Next Meeting
University of Birmingham - Thursday 15th May
The next meeting of the COW will take place at the University of Birmingham on Thursday 15th May 2025. The meeting will start at 1pm and finish at 5pm. All talks will be held in Watson A, on the ground floor of the Watson Building. A campus map is below; the Watson Building is R15 on this map.
Speakers:- Veronica Arena (Cambridge)
- Andrea Brini (Sheffield)
- Chunyi Li (Warwick)
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 | Veronica Arena | The Chow ring of weighted blow-ups |
| 2:30pm | Chunyi Li | On a real reduction of the Bridgeland stability manifold |
| 4:00pm | Andrea Brini | Refined Gromov-Witten invariants |
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
- Veronica Arena (Cambridge) - The Chow ring of weighted blow-ups
- I'll start with a short overview of some classical results for blow-ups. When looking at the case of weighted blow-ups, some caution is needed as we take the weights into account. After introducing weighted blow-ups, I will give a presentation for the Chow ring of one. I will then obtain the integral Chow ring of the moduli space of genus 1 curves with two marked points.
- Chunyi Li (Warwick) - On a real reduction of the Bridgeland stability manifold
-
For a smooth projective surface X, the set of all Bridgeland stability conditions on Db(X) forms a complex manifold Stab(X). Fixing a character v, one can study how the moduli space Mσ(v) varies as the stability condition \sigma varies in Stab(X), yielding meaningful insights and results.
When X is three-dimensional, characterizing the chamber structure of Mσ(v) becomes highly nontrivial. One reason is the high dimensionality of Stab(X)—even after quotienting out redundant dimensions, it remains a complex two-dimensional space, and the chamber boundaries are defined by quadratic equations. In this talk, I will introduce an approach to real reduction of Stab(X), leading to a new real manifold StaR(X). The full chamber structure of Mσ(v) can then be described on the real two-dimensional space StaRv(X), with all boundaries given by linear subspaces. If time permits, I will also discuss some conjectures regarding the structure of StaR(X).
- Andrea Brini (Sheffield) - Refined Gromov-Witten invariants
- I will discuss a conjectural definition of refined curve counting invariants of Calabi-Yau threefolds with a C*-action in terms of stable maps on Calabi-Yau fivefolds. The corresponding disconnected generating function should conjecturally equate the Nekrasov-Okounkov K-theoretic membrane index under a refined version of the Gromov-Witten/Pandharipande-Thomas correspondence. I'll present several acid tests validating the conjecture, both in the A and the B-model. This is based on joint work with Yannik Schuler (ETH Zurich), arXiv:2410.00118.
This page is maintained by Alan Thompson and was last updated on 09/05/25. Please email comments and corrections to A.M.Thompson (at) lboro.ac.uk.