The LMS Research School AGGITatE 2024 will take place at the University of Essex 22-26th July 2024 and focus on Moduli Theory in Algebraic Geometry. The school is funded by the London Mathematical Society, Foundation Compositio Mathematica and the School of Mathematics, Statistics and Actuarial Science of the University of Essex and organised in partnership with the Clay Mathematics Institute. AGGITatE is an annual workshop taking place at the University of Essex. Its aim is to bring together researchers working in algebraic geometry and algebraic groups. It has run in 2022 and 2023.
| LectureR | INSTITUTION | TOPIC |
|---|---|---|
| Kristin DeVleming | UMass Amherst | Wall crossings for moduli spaces of varieties |
| Victoria Hoskins | Radboud University Nijmegen | Non-reductive Geometric Invariant Theory |
| Chenyang Xu | Princeton University | K-moduli of Fano Varieties |
| Jarod Alper | University of Washington | Geometric Invariant Theory and good moduli spaces |
The lecture courses will be further supported by Eloise Hamilton (Cambridge), Liana Heuberger (Bath) and Chuyu Zhou (Yonsei University).
Organisers
- Anne Sophie Kaloghiros (Brunel)
- Jesús Martínez-García (Essex)
- Alastair Litterick (Essex, local organiser)
Please, write to *aggitate2024 (AT) gmail (DOT) com* for any queries.
Schedule
All lectures taking place in NTC 3.05 with tea and coffee being served in breaks in NTC 3.06
| TIME | Monday |
|---|---|
| 9.00-9.30 | Registration |
| 9.30-11.00 | Xu I |
| 11.00-11.30 | Break |
| 11.30-12.30 | Alper I |
| 12.30-2.00 | Lunch |
| 2.00-3.00 | Hoskins I |
| 3.00-3.30 | Break |
| 3.30-5.00 | Xu’s problem session (led by Zhou) |
| 5.00-6.00 | Welcome reception (Start 5.30, STEM 3.1) |
| TIME | Tuesday | wednesday | Thursday |
|---|---|---|---|
| 10-11.30 | DeVleming I | Hoskins III | DeVleming II |
| 11.30-12.00 | Break | Break | Break |
| 12.00-13.00 | Hoskins II | Xu II | Alper III |
| 13.00-14.30 | Lunch | Lunch | Lunch |
| 14.30-15.30 | Alper II | Free afternoon (see activities) | Xu III |
| 15.30-16.00 | Break | Break | |
| 16.00-17.30 | Hoskins’s problem session (led by Hamilton) | DeVleming’s problem session (led by Heubeger) | |
| 17.30-18.30 | Poster Session (STEM 3.1) |
| TIME | Friday |
|---|---|
| 9.00-10.30 | Hoskins IV |
| 10.30-11.00 | Break |
| 11.00-12.00 | DeVleming III |
| 12.00-1.00 | Lunch |
| 1.00-2.00 | Xu IV |
| 2.00-3.00 | DeVleming IV |
Logistics
Arrival date is Sunday 21st July. The School will start on Monday 22nd July in the morning and finish just before lunch on Friday 26th July. Everyone who is not a local participant and has not already been told otherwise will be staying at Rowhedge Court (part of South Courts) on an ensuite single room. Check-in time is from 14:00 on Sunday and check-out time is at 9:00 on Friday. In order to access the court, you should first collect your welcome pack (including keys) from Art Exchange (between 14:00 and 21:45). If you arrive after 21:45 on Sunday, you can collect your keys from the UoE Security Office in Square 3 (Telephone: +44 (0)1206 872125). As part of your Welcome Pack you will receive lunch and dinner card (don’t lose it!).
Accommodation: unless otherwise told so, participants are staying at Alresford Court, which is part of South Courts. You will receive information by e-mail on how to get access to it on Sunday evening. Speakers are staying at Wivenhoe House Hotel. All Monday-Friday meals are included. You will be given vouchers that you can exchange on certain campus venues.
Transportation: Essex is in Colchester. There is some info on how to get to campus. If you use buses, please be aware they can be unreliable, so leave extra time when using them. Find here a map of the university of Essex.
Travel: If you have not yet bought your tickets, we advise you to do so ASAP. Please, consult the university’s website on how to reach Colchester Campus. The closest railway station is Colchester Hythe, but Colchester North (AKA as Colchester, which is different from Colchester Town) is the one with the best connections. The closest airport is Stansted and it is best connected to Colchester by bus. Travelling from Gatwick or Stansted by train is not too long (2-3 hours). The cost of a taxi within Colchester is usually £9. There are a number of companies (google ‘Colchester taxi’ for a list) that operate independently from each other and the best way to arrange a taxi is to call them directly. It is very difficult to book a taxi at around school ‘rush hour’ or early in the morning, unless arranged in advance.
Reception: we will have a reception on Monday evening, joint with the participants of the LMS Undergraduate Summer School, which is taking place at the University of Essex at the same time. It will take place in STEM 3.1 at 5.30pm.
Poster session and Barbeque: We are having a poster session on Thursday 5-6pm in STEM 3.1 (see below for posters presented). After that we will have a barbeque (with vegan options) in Silberrad Plaza, in front of Silberrad Student Centre, starting at around 6.30pm (TBC). Please, consider contributing a poster. It is a great way to practice presentation skills and make others aware of your research.
Wednesday afternoon: we will not have scheduled lectures. However, we have a couple of activities that you can take part on: a visit of Colchester (the oldest recorded town in the United Kingdom, founded by the Romans) or a Disc Golf game. The University of Essex is the home of the first Disc Golf course in England and the eighth oldest in the world. It has been recently redesigned.
Registration: The registration fee (£150 for PhD students, £250 for other participants) will cover accommodation and meals. Please indicate on the registration form if you wish to apply for support with this fee or with travel costs. Registration is now closed.
Titles and abstracts
- Speaker: Kristin DeVleming (UMass Amherst)
Title: Wall crossings for moduli spaces of varieties (course)
Abstract: In these lectures, I will introduce KSB(A) moduli spaces of varieties of (log) general type and K moduli spaces of Fano varieties. We will survey KSB(A) stability and K stability in abstraction and with explicit examples. Using moduli of pairs, we will also discuss wall-crossing (roughly: critical values where stability conditions change) and use the theory of wall crossing to study several applications.
Notes.
Problem sheet. - Speaker: Victoria Hoskins (Radboud University Nijmegen)
Title: Non-reductive Geometric invariant theory (course)
Abstract: Geometric Invariant Theory (GIT) is a method for constructing quotients
in algebraic geometry and is used to construct many moduli spaces. We will begin with a review GIT for reductive groups and outline some of the moduli spaces one can construct using reductive GIT. The heart of the course will focus on explaining a recent extension of this theory to non-reductive groups and describing applications to the construction of new moduli spaces, including moduli spaces of hypersurfaces in weighted projective spaces and moduli spaces of unstable objects.
Reference: https://www.math.ru.nl/~vhoskins/SurveyModuliGIT.pdf
Problem sheet. - Speaker: Chenyang Xu (Princeton University)
Title: K-moduli of Fano varieties (course)
Abstract: Moduli of varieties is a central topic in algebraic geometry. In the last decade, one of the most exciting stories in algebraic geometry is the observation that K-stability can be used to provide a robust moduli theory of Fano varieties, which are varieties with an ample first Chern class. Its construction uses a wide range of tools, from different subfields of algebraic geometry. In this mini-course, I will explain the notion of K-stability, sketch the construction of the K-moduli space, as well as prove its some fundamental properties.
Reference: https://web.math.princeton.edu/~chenyang/Kstabilitybook.pdf - Speaker: Jarod Alper (University of Washington)
Title: Geometric Invariant AG and good moduli spaces (plenary talks)
Abstract: Until the introduction of the theory of good moduli spaces by Alper, moduli problems were often studied separately with properties detected ad hoc for each problem. By studying local properties of Artin stacks, Alper gave a uniform approach to the study of moduli spaces, giving sufficient conditions for the existence of good moduli spaces from the study of étale charts and generalising Mumford’s geometric invariant theory. His work has been applied to the construction of the K-moduli of Fano varieties as well as to understand other moduli spaces.
Reference: https://sites.math.washington.edu/~jarod/moduli.pdf
Poster session
- James Jones (Loughborough University): “Type II Degenerations of K3 Surfaces”.
- Vicente Monreal (Pontificia Universidad Católica de Chile): “Classification of stable surfaces with T-singularities and small $K^2$”.
- Clemens Nollau (University of Tübingen): “Brill-Noether theory of spectral curves”.
- Vicenzo Reda (Trinity College Dublin): “Universal piecewise polynomiality for counting curves in toric surfaces”.
- Marc Truter (University of Warwick): “Classifying Fano 4-folds”.
On the AGGITatE series
The first AGGITatE conference was to take place in 2020 but was delayed to 2022 due to the CoViD panemic and, back then it stood for “Algebraic Groups and Geometric Invariant Theory at Essex” as a way to bring together researchers working in algebraic groups and algebraic geometry. The second AGGITatE took place in 2023, focused in algebraic groups and the Cremona group. Going forward AGGITatE will likely alternate between algebraic geometry and algebraic topics.
