All people have a sense of beauty, and while there is no universal agreement, huge numbers of people do agree on the same shapes, color combinations, musical pieces, etc. as being "beautiful". Symmetries often play an important role in what we consider beautiful. And there is something mathematically striking about it: Objects with the most symmetry also frequently have the least amount of energy, or length, or area, or volume, etc. The laws of Nature herself seem to be expressible in terms of minimal principles, or some closely related optimality principles.
After an introductory lecture or two by myself, students (perhaps in teams of two) will present seminar lectures on a selection of topics picked from the wonderful textbook "The parsimonious universe" by Hildebrandt and Tromba, and also from literature available online about some problems (especially the 7th problem), from the list of math problems for the 21st century posed by Fields Medallist Steve Smale.
Admission to the course is by application. Please complete the online application form .