As part of the R.W. Yeagy Colloquium Series, on Monday, April 10 at 2:30pm in Math Building 357, Lizzy Huang will speak on Harmonic Maps with Repulsive Potentials.
Abstract: Many questions in topology and physics can be expressed in terms of finding a function between a curved space (the domain) and another curved space (the target) which minimizes a natural energy functional: . Functions that minimize this energy are called harmonic maps. One method to obtain a harmonic map is to consider a family of maps which follow a path of ‘steepest descent’. In this talk, I will discuss a modification of this approach in which an unbounded potential energy is added to the total energy. Then I will discuss the behavior and singularities of the limiting maps in cases of special significance to topology. I will only assume knowledge of multivariable calculus and linear algebra for this talk.