Florica Cirstea School of Mathematics & Statistics, University of Sydney Semilinear elliptic equations with isolated singularities Wednesday 3rd September 14:05-14:55pm, Eastern Avenue Lecture Theatre. We consider semilinear elliptic equations in a punctured domain and give a complete classification of isolated singularities of positive solutions when the nonlinearity is regularly varying at infinity with index greater than 1. We extend an important result of Veron (1981, 1986) (also proved by Brezis and Oswald in 1987) for the power case, whose study was motivated by the understanding of some physical phenomena (in connection with Thomas--Fermi theory). It remained an open question whether this type of result is valid in a more general framework. The difficulties of this problem required the development of new techniques, which we provide using Karamata's theory of regular variation. Our approach offers a third alternative proof in the literature even in the special power case treated by Veron. (This is joint work with Y. Du from UNE)