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Next Meeting

University of Warwick - 20th February 2025

The next meeting of the COW will take place at the University of Warwick on Thursday 20th February 2025. The meeting will begin at 2pm. All talks will be held in room D1.07 in the Zeeman Building.

Speakers:

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
2:00pm Karim Adiprasito Semigroup algebras, character rings and Parseval-Rayleigh identities
4:00pm Naoki Koseki Degree two Gopakumar-Vafa invariants of local curves
5:00pm Anya Nordskova Bondal-Polishchuk’s conjecture for Fano threefolds of Picard rank one

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 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

Karim Adiprasito (Jussieu) - Semigroup algebras, character rings and Parseval-Rayleigh identities
I will present some recent new developments in the study of semigroup algebras of lattice polytopes. In particular, we will show that their canonical modules satisfy a curious identity that seems to be reminiscent of Parseval-Rayleigh identities, and give new insights of why this is true. We furthermore introduce the character ring of a lattice polytope, and connect the previous research to classical Hodge Theory and intermediate Jacobians. The talk will attempt to be very basic, and we will apply all this to resolve several classical problems in combinatorics. Ongoing joint work with Vasiliki Petrotou and Stavros Papadakis.
Naoki Koseki (Liverpool) - Degree two Gopakumar-Vafa invariants of local curves
Gopakumar-Vafa (GV) invariants for a Calabi-Yau 3-fold (CY3) were originally introduced by physicists in the 1990s. GV invariants are conjecturally equivalent to other curve counting invariants such as Gromov-Witten invariants (GV=GW conjecture). I will present an approach to determine the GV invariants for the so-called local curves, and provide some evidence to the GV=GW conjecture. This talk is based on a joint work with Ben Davison and another work with Tasuki Kinjo.
Anya Nordskova (Hasselt) - Bondal-Polishchuk’s conjecture for Fano threefolds of Picard rank one
In 1993, Bondal and Polishchuk conjectured that the braid group action on the set of full exceptional collections in a triangulated category is always transitive. In this general form the conjecture has been disproved just recently by Chang, Haiden and Schroll. However, if one restricts to derived categories of smooth projective varieties, the question is still widely open. I will sketch the proof of Bondal-Polishchuk’s conjecture for threefolds admitting a full exceptional collection of length 4 (in particular, the projective space P3). This is the first 3-dimensional case where the transitivity has been verified. Our proof employs a detailed analysis of the group generated by spherical twists on an anticanonical divisor, which we believe to be of independent interest. The talk is based on joint work with Michel Van den Bergh.

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This page is maintained by Alan Thompson and was last updated on 03/02/25. Please email comments and corrections to A.M.Thompson (at) lboro.ac.uk.