2018 John Barrett Memorial Lectures

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The 2018 Barrett Lectures will take place during May 29-June 1, 2018 at the University of Tennessee, Knoxville. This year's Lectures will take the format of a workshop on recent developments in mean curvature flow, a mathematical model for the deformation of surfaces (and higher-dimensional objects) that decreases area most rapidly. The workshop is aimed at graduate students and early career researchers, as well as researchers from related applied fields in which processes like the mean curvature flow naturally arise. The workshop will consist of a one-day introductory course on mean curvature flow, followed by a series of longer form survey lectures from a selection of preeminent researchers which will introduce participants to some of the most important recent breakthroughs in the field. These lecture series will be supported by auxiliary talks from further leading researchers and a series of short talks by graduate students and early career researchers.Geometric flows, such as the mean curvature flow, have proved to be a powerful tool in the analysis of a large number of important problems in differential geometry, image processing and mathematical physics, leading to a profound impact on each of these fields. They also arise naturally in such diverse physical contexts as thermomechanics, annealing metals, crystal growth, flame propagation, wearing processes and conformal field theory, where they model physical processes involving interfaces and surface energies. The mean curvature flow is the prototypical geometric flow equation and, as such, tools developed to understand its behavior often lead to insights into the behavior of other flow-based models. The main themes to be explored at the workshop will be the uniqueness, rigidity and genericity of cylindrical singularities, the classification of ancient and soliton solutions, and recently developed entropy and noncollapsing methods.Conference website: http://www.math.utk.edu/barrett/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.