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Anthony Quas - Mathematics and Statistics

What does chaos theory have to do with math? Mathematician Anthony Quas is an expert in dynamical systems, an important area of mathematics that's blossomed in the computer era.

He applies the techniques of probability to the study of ergodic theory, which makes predictions about the average long-term behaviour of chaotic dynamic systems. A dynamical system is any system that changes over time according to some predetermined rule, such as planetary motion being governed by the laws of gravity, or systems that model weather behaviour.

“Dynamical systems is the fancy term for chaos theory,” he explains. Chaos in mathematics is studied in the form of these systems, in which small disturbances in initial conditions can have a dramatic long-term effect.

This sensitivity is known in popular culture as the “butterfly effect,” from a paper by Edward Lorenz—a pioneer of chaos theory—titled: Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas? “It’s fascinating, because despite things having a random, unpredictable element, you can make strong predictions about the cumulative efforts of random things,” he says.

Research mathematics is about constructing a theory that describes the relationship between phenomena, he explains. A particular focus for his work recently has been the use of dynamical systems methods in the study of mixing in ocean systems. 

The principal goal is to describe obstructions to mixing in the ocean. Many things get pumped into the ocean and one would assume it’s all gradually incorporated and becomes equally dispersed. In practice, though, that does not always happen. There are great regions of the ocean that mix very poorly, such as in gyres—large systems of rotating ocean currents. Anthony’s theory is geared towards locating these gyres and the mechanisms behind them.

Anthony, a Canada Research Chair, is also interested in the dynamics of expanding maps, information theory, statistical mechanics and percolation theory.

Learn more about Anthony Quas’ research.

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