Special Metrics and Group Actions in Geometry

This volume is a follow-up to the INdAM workshop “New perspectives in differen- tial geometry” that took place on 16–20 November 2015: https://newperspectivesindg.wordpress.com The editors are deeply grateful to the Istituto Nazionale di Alta Matematica “Francesco Severi” (INdAM) for generously sponsoring and hosting the event in Rome, and to the Institute’s President, Giorgio Patrizio, for his steadfast support. We are indebted to Diego Conti and Caterina Stoppato for the invaluable hard work in organising the workshop, and to Graziano Gentili and Andrew Swann for playing a key role on the scientific committee. We would also like to thank wholeheartedly the conference speakers: Ilka Agricola, Adrián Andrada, Vestislav Apostolov, John Armstrong, Fiammetta Battaglia, Roger Bielawski, Fran Burstall, Vicente Cortés, Johann Davidov, Paul Gauduchon, Marisa Fernández, Nigel Hitchin, Claude LeBrun, Thomas Madsen, Stefano Marchiafava, Vicente Muñoz, Paolo Piccinni, Uwe Semmelmann and Luis Ugarte. On the occasion of the workshop we celebrated the 60th birthday of Simon Salamon, a worldwide leading scholar at the forefront of research in differential geometry whose extensive body of work centres around Riemannian and com- plex manifolds defined with reference to the action of a Lie group. The unique contributions appearing in this book focus on a variety of cutting-edge topics revolving around Salamon’s interests: quaternionic and octonionic geometry, twistor spaces, almost-complex manifolds, harmonic maps, exceptional holonomy, Einstein metrics, spinors, homogeneous spaces and nilmanifolds, special geometries in dimensions 5, 6, 7 and 8, conformal geometry, moduli spaces, gauge theory, 4- manifolds, symplectic manifolds and integrable systems. Simon Salamon is Professor of Geometry at King’s College, London, and previously worked at Politecnico di Torino, Imperial College and Oxford University. The workshop was widely attended by his colleagues, friends and former students from all over the world, and this volume represents both a fitting tribute to a trailblazing force in the field and a compelling testimony to the profound and longstanding impact that Salamon has on the mathematical community. Heartfelt thanks go to the authors who accepted the invitation to publish here: Fiammetta Battaglia, Giovanni Bazzoni, Indranil Biswas, Fran Burstall, Vicente Cortés, Andrew Dancer, Johann Davidov, Malte Dyckmanns, Marisa Fernández, Paul Gauduchon, Claude LeBrun, Andrea Loi, Jason Lotay, Thomas Madsen, Andrei Moroianu, Vicente Muñoz, Antonio Otal, Paolo Piccinni, Simon Salamon, Stefan Suhr, Andrew Swann, Aleksy Tralle, Luis Ugarte, Raquel Villacampa, Dan Zaffran and Fabio Zuddas. We strongly believe these papers will be extremely relevant to the advancement of academic research and are certain they will serve generations to come.