Vortex dynamics is at the heart of many unresolved problems in fluid mechanics and is also central to numerous applications in science and engineering. The goal of the proposed meeting is to survey the recent progress in this field focusing on applied mathematics aspects of both classical and emerging problems. We are planning to bring together about 40 researchers at different career stages working on various aspects of vortex dynamics, spanning applied mathematical analysis, scientific computing, physical modeling as well as scientific and engineering applications. A highlight of the workshop will be events designed to foster cross-fertilization between applied mathematics and different application areas.