Research summary
Mathematics offers a universal language for modelling physical systems.
In math, partial differential equations (PDEs) express how physical quantities in a system change in space and time. They can describe a wide variety of physical phenomena, so studying them is fundamental for applications from math to general sciences.
But access to precise details about heterogeneous effects (the physical properties that vary in the medium) may not be possible due to uncertain measurements or a lack of information about the physical setting. Dr. Jessica Lin is developing tools to analyze physical systems subject to random effects. She specializes in “stochastic homogenization,” which identifies the effective behaviour of PDEs subject to random and microscopic heterogeneous effects. She and her research team are combining analytical and probabilistic tools to tackle problems in stochastic homogenization.
Their research will have countless applications for mathematical modelling, including for forest fires, population spread, and diffusion processes.