John Ross

Notable Achievements

Assistant Professor of Mathematics John Ross  and Professor of Mathematics Kendall Richards ’ book Introductory Analysis: An Inquiry Approach  was released by Taylor & Francis–CRC Press. The text is an inquiry-based exploration of the real number line, seriously examining fundamental topics in the field of real analysis. Beyond the main content, the text features an extended prologue that introduces readers to inquiry-based proof writing, as well as a suite of extended explorations into advanced special topics in the field. An early version of this text was read by SU math majors Morgan Engle  ’18 and Elyssa Sliheet  ’19, and improvements were made based on their suggestions.

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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.