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Student Projects

 

Student Projects

 
 
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Final Projects in Differential Geometry

Fall 2023, Fall 2019 - Geometry Class

Each student in my Geometry class selected an advanced topic in Differential Geometry to study. Topics ranged from map projections, to the isoperimetric problem and minimal surfaces, to the mathematics of higher dimensional manifolds and orbifolds. Students read outside sources to develop their understanding of these topics, and presented their findings in a poster presentation open to the Southwestern University community.

 
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Cost minimization on Michell Trusses

Summer 2016 - Joint w. Kristen McCrary, William Soller

We examined geometric objects called Michell trusses, exploring questions of existence, uniqueness, and cost-optimization of these trusses (under a natural cost function). Using the Calculus of Variations, we proved that a Michell Truss which equilibrates a fixed set of point forces and has an exterior 4-corner cannot be cost minimizing, and that it is always possible to lower the cost by "shaving" off the corner in a way that does not change the underlying set of point forces.