci

"Aequam memento rebus in arduis sevare mentem." -Horace

"Among the great philosophers through all the ages, there is one great truth: that he who truly lives by the words of others has not the wit to know his own mind and that he who knows his own mind has not the temerity to truly live." -K. Holmmad