Ph.D., School of Mathematics and Statistical Sciences, Arizona State University, Tempe, Arizona (2019)
Academic and Research Interests
My main mathematical research interest lies in mathematical analysis and application. Throughout my career, my research has been to develop new analytical mathematical tools to solve real-life problems. Meanwhile, my mathematical research focuses on multi-scale modeling, optimal control theory, non-linear and non-local hyperbolic conservation laws, hybrid systems, measure differential equations, and optimal transport. My research has been applied to subjects such as traffic flow, epidemiology, and supply chains.
Traffic flow models with autonomous vehicles
Traffic behaves in a complex and nonlinear way, depending on the interaction of a large number of vehicles and the individual reactions of human drivers. Vehicles do not simply follow the laws of mechanics to interact with each other but show the formation of clusters and propagation of stop-and-go waves. My goal in studying traffic flow modeling is to understand and develop optimal traffic networks with efficient movement of traffic and minimal traffic congestion.
Epidemiological models: A measure model for the spread of viral infections with mutations
Genetic variations in the COVID-19 virus are one of the main causes of the COVID-19 pandemic outbreak recently. We use a new type of model, a system coupled with ordinary differential equations (ODEs) and measure differential equation (MDE), stemming from the classical SIR model to study the COVID variants distribution. The proposed ODE-MDE model coincides with the classical SIR model in the case of constant or time-dependent parameters as special cases.
Supply chain models: An application of non-local hyperbolic conservation law
The highly re-entrant semiconductor manufacturing systems that involve a large number of products and many steps can be modeled using conservation laws for a continuous density variable in production processes. We study the resulting non-local non-linear hyperbolic conservation law in the setting of states, in-and-out outfluxes being Borel measures. This is motivated by the lack of optimal solutions in the L1 setting for transitions from a smaller to a larger equilibrium with zero backlogs. The key innovations involve dealing with discontinuous velocities in the presence of point masses, and a finite domain with in- and outfluxes.
Teaching mathematics means perpetuating mathematical knowledge and inspiring learning. More specifically, I take every lecture as a unique opportunity to show my students strategies of problem-solving that can be used in different areas and to motivate their critical thinking. I am blessed to be passionate about mathematics, and my goal is to convey that passion to my students.