Next Meeting
University of Liverpool - 2nd May 2024
Our next meeting is planned for Thursday 2nd May at the University of Liverpool. The meeting will start at 1pm and finish at 5pm. All talks will take place in room MATH-106, on the first floor of the Department of Mathematical Sciences building.
Speakers:- Barbara Fantechi (SISSA)
- Navid Nabijou (Queen Mary)
- Rob Silversmith (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 | Rob Silversmith | r-spin theory and tropical geometry |
| 2:30pm | Navid Nabijou | Logarithms, roots, and negative tangencies |
| 4:00pm | Barbara Fantechi | Moduli of zero dimensional coherent sheaves |
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
- Rob Silversmith (Warwick) - r-spin theory and tropical geometry
- String theory has had a significant influence on algebraic geometry since 1990, when Candelas-de la Ossa-Green-Parkes predicted certain enumerative invariants of quintic threefolds. One manifestation of this influence is that the intersection theory of moduli spaces of curves has a much richer and broader structure than had previously been suspected. I’ll focus on one so-called “model” introduced by Witten called r-spin theory — mathematically, this is simply a particular collection of intersection numbers on moduli spaces of curves whose collective combinatorial behavior is very orderly. I’ll discuss our progress in trying to study these r-spin numbers using tropical geometry, including a closed formula for the "genus-zero case”. Most of the talk will be joint work with Renzo Cavalieri and Tyler Kelly.
- Navid Nabijou (Queen Mary University of London) - Logarithms, roots, and negative tangencies
Logarithmic and orbifold structures provide two independent ways to model curves in a variety with tangency along a normal crossings divisor. The associated enumerative theories benefit from complementary techniques; this has motivated extensive interest in comparing the two approaches.
I will report on recent work establishing a complete comparison which, crucially, incorporates negative tangency orders. Negative tangency orders appear naturally in the boundary splitting formalisms of both theories. As such, our comparison opens the way for the wholesale importation of techniques from one side to the other. Contemporaneous work of Sam Johnston uses our comparison to give a new proof of the associativity of the Gross-Siebert intrinsic mirror ring.
Along the way, I will explain the pathological geometry of negative tangency mapping spaces, and how this can be described and controlled in concrete terms. A crucial part of our work is the discovery of a "refined virtual class" on the moduli space, which gives rise to a distinguished sector of punctured Gromov-Witten theory.
This is joint work with Luca Battistella and Dhruv Ranganathan.
- Barbara Fantechi (SISSA) - Moduli of zero dimensional coherent sheaves
- We define the stack of zero dimensional coherent sheaves on a quasi projective scheme X. Then we discuss its relationship with Quot schemes, and the definition and properties of the morphism to the symmetric product of X.
This page is maintained by Alan Thompson and was last updated on 26/04/24. Please email comments and corrections to A.M.Thompson (at) lboro.ac.uk.