The meeting was attended by approximately 45 people, and the workshop similarly. The organisers were Dr Jan Grabowski, Professor Andrey Lazarev, Dr Paul Levy and Dr Mark MacDonald.
Participants were welcomed to Lancaster by the Pro-Vice Chancellor for Research, Professor Stephen Decent. The meeting was then formally opened by the LMS President, Professor Terry Lyons, who also invited members of the LMS who had not signed the Membership Book to do so. Three mathematicians took the opportunity to do so.
The first talk at the meeting was given by Dr Peter Neumann (University of Oxford), who spoke about the development of algebra in Britain over the 150 year period of the LMS's existence. He highlighted the various shifts in style and topics of interest over the period, especially the transition that occurred in the early years of the 20th century.
Next, Professor Ieke Moerdijk (Radboud University Nijmegen/University of Sheffield) spoke about the homotopical algebra of operads and trees. He explained how homotopical algebra has recently been enriched with an entirely new way of looking at operads, as realisations of combinatorial structures built up from trees, which is in many ways inspired by and analogous to the way in which one studies topological spaces as realisations of combinatorial simplicial complexes.
Lastly Dr Michael Batanin (Macquarie University) introduced the notion of polynomial monads, examples of which include nonsymmetric and symmetric operads, cyclic and modular operads, n-operads, dioperads, properads and many others. In particular, he explained why polynomial monads and their algebras have special categorical properties suitable for explicit combinatorial calculations.
The Regional Meeting ended with a dinner at the Gatehouse restaurant in Lancaster city centre, attended by many of those present.
The subsequent workshop had twenty talks, given by participants from many different areas of mathematics with relations to homotopical algebra. The talks were very diverse and the relaxed open atmosphere meant participants felt comfortable to ask questions of the speakers throughout. Further details of the talks and a list of participants may be found on the conference web pages.
A PhD student who attended the workshop commented that: “The conference was very well organised and enjoyable. This week has been a great opportunity to meet other students and academics interested in homotopical algebra and develop my knowledge of the subject. Lancaster University is a great campus and the atmosphere has been fantastic. Of particular interest to me was Muriel Livernet’s talk on Massey operadic products and non-formality of operads. My main focus since starting my PhD has been regarding A∞-algebras, a topic on which Muriel herself has written several papers. A highlight of my experience at the conference was the opportunity to meet Muriel and discuss my research project with her.”
A particular feature of the meeting and workshop was a Wikipedia editathon, run by Dr Mark MacDonald with help from volunteers from the Wikimedia Foundation. At the editathon, a mix of participants from the meeting and workshop were shown how to edit Wikipedia pages, with a particular focus on mathematical topics. In all, fourteen pages were created or improved during the two hours of the editathon, and several participants spoke of being enthused to continue to make further edits in the future.