# Warwick Algebraic Geometry Seminar

The Warwick Algebraic Geometry Seminar will be taking place this term on Tuesday afternoons at 2pm in MS.05, unless otherwise stated. We also have a later slot available to us on Tuesdays at 4pm in B3.03, which we may make use of occasionally.

In addition to our own activities, we will also be arranging regular trips to various algebraic geometry activities running in the UK, including the COW seminar, the East Midlands Seminar in Geometry (EmSG), the London Geometry and Topology Seminar, the GLEN seminar, and the British Algebraic Geometry meeting (BrAG).

If you are interested in receiving announcements about upcoming seminars and other algebraic geometry activities at Warwick, you're welcome to join our mailing list. To do this, just send an email to Chunyi Li (c.li.25 (at) warwick (dot) ac (dot) uk) and ask to be added to the list.

Week | Date | Speaker | Title |

1 | 30th April | Martijn Kool | New directions in Vafa-Witten theory |

2 | Thu 9th May, 3pm in MS.03, joint with G&T Seminar | Weiwei Wu | Semi-toric spherical systems and symplectomorphism groups |

3 | 14th May | Yoav Len | Algebraic and tropical Prym varieties |

5 | 28th May | Clélia Pech | Quantum cohomology and mirror symmetry for odd symplectic Grassmannians |

7 | 11th June | Travis Mandel | Tropical multiplicities from mirror polyvector fields and tropical quantum field theory |

9 | 25th June | Christopher Lazda | A Neron-Ogg-Shafarevich criterion for K3 surfaces |

## Abstracts

**Martijn Kool (Utrecht) - New directions in Vafa-Witten theory**- In this talk I discuss (virtual) Euler characteristics of moduli spaces of stable sheaves on general type surfaces. These are part of so-called Vafa-Witten invariants, which were discovered in the context of supersymmetric Yang-Mills theory by Vafa-Witten in 1994 and mathematically defined by Tanaka-Thomas in 2017. The generating functions of these invariants have interesting modularity properties predicted by physics. Using virtual intersection theory, we can verify Vafa-Witten's original predictions in examples and generalize in several new directions. Joint work with Göttsche.
**Weiwei Wu (University of Georgia) - Semi-toric spherical systems and symplectomorphism groups**- We will explain a generalization of semi-toric systems. In dimension four, such systems can be easily obtained by generalizing the notion of "toric blow-up". As it turns out, this construction gains new understandings of the symplectic mapping class groups. We will explain its relation to a long-standing question between Lagrangian Dehn twists and symplectic mapping class groups of rational manifolds, and potential construction of exotic finite group actions. This talk is based on several on-going joint works with Liat Kessler, Jun Li and Tian-Jun Li.
**Yoav Len (Georgia Tech) - Algebraic and tropical Prym varieties**- My talk will revolve around combinatorial aspects of Abelian varieties. I will focus on Pryms, a class of Abelian varieties that occurs in the presence of double covers, and have deep connections with torsion points of Jacobians, bi-tangent lines of curves, and spin structures. I will explain how problems concerning Pryms may be reduced, via tropical geometry, to problems on metric graphs. As a consequence, we obtain new results concerning the geometry of special algebraic curves, and bounds on dimensions of certain Brill–Noether loci. This is joint work with Martin Ulirsch.
**Clélia Pech (Kent) - Quantum cohomology and mirror symmetry for odd symplectic Grassmannians**- Odd symplectic Grassmannians are two-orbit algebraic varieties which share a lot of common features with homogeneous varieties, and are one of the nicest examples of a wider family of objects called horospherical varieties. In this talk, I will explain some old and new results about them concerning their quantum cohomology, their derived category, and their mirrors. Part of this work is joint with R. Gonzales, N. Perrin and A. Samokhin.
**Travis Mandel (Edinburgh) - Tropical multiplicities from mirror polyvector fields and tropical quantum field theory**- I will explain a formula for the multiplicity of a genus 0 tropical curve in terms of certain iterated brackets of polyvector fields. This formula follows from a more general (arbitrary genus) formula given in terms of a certain tropical quantum field theory, i.e., a symmetric monoidal functor whose domain is the category of "tropical cobordisms." This is joint work with H. Ruddat.
**Christopher Lazda (Amsterdam) - A Neron-Ogg-Shafarevich criterion for K3 surfaces**- The naive analogue of the Néron-Ogg-Shafarevich criterion fails for K3 surfaces, that is, there exist K3 surfaces over Henselian, discretely valued fields K, with unramified etale cohomology groups, but which do not admit good reduction over K. Assuming potential semi-stable reduction, I will show how to correct this by proving that a K3 surface has good reduction if and only if is second cohomology is unramified, and the associated Galois representation over the residue field coincides with the second cohomology of a certain “canonical reduction” of X. This is joint work with B. Chiarellotto and C. Liedtke.

## Getting Here

Directions to the university may be found here. Once you're on campus, the Mathematics Institute is located in the Zeeman building; you can download a map of the campus here.

Please note that if you are arriving by public transport, the University of Warwick is not in fact in the town of Warwick, or indeed anywhere near it. Instead, it is located a short distance southwest of Coventry. If you are coming by train the closest stations are Coventry and Leamington Spa.

To get to campus from Coventry station, the fast option is the direct bus 12X, the slower option the buses 11, 11U; all three leave from stand ER3 at the bus hub outside the railway station. At the time of writing, a single ticket from Coventry station to the university costs £2.10 (contactless) or £2.20 (cash); a day ticket is £3.90 (contactless) or £4 (cash); an all day group ticket costs £8 (£5 after 6pm); please note that the buses from Coventry only accept exact change.

To get to campus from Leamington Spa station you should take bus U1, U2, or U17. Please note that these buses do not leave from directly outside the station; instead, the nearest bus stop is just around the corner on Victoria Terrace. A map of the route may be found here. At the time of writing, a single ticket from Leamington Spa station to the university costs £2.75.

This page is maintained by Michel van Garrel. Please email comments and corrections to michel (dot) van (hyphen) garrel (at) warwick (dot) ac (dot) uk.

Many thanks to Alan Thompson and Liana Heuberger for designing and updating this page and for allowing its carbon copy to appear here.