Workshop: Homotopical algebra and geometry
Lead Research Organisation:
Lancaster University
Department Name: Mathematics and Statistics
Abstract
The proposal is for funding a week-long workshop `Homotopical algebra and geometry'. It will be held on April 6-10, 2015. Homotopical algebra was created in the 1960's in seminal works of Quillen, Grothendieck-Verdier and Dold-Puppe. Since then it has found innumerable applications in various fields of Pure Mathematics, most notably in algebraic topology and algebraic geometry.
In the last couple of decades the influence of homotopical algebra extended to representation theory, differential geometry and aspects of theoretical physics; its role and importance has been steadily increasing. The workshop aims to bring together a group of international experts using homotopical algebra in their research, foster new collaboration and contribute to developing the new generation of UK mathematicians.
The workshop will be held on Monday, Wednesday, Thursday and Friday. Morning plenary lectures will be delivered by top contemporary mathematicians from the UK and overseas. The afternoon sessions will consist of invited and contributed talks.
An important aspect of the workshop is the Northern Regional LMS meeting embedded into it. The LMS meeting will be commemorating the 150th anniversary of the London Mathematical Society and the talks will reflect this theme. Part of the funding for the workshop and the meeting comes from the LMS.
The meeting will be held on Tuesday afternoon. There will be three talks: one of the historical nature and the other two given by prominent mathematicians who helped shape our modern understanding of homotopical algebra and related fields.
Furthermore, it is planned to conduct a Wikipedia Editathon, a training event for prospective Wikipedia editors. Given the profound role played by Wikipedia in our world, this event will have an immediate and lasting impact on the UK and worldwide academic community and the society in general.
In the last couple of decades the influence of homotopical algebra extended to representation theory, differential geometry and aspects of theoretical physics; its role and importance has been steadily increasing. The workshop aims to bring together a group of international experts using homotopical algebra in their research, foster new collaboration and contribute to developing the new generation of UK mathematicians.
The workshop will be held on Monday, Wednesday, Thursday and Friday. Morning plenary lectures will be delivered by top contemporary mathematicians from the UK and overseas. The afternoon sessions will consist of invited and contributed talks.
An important aspect of the workshop is the Northern Regional LMS meeting embedded into it. The LMS meeting will be commemorating the 150th anniversary of the London Mathematical Society and the talks will reflect this theme. Part of the funding for the workshop and the meeting comes from the LMS.
The meeting will be held on Tuesday afternoon. There will be three talks: one of the historical nature and the other two given by prominent mathematicians who helped shape our modern understanding of homotopical algebra and related fields.
Furthermore, it is planned to conduct a Wikipedia Editathon, a training event for prospective Wikipedia editors. Given the profound role played by Wikipedia in our world, this event will have an immediate and lasting impact on the UK and worldwide academic community and the society in general.
Planned Impact
The present proposal seeks to bring together experts in various parts of Pure Mathematics for which homotopical algebra is relevant, explore possibilities for collaboration and disseminate newest results.
The impact will be achieved as a result of:
Interaction of experts in neighbouring fields.
Facilitating transfer of knowledge between leading international and UK experts.
Strengthening the UK-based research centres in the relevant fields.
Training PhD students in homotopical algebra and cognate areas.
In a different direction, impact will be achieved by making the mathematical community in the UK and worldwide more aware of the mission of the London Mathematical Society and its role it has played and continues to play in promoting intellectual pursuit and supporting individual scientists.
Finally, the impact of the Wikipedia editathon will be felt both inside the global mathematical community and in the society in general. Having a training session for a few dozen prospective Wikipedia editors answers a clear demand and will have an immediate and lasting effect.
The impact will be achieved as a result of:
Interaction of experts in neighbouring fields.
Facilitating transfer of knowledge between leading international and UK experts.
Strengthening the UK-based research centres in the relevant fields.
Training PhD students in homotopical algebra and cognate areas.
In a different direction, impact will be achieved by making the mathematical community in the UK and worldwide more aware of the mission of the London Mathematical Society and its role it has played and continues to play in promoting intellectual pursuit and supporting individual scientists.
Finally, the impact of the Wikipedia editathon will be felt both inside the global mathematical community and in the society in general. Having a training session for a few dozen prospective Wikipedia editors answers a clear demand and will have an immediate and lasting effect.
Organisations
| Description | The funding under this grant was awarded in order to carry out a workshop on homotopical algebra and geometry (co-funded by the LMS). The workshop was conducted on April 8 --11, 2015, preceded by a Northern Regional Meeting of the London Mathematical Society, and it was a success. The Meeting was attended by approximately 45 people, and the Workshop similarly. Here is a link to the relevant webpage http://www.lancaster.ac.uk/maths/homotopical/. The original application envisaged the event to be mathematically focused on derived categories and their applications. As preparations were underway, it was decided to shift the focus somewhat so as to make a contribution that is distinct from the programme on derived categories conducted in Warwick approximately at the same time. As a result, the subject matter of the workshop and the meeting was homotopical algebra and geometry (which, of course, includes derived categories but is broader). 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. Several mathematicians took the opportunity. 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 and highlighted the prominent role that the LMS played in that development. His talk was particularly relevant to the celebratory occasion. 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 Professor 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. Among the speakers were Wendy Lowen, Vic Snaith, Dominic Joyce, Bruno Vallette, and Andrew Baker. The talks were very diverse and the relaxed open atmosphere meant participants felt comfortable to ask questions of the speakers throughout. Several participants commented that the conference was very well organised and enjoyable. 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. |
| Exploitation Route | N/A |
| Sectors | Other |
| URL | https://www.lancaster.ac.uk/maths/homotopical/ |
| Description | 150th Anniversary LMS Northern Regional Meeting & Workshop |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | The 2015 Northern Regional Meeting of the London Mathematical Society was held at Lancaster University on Tuesday 7th April, followed by a workshop on Homotopical Algebra and Geometry (Wednesday 8th-Saturday 11th). The Meeting was attended by approximately 45 people, and the Workshop similarly. The talks were very diverse and the relaxed open atmosphere meant participants felt comfortable to ask questions of the speakers throughout. Several participants commented that the conference was very well organised and enjoyable. The event was funded by the LMS and EPSRC. 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. |
| Year(s) Of Engagement Activity | 2015 |
| URL | http://www.lancaster.ac.uk/maths/homotopical/ |