The Euclidean Distance Degree of Fermat Hypersurfaces
  Finding the point in an algebraic variety that is closest to a given point is an optimization problem with many applications. We study the case when the variety is a Fermat hypersurface. Our formula for its Euclidean distance degree is a piecewise polynomial whose pieces are defined by subtle congruence conditons. 
Hwangrae Lee
math.AG math.OC