Ruth J. Williams

University of California, San Diego


Primary Section: 32, Applied Mathematical Sciences
Secondary Section: 11, Mathematics
Membership Type: Member (elected 2012)

Biosketch

Ruth Williams holds the Charles Lee Powell Chair in Mathematics I at the University of California, San Diego (UCSD). She is a mathematician who works in probability theory, especially on stochastic processes and their applications. She is particularly known for her foundational work on reflecting diffusion processes in domains with corners, for co-development with Maury Bramson of a systematic approach to proving heavy traffic limit theorems for multiclass queueing networks, and for the development of fluid and diffusion approximations for the analysis and control of more general stochastic networks, including those described by measure-valued processes. Her current research includes applications to Internet congestion control and systems biology.  Williams is a Corresponding Member of the Australian Academy of Science, a member of the American Academy of Arts and Sciences, a former Guggenheim Fellow, Sloan Fellow and NSF Presidential Young Investigator, and a Fellow of multiple mathematical societies. In 2016 she was awarded (jointly with M. Reiman) the John von Neumann Theory Prize by INFORMS and in 2017 received the Award for the Advancement of Women in Operations Research and Management Sciences. Williams has served as President of the Institute of Mathematical Statistics (2012), on the NAS Council (2019-2022) and COSEMPUP (2020-2023).    

Research Interests

Ruth Williams' current research concerns mathematical problems stemming from the challenges of analyzing and controlling the dynamics of stochastic models of complex networks. Such "stochastic networks" arise in a variety of applications in science and engineering, e.g., in systems biology, high-tech manufacturing, computer systems, telecommunications, transportation, and business service systems. Modern networks, such as the Internet, are often highly complex and heterogeneous, presenting interesting mathematical challenges for their analysis and control. Some aspects of Williams' work involve the development of general theory for broad classes of networks, while others focus on mathematical problems directly motivated by specific applications. As examples of the latter, Williams has recently analyzed models of the Internet to understand the effects of using fair bandwidth-sharing policies, and has developed theory to study coupled enzymatic processing in protein networks, in collaboration with researchers in synthetic biology. Some stochastic process aspects of her research include justifying the approximation of density dependent Markov chains by reflected diffusion processes, analyzing measure-valued processes used to track residual job sizes or ages of jobs in stochastic network models with resource sharing, solving singular diffusion control problems, and addressing foundational questions for reflected diffusion processes in non-smooth domains.

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