AGMP seminar 2022-23

A tasting menu in non-reductive GIT

Thursday 20 October 2022

Speaker: Josh Jackson (Sheffield)
Location: J11
Time: 2.00pm

Abstract: Non-reductive GIT is a new generalisation of Mumford's classical GIT, that allows quotienting algebraic varieties by actions of non-reductive groups. I will explain how it works, and indicate the range of applications it has seen so far.

Curve counting on surfaces and topological strings

Thursday 3 November 2022

Speaker: Andrea Brini (Sheffield)
Location: J11
Time: 2.00pm

Abstract: I will describe some correspondences relating different types of enumerative invariants associated to a pair (X,D), with X a complex projective surface and D a singular anticanonical divisor in it. These include the log Gromov-Witten invariants of the pair, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi--Yau threefolds, the Donaldson-Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar-Vafa-type invariants. A lot of my personal motivation to believe in the correspondences comes from dualities in physics, but the talk won't require any knowledge of string theory, and nobody will get hurt as a result. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants. Based on past&present work with Bousseau, van Garrel, Nabijou, and our very own Yannik.

Stability conditions with massless objects

Thursday 10 November 2022

Speaker: Jon Woolf (Liverpool)
Location: J11
Time: 2.00pm

Abstract: The Bridgeland stability space of a triangulated category is a non-compact complex manifold with a wall-and-chamber structure capturing interesting aspects of the category’s structure. I will describe joint work with Broomhead, Pauksztello and Ploog in which we partially compactify the stability space by allowing `degenerate’ stability conditions with massless objects. One reason this is interesting is that the added boundary points are closely related to the walls. I will illustrate this connection in low-dimensional examples arising from quivers with two vertices.

The logarithmic Hilbert scheme

Thursday 17 November 2022

Speaker: Patrick Kennedy-Hunt (Cambridge)
Location: J11
Time: 2.00pm

Abstract: The Hilbert scheme of a projective variety X is the moduli space of closed subschemes of X. In this talk we will discuss a version of the Hilbert scheme for a pair (X,D) with D a (reasonable) divisor on X. This logarithmic Hilbert scheme is a special case of the logarithmic Quot scheme. As motivation, note hard algebraic geometry problems can be studied by degenerating to simpler situations. Logarithmic geometry provides a suite of tools to study such degenerations. For example, these techniques have been applied to study (logarithmic) GromovWitten theory and more recently (logarithmic) Donaldson-Thomas theory. The logarithmic Hilbert scheme of curves on a threefold is the moduli space studied in logarithmic Donaldson-Thomas theory. A long-term hope is to study other moduli spaces of coherent sheaves with techniques from logarithmic geometry.

**** Cancelled ****

Thursday 24 November 2022

Speaker: Omar Kidwai (Birmingham)
Location: J11
Time: 2.00pm

Abstract: ...

TBA

Thursday 1 December 2022

Speaker: Rob Silversmith (Warwick)
Location: J11
Time: 2.00pm

Abstract: ...

TBA

Thursday 12 January 2023

Speaker: Misha Feigin (Glasgow)
Location: J11
Time: 2.00pm

Abstract: ...

TBA

Thursday 19 January 2023

Speaker: Omar Kidwai (Birmingham)
Location: J11
Time: 2.00pm

Abstract: ...