Notable Achievements

Assistant Professor of Mathematics John Ross has had a paper accepted for publication in the Annals of Global Analysis and Geometry. The paper, “Solution to the n-bubble problem on R with log-concave density,” extends the results of his work with his SCOPE students (mentioned above) in two meaningful ways: it allows for configurations of any number of bubbles (not just 3 or 4), and it relaxes the restrictions on the density function being considered

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Expertise

Differential Geometry, Riemannian Geometry, Geometric Analysis. Minimal surfaces, Mean Curvature Flow. The mathematics of bubbles and similar surfaces.

John Ross received his PhD in Mathematics from Johns Hopkins University in 2015 and his BA in Mathematics from St. Mary’s College of Maryland in 2009.

  • John Ross received his PhD in Mathematics from Johns Hopkins University in 2015 and his BA in Mathematics from St. Mary’s College of Maryland in 2009.

  • Dr. Ross’ research focuses on theory and applications of minimal surfaces and mean curvature flow. Taken together, these subjects describe how surfaces (or higher-dimensional manifolds) can evolve in time to achieve stable structures under certain constraints. The most accessible example is the creating of bubbles via soap film - a two-dimensional elastic surface that aims to minimize surface area subject to some additional structural constraint (eg. constant volume enclosure in the case of a free-floating bubble, or fixed boundary in the case of a bubble wand). The geometry of the surface with minimal surface area - or the evolution a soap film undergoes as it evolves to shrink surface area - is of broad interest to mathematicians, materials scientists, and physicists. Dr. Ross studies the differential equations that govern this process, and the connection between these equations and the underlying geometry of the surfaces.