Next Meeting
University of Oxford - 24th October 2024
The next meeting of the COW will take place at the University of Oxford on Thursday 24th October. The meeting will run from 1pm to 5pm. All talks will take place in room L6 of the Andrew Wiles Building.
Speakers:- Will Donovan (Tsinghua)
- Klaus Hulek (Hannover)
- Ailsa Keating (Cambridge)
For those who do not wish to attend the meeting in-person, we also plan to broadcast talks live using Microsoft Teams. Information about how to join the Teams meeting will be circulated to the COW mailing list the day before the meeting. If you would like to join the COW mailing list, instructions on how to do so may be found on the mailing lists page. If you would like to attend the meeting remotely but do not want to join the mailing list, please send an email to Alan Thompson (A.M.Thompson (at) lboro.ac.uk) requesting the meeting information.
Schedule
| Time | Speaker | Title |
| 1:00pm | Klaus Hulek | Ball quotients and moduli spaces |
| 2:30pm | Ailsa Keating | Homological mirror symmetry for K3 surfaces |
| 4:00pm | Will Donovan | Derived symmetries for crepant resolutions of hypersurfaces |
Funding and Travel Claims
The COW has some funding to cover travel expenses for UK-based PhD students and postdocs. The COW is currently funded by the Heilbronn Institute for Mathematical Research under the UKRI/EPSRC Additional Funding Programme for Mathematical Sciences and the London Mathematical Society under a scheme 3 grant. To ensure that we can fund as many participants as possible, we ask that participants purchase "advance" or "off-peak" train tickets where practical, and non-travel expenses (e.g. accommodation, food) cannot be covered. For those under the age of 30, we also recommend looking into getting a railcard, which can offer substantial savings on the cost of train travel around the UK. Information about how to submit a claim is available on the COW homepage here.
Abstracts
- Klaus Hulek (Hannover) - Ball quotients and moduli spaces
- A number of moduli problem are, via Hodge theory, closely related to ball quotients. In this situation there is often a choice of possible compactifications such as the GIT compactification´and its Kirwan blow-up or the Baily-Borel compactification and the toroidal compactificatikon. The relationship between these compactifications is subtle and often geometrically interesting. In this talk I will discuss several cases, including cubic surfaces and threefolds and Deligne-Mostow varieties. This discussion links several areas such as birational geometry, moduli spaces of pointed curves, modular forms and derived geometry. This talk is based on joint work with S. Casalaina-Martin, S. Grushevsky, S. Kondo, R. Laza and Y. Maeda.
- Ailsa Keating (Cambridge) - Homological mirror symmetry for K3 surfaces
- Joint work with Paul Hacking (U Mass Amherst). We first explain how to prove homological mirror symmetry for a maximal normal crossing Calabi-Yau surface Y with split mixed Hodge structure. This includes the case when Y is a type III K3 surface, in which case this is used to prove a conjecture of Lekili-Ueda. We then explain how to build on this to prove an HMS statement for K3 surfaces. On the symplectic side, we have any K3 surface (X, ω) with ω integral Kaehler; on the algebraic side, we get a K3 surface Y with Picard rank 19. The talk will aim to be accessible to audience members with a wide range of mirror symmetric backgrounds.
- Will Donovan (Tsinghua) - Derived symmetries for crepant resolutions of hypersurfaces
- Given a singularity with a crepant resolution, a symmetry of the derived category of coherent sheaves on the resolution may often be constructed using the formalism of spherical functors. I will introduce this, and new work (arXiv:2409.19555) on general constructions of such symmetries for hypersurface singularities. This builds on previous results with Segal, and is inspired by work of Bodzenta-Bondal.
This page is maintained by Alan Thompson and was last updated on 10/10/24. Please email comments and corrections to A.M.Thompson (at) lboro.ac.uk.