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Sheldon Miller will officially receive his Master of Science degree at USask’s 2021 Fall Convocation virtual celebration on Nov. 10. (Photo: Submitted)

‘We are on the precipice of a technological revolution’: New USask mathematics graduate begins PhD studies in quantum science

When Sheldon Miller receives his Master of Science (MSc) degree in mathematics this November, he will join a growing group of more than 164,000 University of Saskatchewan (USask) alumni from around the world—including a Nobel Prize winner.

“I feel incredibly honoured to be joining the incredible alumni of the University of Saskatchewan and the Department of Mathematics and Statistics,” he said. “Receiving my master’s degree will certainly be one of my largest accomplishments to date.”

Miller and his fellow USask graduates will be celebrated during 2021 Fall Convocation events that will be held online due to the ongoing COVID-19 pandemic. The virtual graduation celebrations will be livestreamed on Nov. 10, 2021.

Miller, who was born in Winnipeg and raised in Okotoks, Alta., joined the Department of Mathematics and Statistics in USask’s College of Arts and Science after completing his undergraduate degree at Indiana University. One of the reasons he was drawn to USask was the opportunity to work with mathematicians Dr. Steven Rayan (PhD) and Dr. Jenna Rajchgot (PhD), who is now a faculty member at McMaster University.

“Both Dr. Rayan and Dr. Rajchgot have established themselves as accomplished researchers within their respective fields. The ability to work with them both was certainly a major draw to attending the University of Saskatchewan,” Miller said. “I also loved the environment of the department during my initial visits to campus.”

While Miller’s master’s degree is now complete, his journey at USask is far from over. In September, he began his PhD in mathematics under the supervision of Rayan, a faculty member in the Department of Mathematics and Statistics and the director of the Centre for Quantum Topology and Its Applications (quanTA). Miller will work with Rayan at the interdisciplinary institute, which is devoted to the mathematics and physics of novel new quantum materials, inspired by the discovery of topological materials that have revolutionized condensed matter physics, as well as the next-generation technologies that will be enabled by these materials, such as quantum computing.

“I strongly believe the quanTA Centre is becoming one of the most pre-eminent interdisciplinary research centres here at USask,” said Miller. “During my master’s degree, I had the chance to meet many of the researchers—faculty, fellows and graduate students—involved in the centre and learn more about the incredible research being undertaken there. When the opportunity was available to continue my studies as a student affiliated with the centre, I was more than thrilled.”

At quanTA, Miller will work on novel mathematical approaches to quantum information and quantum computing. In particular, he hopes to work on—and solve—theoretical problems in quantum information and quantum computing by rephrasing these problems in the language of quivers, which are diagrams that help researchers to visualize mathematical relationships.

“I strongly believe we are on the precipice of a technological revolution fueled by quantum information and quantum computing,” he said. “In the coming decades, quantum computing will allow researchers to solve problems which are impossible to solve using classic computing, and I am absolutely thrilled to play my small part in developing this technology.”

As a master’s student, Miller took a deep look at how certain problems in theoretical physics can lead to interesting new geometries. His MSc thesis was entitled Interpretations of Stability for Twisted Quiver Representations on the Projective Line.

“My primary focus was the study of these twisted quiver representations, which are mathematical diagrams constructed from studying the topology and geometry of certain mathematical spaces,” he said. “My work involves the study of geometric objects arising from mathematics whose origins lie in theoretical physics.”

As he pursued his MSc degree, Miller also became involved with the Math & Stats Student Society (MS^3) in the Department of Mathematics and Statistics, as well as the newly formed Math and Stats Graduate Student Social Committee. One of his biggest academic achievements was receiving a prestigious Canada Graduate Scholarship – Master’s program (CGS M) from the Natural Sciences and Engineering Research Council of Canada (NSERC).

“I was awarded an NSERC CGS M Scholarship, which provides one year of funding to master’s researchers. I am incredibly grateful to NSERC for all their support. This funding allowed me more time to focus on research and scholarship,” Miller said.

Another highlight of Miller’s master’s degree was serving as a teaching assistant for the first two terms of the College of Arts and Science’s new MATH 101: Quantitative Reasoning course. The course is offered by the Department of Mathematics and Statistics to undergraduate students to help fulfil the new quantitative reasoning requirement in the college, which came into effect as part of the renewed curriculum launched in the fall of 2020.

“In this course, we use real-world examples to help students strengthen their reasoning skills through quantitative analysis and deduction—think using math as evidence to support an argument,” Miller said. “Given the ever-increasing complexity of our world, I strongly believe we need to continue to work to develop the reasoning skills needed to assess information accurately, and MATH 101 helps students to develop a mathematical toolkit to complete these assessments.”

In August, Miller was also offered a position at Saskatchewan Polytechnic, where he will serve as a faculty mathematics instructor.

“My primary responsibility will be instructing and teaching students mathematics, which is something I love to do,” he added.

Miller said the best part of studying at USask so far has been “the incredibly supportive academic environment developed by the faculty and students within the Department of Mathematics and Statistics.” He has fond memories of informal social gatherings during which students and faculty members discussed mathematics together.

“The math and stats department at the University of Saskatchewan is currently undergoing a tremendous amount of growth and rejuvenation,” he said. “I strongly believe this is due to the incredible faculty, the department head, Dr. Artur Sowa (PhD), and Dr. Rayan, who is the graduate chair of the department and whose relentless service to the department is incredibly inspiring.”

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