A biomembrane is a selectively permeable layer that defines an enclosed region within or around a cell. These layers are heterogeneous assemblies of lipids, proteins, and various other small molecules all of which are held together by noncovalent bonds. Cell function is strongly influenced by the distribution of membrane constituents. For instance, collections of lipids known as rafts and ranging in size from 10-500 nm are thought to serve as platforms for signaling, trafficking, and material transport across the membrane. Such processes are inferred to be closely related to the expression of disease. Membrane shape is also known to be important. Geometry is generally coupled tightly with chemistry and, in particular, the distribution of constituents. Coupling to interior and exterior flows can also be crucial.

During the 1970s, the study of the variety of membrane shapes attainable in equilibrium was initiated in the biophysics community. Activity in this and related areas has grown rapidly over the intervening decades. The study of the shape and evolution of cell membranes provides a broad spectrum of challenging mathematical problems. Over the past several years there has been an increased interest in this topic among geometers, analysts, and numericists.

The purpose of this proposed workshop is to:
(1) bring together members of the various relevant mathematical subcommunities to gives tutorial lectures for graduate students, postdoctoral researchers, and junior faculty members,
(2) report on recent progress,
(3) engage in discussions with the goal of developing a comprehensive understanding of the most relevant questions and challenges and formulating approaches to making further advances.

Key words
Multiscale methods; nucleation; budding; fission; phase stability; curvature.