Nicholas D. Kazarinoff Collegiate Professor of Complex Systems, Mathematics and Physics, and Director of the Center for the Study of Complex Systems

### About

Charles Rogers Doering, Ph.D., an eminent interdisciplinary mathematician, dedicated mentor, and campus leader, passed away on May 15, 2021. Prof. Doering was the Nicholas D. Kazarinoff Collegiate Professor of Complex Systems, Mathematics and Physics, and the Director of the Center for the Study of Complex Systems for the past six years.

An acclaimed scholar and beloved colleague with a rare combination of depth and breadth—he was equally at home dissecting a chalkboard full of equations and pondering fundamental questions about the nature of life. Professor Doering was perhaps most notable for the energy he brought to every endeavor—from refining a proof to running a faculty meeting—and for the variety of parts of campus life and scholarship that he impacted. His untimely passing creates a deep sense of loss spanning diverse communities, while also reminding us all of the joy that emanates from a life well lived in the service of others and in the pursuit of knowledge.

Professor Doering was a prominent polymath with a highly interdisciplinary research program—his work spanned stochastic dynamical systems and partial differential equations arising from applications across biology, chemistry, and physics. He made fundamental contributions to the analysis of noisy and nonlinear dynamical systems, including co-discovery of resonant activation, current reversals in stochastic ratchets and rigorous dissipation rate bounds for incompressible turbulence. Over the past 25 years, much of Prof. Doering’s work has focused on understanding some of the most foundational questions in applied mathematics and fluid dynamics, including whether the Navier Stokes equations—a key model in classical mechanics that underlies an enormous range of engineering applications—are actually self-consistent. These equations describe dynamics ranging from microscopic turbulence in blood flow, to wind and ocean currents, to stars and the interstellar medium, and yet very little is known about the basic properties of this model, including whether smooth solutions always exist for all time. Indeed, understanding the Navier Stokes equations is one of the unsolved $1M Clay Institute millennium challenges and a fundamental open question in mathematics and physics.

Prof. Doering made key contributions to understanding fluid dynamics and the Navier Stokes equations, including co-authoring one of the seminal books on the subject, Applied Analysis of the Navier-Stokes Equations (Cambridge University Press, co-authored with J. D. Gibbon). His book is a translation of the Navier Stokes problem from the traditionally more pure mathematics subfields it had previously been restricted to, to the broader audience of applied mathematicians and mathematical physicists. It opened this highly technical problem up for new researchers, allowing new approaches and ideas to be brought to bear. More recently, Prof. Doering also made important contributions to another open problem in fluid dynamics, understanding Rayleigh–Bénard convection. Rayleigh-Bénard convection plays a significant role in a wide range of problems across engineering, physics, oceanography, and meteorology. Prof. Doering and his colleagues recently developed a new numerical simulation method that allowed them to begin to answer a long outstanding question on the structure of heat transport in turbulent Rayleigh-Bénard convection.

Prof. Doering’s work often focused on connecting different areas of mathematics, physics, and complex systems—as Prof. Jean-Luc Thiffeault, a collaborator of Prof. Doering, noted, “Charlie was almost single-handedly responsible for making sure that the pure mathematics ‘applied analysts’ were aware of developments in the fluid dynamics community, and vice versa.” More broadly beyond his fluid dynamics and stochastics research, Prof. Doering was well known for extending himself as a collaborator and lending his skills to help colleagues solve problems even when they weren’t closely related to his own focus area.

"Charlie was almost single-handedly responsible for making sure that the pure mathematics ‘applied analysts’ were aware of developments in the fluid dynamics community, and vice versa." *-- Professor Jean-Luc Thiffeault*

Prof. Doering’s work in these areas builds on his distinguished career that began with his doctorate in mathematical physics from the University of Texas at Austin, followed by a career at Clarkson University and Los Alamos National Laboratory, where he served as Deputy Director of the Center for Nonlinear Studies. He joined the University of Michigan in 1996, where he became a leader and champion of interdisciplinary research, serving as Director of the Center for the Study of Complex Systems. Additionally, Prof. Doering was a Fellow of the American Physical Society (since 2001), a Fellow of the Society of Industrial and Applied Mathematics (since 2011), a Guggenheim Fellow (since 2016), and a Simons Fellow (since 2021), and received the Presidential Young Investigator Award (1989), a Fulbright Scholarship (1995), and a Humboldt Research Prize (2003).

Importantly, Professor Doering was also a dedicated educator and mentor at all levels, from undergraduate to faculty. He earned an Outstanding Advisor Award while at Clarkson and advised over 40 doctoral students and postdocs over the course of his career. He also served on the dissertation committees of over 60 additional students, in a diverse range of departments including Mathematics, Physics, Chemistry, Geological Sciences, Naval Architecture & Marine Engineering, Mechanical Engineering, Nuclear Engineering, and Education. He was also a supportive mentor to many junior faculty and colleagues, both within his own departments and across the university. Professor Doering was a devoted and engaging educator who was highly responsive to student needs and interests—for instance, on hearing from the Complex Systems student community that they were interested in learning evolutionary game theory and adaptive dynamics, he took it upon himself to learn the material and developed a new course. He brought the same spirit of enthusiasm and interest to his courses as he did to all of his work, and was always greatly appreciated by his students. The impacts of his teaching and mentoring will be felt for years to come, as many of his students and mentees are themselves now professors and passing on the ideas they developed with Prof. Doering to the next generation of mathematicians and physicists.

As Director of the Center for the Study of Complex Systems, Professor Doering fostered a wonderful spirit of community and grew the Center as a haven for interdisciplinary exploration, overseeing the expansion of the Center with new faculty and postdoctoral fellows from a range of disciplines. Professor Doering’s leadership of the Center allowed it to flourish and grow, while staying centered on the interdisciplinary, interactive connectedness on which it thrives.

In addition to Professor Doering’s research and academic roles, he was also a pillar of the University of Michigan community, and a true superfan of the University of Michigan football team. He attended nearly every game in his characteristic maize and blue suit, complete with Michigan socks, cufflinks, and pocket squares—regalia so striking that it was featured in the New York Times. He had Michigan-themed buttons for nearly every occasion and an irrepressible (and irreverent) spirit that made him nearly an institution unto himself. Professor Doering was a leading light of the University and the communities of mathematics, physics, and complex systems, and his spark will be keenly missed.

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