Geometric Analysis Conferences and Seminars

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This award supports a series of three two-day Geometric Analysis conferences at Rutgers University, on October 27-28 in 2016, October 26-27 in 2017, and October 25-26 in 2018, that highlight recent developments in the analysis of non-linear elliptic and parabolic partial differential equations arising in the study of Riemannian manifolds and geometric flows. Riemannian manifolds are higher-dimensional generalizations of the familiar concept of a surface in three-dimensional space, such as the surface of a ball or a donut. Four-dimensional manifolds (with three spatial and one temporal direction) are used in general relativity as models for the universe. Manifolds of other dimensions are used by theoretical physicists in string theory, which may lead to a unification of quantum field theory and gravity. The conferences will bring together distinguished senior speakers and a wide range of junior mathematicians to disseminate recent research progress and catalyze future research in the subject. The opportunities presented by the meetings to discuss research with leaders in the field will help to train and encourage the next generation of researchers. The conference series makes special efforts to encourage women and minority mathematicians to participate in the meetings. The field of geometric flows is of great current interest due its many applications to the understanding of Riemannian manifolds. Within Ricci flow for a Riemannian metric, there has been progress in understanding the structure of solutions, their singularities, their asymptotics, and uniqueness. Flows starting from more general initial data (for example, a metric space, or a manifold with unbounded curvature, or an incomplete metric) are becoming better understood. A better understanding of Ricci flow may lead to advances in areas such as general relativity, string theory, the geometry of closed four-dimensional smooth manifolds, and renormalization in quantum field theory. The study of mean curvature flow may lead to advances in knot theory, image processing, materials science, and minimal surfaces. The conference series brings together experts at the frontier of research in these various topics from around the United States. The conference is expected to generate transfers of knowledge, new collaborations, and a cross-fertilization of ideas, and further inspire graduate students and junior mathematicians. The 2016 conference website is www.finmath.rutgers.edu/ga2016/index.php