The LMS Research School **AGGITatE 2024** will take place at the **University of Essex 22-26 ^{th} 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.

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 Jesus Martinez-Garcia (jesus.martinez-garcia (AT) essex.ac.uk) for any queries.

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.

**To apply to participate, please fill in the following form by 10th May.**

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.

## 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.**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.**Speaker:**Chenyang Xu (Princeton University)**Title:**K-moduli of Fano varieties (course)**Abstract:**TBA**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.

## 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.