Robert B. Kusner

Director of the Center

(This page is like a cathedral: always under reconstruction ;-)

Rob Kusner's Math299/550 at Penn

While on sabbatical at Penn in the fall of 2015, Rob is teaching a topics course (Math299/550) on Geometric Variational Problems (Research/Selections in Math) for advanced undergraduates and interested graduate students.

This course will focus on geometric variational problems such as: optimal configurations of points on spheres (think electrons or inimical dictators); the geometry of energy-minimizing knots and links (imagine tight ropes or charged wires); and minimal or constant mean curvature surfaces (analysis of soap films or bubbles). Student interaction through presentations and research projects will be a principal feature of the course.


Our class meets Monday & Wednesday 1:30-3PM in 3C2 DRL starting Wednesday 26 August - I'll be available for office hours immediately after class and on most Tuesday afternoons in 4N34 DRL until our informal geometry & topology seminar (usually minimal surfaces and mean curvature flow) begins (usually Tuesdays at 4:30) nearby (usually in 4N30).

Topics (in progress :-)

Mon 31 August Project 0: Platonic Polyhedra and Configurations on the Sphere
Wed 09 September Project 1: Energy Minimizing and Critical k-point Configurations
Mon 28 September Project 2: Uniqueness of Critical k-point Configurations on the Circle
Wed 14 October (updated Wed 4 November) Project 3: Topology of Configuration Spaces on the Circle and Sphere
Wed 11 November Project 4: Linking Number and Möbius Energy

Resources (in progress too :-)

Geometry of Curves and Surfaces by M. doCarmo
Vector Calculus by J. Marsden & A. Tromba
Morse Theory by J. Milnor
Topology from the Differentiable Viewpoint by J. Milnor (or the "expanded" version Differential Topology by V. Guillemin & Pollack for degree and linking number and more)
Henry Cohn's PCMI lecture 1 on sphere packing and universal optima
Henry Cohn's PCMI lecture 2
Henry Cohn's PCMI lecture 3
Henry Cohn's PCMI lecture 4
Cohn's paper with Kumar in JAMS
5-electrons by Rich Schwartz
10-or-more-electrons by David Wales's team
13-spheres by Musin & Tasarov
14-spheres by M & T in Exp Math
Harvey (not Henry!) Cohn's 1960 Monthly paper about electrons on the circle
papers by Ohara (Topology), Kim & Kusner [3.12](Exp. Math.), Freedman, He & Wang (Annals), Kusner & Sullivan [3.23](1993 Georgia Topology) in early 1990s on Möbius Energies for knots and links.


Kelsey Bacon
Sarah Dean
Jay Havaldar
Kevin Procopio
Robert Scheyder
Anirudh Singh

More (more details to follow soon :-)!

Please watch here for further developments.

Penn Address

        4N34 David Rittenhouse Laboratory
        Department of Mathematics
        University of Pennsylvania
        Philadelphia PA 19104

Penn Phone 215 898 5901

Email profkusner "at" gmail "dot" com

All material on this website is Copyleft* by Rob Kusner.

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