Next Meeting
University of Bath - 14th November 2024
The next meeting of the COW will take place at the University of Bath on Thursday 14th November. The meeting will run from 2pm to 6pm. All talks will take place in room 4W1.2.
Speakers:- Matt Booth (Imperial)
- Kento Fujita (Osaka)
- Renata Picciotto (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 |
2:15pm | Renata Picciotto | Reduced Gromov-Witten invariants via desingularization of sheaves |
3:45pm | Kento Fujita | On the coupled Ding stability for log Fano pairs |
5:00pm | Matt Booth | Calabi-Yau structures and Koszul duality |
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
- Renata Picciotto (Cambridge) - Reduced Gromov-Witten invariants via desingularization of sheaves
- Gromov-Witten invariants are related to counts of curves in X of genus g and class d, but they often encode contributions from degenerate maps with reducible domains. For g<3, some constructions of reduced GW invariants (i.e. invariants capturing only smoothable stable maps) have been suggested, starting with the celebrated Vakil-Zinger desingularization in genus 1. We reframe the problem of defining reduced GW invariants in terms of desingularization of sheaves, then use some classical geometric constructions to define reduced invariants in all genera. This talk is based on arXiv:2310.06727, a work joint with A. Cobos-Rabano, E. Mann and C. Manolache
- Kento Fujita (Osaka) - On the coupled Ding stability for log Fano pairs
- In the last decade, there are significant progresses about the Calabi problem for Fano varieties. I will review a part of the history, and then I will explain its generalization to a coupled setting. This is a joint work with Yoshinori Hashimoto.
- Matt Booth (Imperial) - Calabi-Yau structures and Koszul duality
- Calabi-Yau dg algebras are the derived-noncommutative analogue of smooth Calabi-Yau varieties. I'll talk about a generalised notion of "nonsmooth CY structure" for dg (co)algebras, which for proper schemes specialises to "trivial dualising complex", and for commutative rings recovers Iyama-Reiten's notion of singular Calabi—Yau. I'll indicate why this generalised notion of Calabi—Yau is Koszul dual to a symmetric Frobenius condition. There is also an analogous one-sided version: Gorenstein (co)algebras are Koszul dual to Frobenius (co)algebras. This leads to a surprising example: the ring k[[x]] of formal power series, equipped with its natural topology, is a pseudocompact Frobenius algebra. As an application of the above theory, we obtain a new characterisation of Poincaré duality spaces. This is joint work with Joe Chuang and Andrey Lazarev, to appear on the ArXiv soon.
This page is maintained by Alan Thompson and was last updated on 01/11/24. Please email comments and corrections to A.M.Thompson (at) lboro.ac.uk.