Creativity, innovation and research

Faculty of Mathematics Professor William Slofstra credits the University of Waterloo’s collaborative environment for him receiving a 2021 Sloan Research Fellowship. The pure mathematician is keen to use the monetary prize that comes with the fellowship to enhance the supportive atmosphere he has benefited from at Waterloo.  

“It’s great to be recognized by the Alfred P. Sloan Foundation because I put a lot of work into my research,” says Slofstra, who is also a member of Waterloo’s Institute for Quantum Computing. “Receiving this fellowship is a recognition of the kind of environment that’s created at Waterloo where research is supported. It’s an environment where you can talk to other researchers, there’s time to do research, and great students to speak with about their work. 

“What I’d like to do with this award is help to keep this environment going because that’s what creates the conditions for doing good research.” 

The Sloan Research Fellowship, which has been awarded annually since 1955, honours U.S. and Canadian researchers whose creativity, innovation, and research accomplishments make them stand out as the next generation of scientific leaders. 

Open to scholars in eight scientific and technical fields — chemistry, computational and evolutionary molecular biology, computer science, Earth system science, economics, mathematics, neuroscience, and physics — the Sloan Research Fellowships are awarded in close coordination with the scientific community. Candidates must be nominated by their fellow scientists and winners are selected by independent panels of senior scholars based on a candidate’s research accomplishments, creativity and potential to become a leader in their field. More than 1,000 researchers are nominated each year for 128 fellowship slots. Winners receive a two-year, $75,000 fellowship, which fellows can spend to advance their research. 

“William is a rising superstar in the research community and I’m extremely pleased that the Sloan Foundation has recognized his enormous talent and potential,” says David McKinnon, chair of the Department of Pure Mathematics and the person who nominated Slofstra.  

Professor Slofstra’s most significant research has been on the mathematical foundations of quantum information theory and especially the mathematics concerning the Tsirelson conjectures and the reformulation of the Connes Embedding Problem in terms of joint conditional probability densities. 

Slofstra, in 2016, was the first to prove that some of Tsirelson’s mathematical models yielded different sets of joint quantum probability densities. He has also used his work to show the remarkable result that certain problems in quantum theory are undecidable. He did this by demonstrating that his constructions allowed him to reduce certain problems in quantum theory to the mathematics of groups of symmetries. 

“Congratulations to William on being awarded a Sloan Research Fellowship,” says Mark Giesbrecht, Dean of Waterloo’s Faculty of Mathematics. “William’s work is already driving the research frontier and carrying the field of mathematics and mathematical physics forward.”  

Slofstra's work has been continued by others, who have shown separations between other sets of joint quantum probability densities. A team of computer scientists in a lauded work in 2020 showed the last remaining pair of of Tsirelson’s mathematical models were distinct, resolving the Connes embedding problem.  

Slofstra continues work on connections between the mathematics of groups of symmetries and Tsirelson’s problems.