This NSF award supports a five day CBMS Conference on "The Cahn-Hilliard Equation: Recent Advances and Applications". The conference will be held at Montgomery Bell State Park's Conference Center and Inn, in Burns, Tennessee (about 30 miles outside of Nashville) from May 20-24, 2019. Professor Alain Miranville of the University of Poitiers (France) will deliver the main lecture series. Professor Miranville is an international expert in CH-type equations and applications and a world renowned expositor and lecturer. Miranville's ten lectures will take the participants on a journey through the subject beginning with the derivation of the equation and associated boundary conditions, through the analysis of the problems, numerical methods, and ending with cutting edge applications of Cahn-Hilliard (CH) type equations in fluid dynamics, image inpainting, and tumor growth. The main lectures will be supported by a diverse group of additional speakers and participants. There will be three panel discussions lead by the main lecturers: (1) attracting and training PhD students in applied differential equations and providing the appropriate interdisciplinary background, (2) open problems and applications of CH-type equations in the physical sciences, and (3) future directions for CH-type equations in radiology and tumor analysis. About 30 participants will be supported; women, minorities, graduate students, postdoctoral associates, junior faculty and faculty at primarily undergraduate institutions are encouraged to participate. Ample time and space for private discussions during the week is provided to lead to collaborations that continue to develop long after the conference concludes.

The proposed lectures and panel discussions heavily emphasize open research problems across multiple scientific fields. The discovery that tumor growth can be effectively modeled using CH-type equations is recent and holds great promise. Applications in fluid dynamics and inpainting are equally promising and will be presented. This area promotes interactions among mathematicians, medical researchers, scientists and engineers. Professor Miranville will produce a monograph which will serve as the unique concise reference for the subject and its far reaching, cutting edge applications. For more information, please refer to the conference website:

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Swatee Naik
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University of Memphis
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