The algebraic geometry seminar in Term 1 2024/2025 will usually meet on Wednesdays at 3pm, though we may sometimes change to allow speakers from other time zones.

Each talk will be either in B3.02 or MB0.07 -- see specific information below.

Wednesday 23 October 2024, 3pm. Speaker: Will Donovan (Tsinghua University)

Title: Derived symmetries for crepant resolutions of hypersurfaces

Abstract: Given a singularity with a crepant resolution, a symmetry of the derived category of coherent sheaves on the resolution may often be constructed using the formalism of spherical functors. I will introduce this, and discuss work in progress on general constructions of such symmetries for hypersurface singularities. This builds on previous results with Segal, and is inspired by work of Bodzenta-Bondal.

Wednesday 30 October 2024. Speaker: -

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Wednesday 6 November 2024, 3pm. Speaker: Tarig Abdelgadir (Loughborough)

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Wednesday 13 November 2024. Speaker: Tiago Duarte Guerreiro (Paris-Saclay)

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Wednesday 20 November 2024. Speaker: -

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Wednesday 27 November 2024. Speaker: Elena Denisova (Edinburgh)

Title: Delta-invariants of Du Val del Pezzo surfaces

Abstract: It is known that a Fano variety with “mild” singularities admits a Kahler Einstein metric if and only if it is K-polystable. For two-dimensional Fano varieties (del Pezzo surfaces) Tian and Yau proved that a smooth del Pezzo surface is K-polystable if and only if it is not a blow up of P2 in one or two points. A lot of research was done for threefolds however, not everything is known and often the problem can be reduced to computing δ-invariant of (possibly singular) del Pezzo surfaces.

In my talk I will describe the status of the problem, present an example of computation of δ-invariant, show the example of application of this result for a singular Fano threefold and explain a possible direction for future research.

Wednesday 4 December 2024. Speaker: -

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