Department of Mathematics Calendar
Ryan Hynd, University of Pennsylvania, A Conjecture of Meissner
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A curve of constant width has the property that any two parallel supporting lines are the same distance apart in all directions. A fundamental problem involving these curves is to ﬁnd one which encloses the smallest amount of area for a given width. This problem was resolved long ago and has a few relatively simple solutions. The volume minimizing shapes in three-dimensions have yet to be determined. We will discuss the two shapes which are conjectured to be volume minimizing and an approach to this outstanding problem.
Ryan Hynd is originally from Jamaica and grew up in south Florida. He developed an appreciation for mathematics while studying at Palm Beach Community College, where he also played on the school’s basketball team. Ryan transferred to Georgia Tech, where he did undergraduate research on soap ﬁlms, rotating drops, and constant mean curvature surfaces. As a PhD student at Berkeley, Ryan got involved in research on partial differential equations. He wrote his thesis on a PDE eigenvalue problem arising in an option pricing model. Ryan then went on to do a postdoctoral fellowship at NYU’s Courant Institute. There he studied systems of PDEs used to model viscoelastic ﬂuids. Since 2012, Ryan has been on the faculty at UPenn. He continues to focus on PDEs coming from control theory, calculus of variations, ﬂuid mechanics, eigenvalue problems, and more.
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