August 4, 2018, 1:39 pm
On the cutting edge of Dynamical Systems research, Lai-Sang Young does not shy away from a challenge. Her primary field of mathematics, Dynamical Systems, is a relatively recent development in mathematics but is quickly growing and branching out into other areas. Dynamical systems look at evolutions through time for processes – the study of change of moving objects and evolving systems.
For Young, the goal is to understand phenomena, but also to describe, analyze, explain and predict them. “All things change with time, so naturally, almost everything is a Dynamical System,” she said. Famous for introducing the method of Markov returns in hyperbolic dynamical systems in the late 90s, she has shifted her gaze towards biology. More specifically – the world of neuroscience.
Young has studyed neuroscience over the past seven years to push the boundaries of her research. “Biology is very complicated, so the degree of complexity is much higher than typical mathematical problems,” she explained. Biology as a quantitative science allows for more precise analysis.
Her research shows how a mathematical approach to ideas, and she said math can be used to understand problems in natural science. “What can mathematicians do about the brain? I’ve asked this question many times.” The dynamical interactions first produce a direction field, a map of edges, and after processing, it is possible to recognize geometric shapes and motion. “Looking at individual neurons, you can’t observe behavior. But put them together and you start seeing patterns. There is every reason for people in dynamical systems to be interested in the brain,” she affirmed. In her lecture, she demonstrated geometric patterns found in images of brain activity.
The first steps have been taken, but there is still a lot to be done on this new frontier of research. Young hopes that more people will follow her lead and understand that this field is not a narrow topic. More specifically, she hopes that it will excite young people and encourage them to enter this impressive field of research. “In the last 100 years, the field of dynamical systems has blossomed, but it must continue to evolve if it is to remain a vibrant field of research,” she said.