This conference is dedicated to Jürgen Jost on the occasion of his 65th birthday. His influential work ranges from countless scientific contributions to the creation of a culture of interdisciplinary thinking in which concepts and abstract mathematical structures are identified as the core instrument for integrating knowledge across scientific disciplines. Over the years, Jürgen Jost has shaped a new kind of interdisciplinary science, with mathematics at its heart, and deeply influenced future generations of scientists. The conference brings together experts working with mathematical concepts in a broad spectrum of fields, comprising contributions from friends, former students and colleagues.