This project will consider spiky behavior of the least energy solution of a semilinear problem in pattern formation, classification of solutions of the conformal curvature equations, symmetry of positive solutions of semilinear elliptic equations, and stability of steady states for a class of semilinear heat equations. The problems to be addressed are state of the art mathematical questions motivated by problems in a wide range of scientific areas including differential geometry, developmental biology, and astronomy.
