Abstract: To function effectively, living cells compartmentalize myriad chemical reactions.  In the classic view, distinct functional volumes are separated by thin oily-barriers called membranes.  Recently, the spontaneous sorting of cellular components into membraneless liquid-like domains has been appreciated as an alternate route to compartmentalization.  I will review the essential physical concepts thought to underlie these biological phenomena, and outline some fundamental questions in soft matter physics that they inspire.  Then, I will focus on the coupling of phase separation to elastic stresses in polymer networks.   Using a series of experiments spanning living cells and synthetic materials, I will demonstrate that bulk mechanical stresses dramatically impact every stage in the life of a droplet, from nucleation and growth to ripening and dissolution.  These physical phenomena suggest new mechanisms that cells could exploit to regulate phase separation, and open new routes to the assembly of functional materials.  Bio: Eric Dufresne is the Professor of Soft and Living Materials at the Swiss Federal Institute of Technology in Zürich (ETH).  His research focuses on the physics of soft materials.  Current topics include interfacial properties, mechanics, and self-assembly in biological and synthetic systems.  Before moving to ETH in 2016, Eric was a graduate student at the University of Chicago, a post-doc at Harvard University, and a professor at Yale University.