Dr. Barnes earned his doctorate in Mathematics at the University of Washington. He has worked in probability theory, stochastic processes and diffusions, as well as probabilistic representations of partial differential equations (PDEs) and free boundary problems.
At the Faculty of Industrial Engineering and Management at the Technion, Dr. Barnes builds on his expertise in the area of probabilistic representations of PDEs and free boundary problems to study the macroscopic behavior of systems of diffusions interacting through their reflection term (local time). He also investigates free boundary problems for stochastic partial differential equations (SPDEs)—an area where very interesting developments have happened in recent years.
Dr. Barnes has used his mathematical knowledge for interdisciplinary collaboration. He participated in the Washington State eXperimental Mathematics Lab (WXML) as a graduate student team lead for a research project on cancer modeling. He and his team of undergraduate students studied the growth rates of tumors for particular cancer models. Later, he worked with architectural design researchers to model the lifespan of American residential housing stock as a probabilistic survival distribution based on available data from the American Housing Survey (AHS). The goal was to help improve the accuracy of environmental impact studies within the built environment.