Research in the Baumgart group is largely centered on the physical chemistry of amphiphile membranes with lateral heterogeneity resulting from non-ideal mixing. Our aims include characterization of biologically relevant membranes including lipids and proteins, where we investigate both composition and shape (curvature) heterogeneity. Both of these aspects are thought to be highly relevant to the function of biological membranes. We focus on freely suspended, rather than solid supported membranes, with an emphasis on bilayer membranes, but we also include monolayer systems. We investigate membranes that laterally segregate into co-existing fluid phases, and are particularly interested in quantitatively understanding the phenomenon of line tension at the phase boundary. We also examine molecular details that govern the partitioning of functionally relevant protein constructs between coexisting membrane phases and thereby aim to contribute to enhancing the biophysical understanding of transmembrane signal transduction, particularly in immune cells such as T-cells, B-cells and mast cells. Our research on aspects of membrane shape is directed at understanding how molecules sort in membrane curvature gradients. This curvature sorting likely contributes substantially to intracellular membrane sorting and trafficking. Furthermore we have recently begun to investigate phase coexistence in binary mixtures of amphiphilic di-block copolymers. Finally, we develop methods to pattern cellular signaling ligands, such as antibodies and adhesion molecules, on pattern scales both above and below optical resolution.