Two University of Toronto Scarborough mathematics professors have been awarded Sloan Research Fellowships to continue their promising work.
Assistant Professors Robert Haslhofer and Giulio Tiozzo – both from the Department of Computer and Mathematical Sciences – are recipients of the prestigious fellowship that recognize early-career researchers.
“It’s a real honour,” says Haslhofer, an expert on geometric evolution equations. “It’s a selective fellowship and it’s nice to be recognized, but I’m also very grateful to my teachers, collaborators and the department for all their support over my career.”
One of the equations Haslhofer studies is something called mean curvature flow, specifically the point at which evolving surfaces like in spheres or dumbells shrink to a singularity. His research explores these singularities in terms of classifying them and finding new ways to continue the curvature flow beyond the singularity.
One of the major research projects the fellowship will help support is Haslhofer’s work on Ricci Flow, a project that has exciting potential applications especially towards finding new geometric shapes.
The work may also have implications for work on general relativity and even for models being developed for certain interfaces used in biology and material science.
“This equation is well understood in a three-dimensional case, but for four and five dimensions we have much less understanding, so there’s a lot of work to be done,” he adds.
Tiozzo, who is an expert on dynamical systems, says he was delighted and honoured to receive the fellowship.
“Many people who have received this fellowship have gone on to do important work, so it’s an honour to be in their company,” he says.
A main aspect of Tiozzo’s research looks at entropy of dynamical systems, which essentially is a number that can be attached to physical systems to determine whether that system is chaotic or not. If a system has high entropy, it means it’s highly chaotic.
“When you have several systems, if you change the parameters you need to know what happens to the entropy,” he says.
A major issue he will be looking at is the entropy of a particular class of dynamical systems that involves the iteration of complex polynomials, specifically defining these polynomials in the complex plane.
Haslhofer and Tiozzo are among 126 researchers from across Canada and the United States to receive 2018 Sloan Research Fellowships. Winners receive a two-year, $65,000 fellowship to further their research.
The fellowships, awarded annually since 1955 by the Alfred P. Sloan Foundation, honour early-career scholars from eight scientific and technical fields including chemistry, computer science, economics, mathematics, computational and evolutionary molecular biology, neuroscience, ocean sciences, and physics.
Past Sloan Research Fellows include many notable figures in the history of science, including physicists Richard Feynman and Murray Gell-Mann, and game theorist John Nash.