**Assistant Professor, Department of Mathematics**

**Applied Analysis, Partial Differential Equations, Fluid Mechanics, Kinetic Theory**

Dr. Sun’s research interests lie in applied mathematics. Within that part of the field of mathematics, she is drawn to the analysis of partial differential equations, especially equations arising from problems in physics. The topics of kinetic theory and fluid mechanics also peek her interest, and as a result her research group explores a variety of questions in these areas, including problems from physics and biology. Dr. Sun’s work is a perfect example of integrating creative problem solving and mathematics into other scientific fields to yield exciting outcomes.

*What kind of research are you working on right now?*

My broad field of study is the analysis of partial differential equations, and the types of equations I look at come from physics and biology – I bring a mathematician’s approach to problems arising in these areas. For instance, one important question in statistical physics is to bridge the microscopic and macroscopic views of gas dynamics. Using the behaviour of airflow in a room as an example, one can take the microscopic view and consider the air as a collection of particles. Alternatively, one can adopt the macroscopic view and treat the airflow like water. Although the connection between these two views can be argued in a formal way, the mathematician’s role here is to provide a solid foundation by rigorously justifying the relation between them in various parameter regimes. And the tools that we use are differential equations.

In both physics and mathematics, there are various types of differential equations. In the airflow case, there are ordinary equations that describe the motion of particles; stepping back a bit, there are partial differential equations that describe density distribution of particles, considering the number of particles present within a certain velocity and position range; leaving out even more details, there are equations that describe the evolution of macroscopic densities of mass, momentum, and energy. My interest is in a medium-detailed or mesoscopic view of the problem, the kinetic description. My research group is trying to understand properties of kinetic equations and connect them to the macroscopic fluid level view. Analyzing this so-called *multiscale phenomenon* involves a lot of advanced mathematical tools.