Xiaofeng Ren Department of Mathematics and Statistics, Utah State University The density functional theory of diblock copolymers Wednesday 28th, April 14:05-15:55pm, Carslaw Building Room 359. The type A and type B monomers in a diblock copolymer system often form A-rich and B-rich microdomains. On a larger scale these phase domains give rise to morphological phases. The most popular ones are the lamellar, the cylindrical and the spherical phases. The lamellar phase is best understood mathematically. For each K there exists a 1-D local minimizer with K+1 microdomains and K domain walls. Among these 1-D local minimizers there is the 1-D global minimizer that has optimal spacing between the domain walls. These 1-D local minimizers are extended trivially to three dimensions. Their stability in three dimensions are studied and their critical eigenvalues found. A 1-D local minimizer is stable in 3-D only if it has sufficiently many microdomains. The 1-D global minimizer is near the borderline of 3-D stability. This interesting phenomenon is related to the existence of wriggled lamellar patterns. Regarding the cylindrical and spherical phases we show the existence of ring solutions in two and three dimensions and analyze their stability. A connection between the diblock copolymer problem and the Cahn-Hilliard will be discussed.