Soft materials are ubiquitous in biology and are ideal candidates for advanced engineering applications including soft, biomimetic robots, self-building machines, shape-shifters, artificial muscles, and chemical delivery packages. In many of these, the material must make a dramatic change in shape with an accompanying re-ordering of the material; in others changes in the ordering can be used to drive or even interrupt shape change. To optimize the materials and structures, it is necessary to have a detailed understanding of how the microstructure and macroscopic shape co-evolve. In this talk, I will present my group's mathematical modelling work on shape shifting in emulsions, liquid crystals and other soft materials. To develop the description, we draw upon differential geometry, topology, optimization theory and computer simulations. I will also describe a second research direction: Elucidating the climate for LGBTQ+ people in Physics & Astronomy, and present ideas and opportunities for the Applied Math community to better support queer people.