This is a 6 year "EPSRC programme" grant that connects research in algebra and geometry happening in Edinburgh, Glasgow and Sheffield, led by Arend Bayer, Tom Bridgeland, Iain Gordon, Agata Smoktunowicz and Michael Wemyss, but involving many more people. We also have systematic connections to and opportunities with Kavli IMPU (Tokyo), Tsinghua University, the University of Toronto, and a US network in algebraic geometry. The success of this grant will therefore depend on building a large interconnected team. If you are interested in joining, please do feel free to contact us. Meanwhile, in the links above you can find more information about the grant, including opportunities to join as a post-doc or PhD student.