# Seminars

We run a weekly Algebraic Geometry Seminar - details below.

On Wednesday at 2pm there is the **Pure maths Colloquium**, and on Monday at 3pm we organise a **learning seminar on K3 surfaces** (calendar, notes, Huybrechts's book).

Talks are usually in room J11.

For a complete list of seminars hosted at the School of Maths and Stats, look at This week's seminars and This semester's seminars.

# AG seminars (2019-20)

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__Francesco Sala__ (IPMU Tokyo)

Categorification of 2d cohomological Hall algebras

Tuesday 17th Sep, 14:00, J11
*Abstract:* Let M denote the moduli stack of either coherent sheaves on a smooth projective surface or Higgs sheaves on a smooth projective... curve X. The convolution algebra structure on the Borel-Moore homology of M is an instance of two-dimensional cohomological Hall algebras. These examples were defined by Kapranov-Vasserot and by Schiffmann and me, respectively. In the present talk, I will describe a full categorification of the cohomological Hall algebra of M. This is achieved by exhibiting a derived enhancement of M. Furthermore, this method applies also to several other moduli stacks, such as the moduli stack of vector bundles with flat connections on X and the moduli stack of finite-dimensional representations of the fundamental group of X. In the curve case, we call the corresponding categorified algebras the Betti, de Rham, and Dolbeaut categorified Hall algebras of the curve X, respectively. In the second part of the talk, I will discuss some relations between these categorified Hall algebras. This is based on a joint work with Mauro Porta.
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__Paul Johnson__ (Sheffield)

Partitions and Hilbert schemes of points

Tuesday 1st Oct, 12:00, J11
*Abstract:* This will be a gentle, expository talk explaining some connections between the two objects in the title. I will begin with... partitions: using the cores-and-quotients formula to motivate the statement of an enriched version of Euler's product formula for partitions, that was conjectured by Gusein-Zade, Luengo, and Melle-Hernández in 2009, and that I proved this summer with Jørgen Rennemo. Most of the talk will be giving the geometric context for this combinatorial formula, namely how Gusein-Zade, Luengo and Melle-Hernández came to discover it by studying Hilbert schemes of points on orbifolds, and how to use Chen-Ruan cohomology to generalise it and connect it to existing results on Hilbert schemes. I will vaguely gesture toward the proof in the last five minutes for the experts, but most of the talk should be accessible to the whole audience.
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__Dhruv Ranganathan__ (Cambridge)

A Mayer-Vietoris theorem for Gromov-Witten theory

Tuesday 8th Oct, 12:00, J11
*Abstract:* The Gromov-Witten theory of a smooth variety X is a collection of invariants, extracted from the topology of the space of ... curves in X. I will explain how the Gromov-Witten theory of X can be computed algorithmically from the components of a simple normal crossings degeneration of X. The combinatorics of the geometry and complexity of the algorithm are both controlled by tropical geometry. The formula bears a strong resemblance to the Mayer-Vietoris sequence in elementary topology, and I will try to give some indication of how deep this analogy runs. Part of this story is still work in progress, joint with Davesh Maulik.
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__Jenny August__ (MPIM Bonn)

The Stability Manifold of a Contraction Algebra

Tuesday 15th Oct, 12:00, J11
*Abstract:* For a finite dimensional algebra, Bridgeland stability conditions can be viewed as a continuous generalisation of tilting theory, providing... a geometric way to study the derived category. Describing this stability manifold is often very challenging but in this talk, I’ll look at a special class of symmetric algebras whose tilting theory is determined by a related hyperplane arrangement. This simple picture will then allow us to describe the stability manifold of such an algebra.
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Pierrick Bousseau (ETH)

Title: Quasimodular forms from Betti numbers

Thursday 17th Oct, 15:00, J11
*Abstract:* I will explain how to construct quasimodular forms starting from Betti numbers of moduli spaces of dimension 1 coherent sheaves on P2. This gives a proof of some stringy predictions about the refined topological string theory of local P2 in the Nekrasov-Shatashvili limit. Partly based on work in progress with Honglu Fan, Shuai Guo, and Longting Wu.

Tuesday 22nd Oct, 12:00, J11
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Noah Arbesfeld (Imperial College London)

Tuesday 29th Oct, 12:00, J11
Tuesday 5th Nov, 12:00, J11
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__Gwyn Bellamy__ (Glasgow)

Resolutions of symplectic quotient singularities

Tuesday 19th Nov, 12:00, J11
*Abstract:* In this talk I will explain how one can explicitly construct all crepant resolutions of the symplectic quotient... singularities associated to wreath product groups. The resolutions are all given by Nakajima quiver varieties. In order to prove that all resolutions are obtained this way, one needs to describe what happens to the geometry as one crosses the walls inside the GIT parameter space for these quiver varieties. This is based on joint work with Alistair Craw.
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Tuesday 26th Nov, 12:00, J11
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__Dimitri Wyss__ (École Polytechnique Fédérale de Lausanne)

Tuesday 3rd Dec, 12:00, J11
Tuesday 10th Dec, 12:00, J11
Tuesday 17th Dec, 12:00, J11
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