Algebraic Geometry Seminar

The algebraic geometry seminar in Term 3 2025/2026 will usually meet on Wednesdays at 3 pm, though we may sometimes change to allow speakers from other time zones.

Most talks will be either in B3.02 or MB0.07 -- see specific information below.

A link to talks from the previous term is here.

Wednesday 29 Apr 2026, 3pm. Speaker: Luca Tasin (Università degli Studi di Milano Statale)

Title: Sasaki–Einstein metrics on spheres

Abstract: The geometry of spheres has long been a source of central problems in mathematics, and Sasaki–Einstein metrics—odd-dimensional analogues of Kähler–Einstein metrics—offer a particularly rich perspective. In joint work with Yuchen Liu and Taro Sano, we construct infinitely many Sasaki–Einstein metrics on odd-dimensional spheres that bound parallelizable manifolds, thereby confirming conjectures of Boyer–Galicki–Kollár and Collins–Székelyhidi. Our approach is based on establishing the K-stability of certain Fano weighted hypersurfaces.

Wednesday 13 May 2026, 3pm. Speaker: BU Chengjing (Oxford)

Title: Semiorthogonal decompositions for stacks

Abstract: I will report on a joint work with Tudor Pădurariu and Yukinobu Toda on a construction of semiorthogonal decompositions on derived categories of coherent sheaves on algebraic stacks. This can be seen as a categorification of a decomposition theorem for cohomology of stacks obtained in an earlier joint work, which is itself a categorification of
the theory of Donaldson–Thomas invariants. I will discuss its applications to categorification of quantum groups and to the Dolbeault geometric Langlands conjecture.

Wednesday 20 May 2026, 3pm. Speaker: Benjamin Sung (University of Southern Denmark)

Title: Stability Conditions on Generalized Complex Tori

Abstract: The theory of Bridgeland stability conditions assigns a complex manifold to the derived category of coherent sheaves on a smooth projective variety. The structure of this complex manifold is central for applications to algebraic geometry, but describing even a connected component is often a difficult, open problem. In this talk, I will give a proposal for the stability manifold of any non-commutative abelian variety in terms of an auxiliary generalized complex torus, extending a conjecture of Kontsevich. As applications, I will describe the stability manifold for many abelian threefolds, and I will complete the description of mirror symmetry for abelian varieties, after Golyshev-Lunts-Orlov. This is based on work in progress, joint with Fabian Haiden.

Wednesday 3 Jun 2026, 3pm. Speaker: Martin de Borbon (Loughborough)

Title: A Miyaoka-Yau inequality for hyperplane arrangements

Abstract: I will present joint work with Dmitri Panov on a version of the Miyaoka-Yau inequality for hyperplane arrangements in complex projective space which characterizes the equality case with the existence of certain differential geometric structures, specifically Dunkl connections and polyhedral Kahler metrics.

Wednesday 17 Jun 2026, 3pm. Speaker: Andrés Ibáñez Núñez (Columbia)

Title: Enumerative geometry of abstract moduli

Abstract: From a moduli stack X parametrizing objects in an abelian category, one gets associative algebras in various flavours – cohomological, motivic or K-theoretic, etcetera. These algebras, called Hall algebras, are fundamental in enumerative geometry, wall-crossing structures and geometric representation theory.

From a more general moduli stack X that does not come from an abelian category, say if X parametrizes G-bundles on a curve or varieties of some kind, one cannot expect to construct algebras out of it. I will explain that we can however obtain algebraic structures of a new kind, whose construction involves a deep analysis of mapping stacks into X from quotients of affine toric varieties by a torus, as well as the combinatorics of real hyperplane arrangements. These structures, called associative inductions, are rich enough to get a theory of enumerative geometry and wall-crossing of general stacks, that we call Intrinsic Donaldson-Thomas theory.

We will also discuss how cohomological Hall induction gives an explicit form of the decomposition theorem for the morphism from a stack to its good moduli space.

The talk will be aimed at a general audience and I will not assume expertise in stacks or enumerative geometry.

This is joint work over different projects with Chenjing Bu, Ben Davison, Daniel Halpern-Leistner, Tasuki Kinjo and Tudor Pădurariu.

Wednesday 17 Jun 2026, 4pm. MB0.07 Speaker: Xiaolei Zhao (University of California at Santa Barbara)

Title: Non-commutative abelian surfaces and Kummer type hyperkähler manifolds.

Abstract: Examples of non-commutative K3 surfaces arise from semiorthogonal decompositions of the bounded derived category of certain Fano varieties. The most interesting cases are those of cubic fourfolds and Gushel-Mukai varieties of even dimension. Using the deep theory of families of stability conditions, locally complete families of hyperkähler manifolds deformation equivalent to Hilbert schemes of points on a K3 surface have been constructed from moduli spaces of stable objects in these non-commutative K3 surfaces. On the other hand, an explicit description of a locally complete family of hyperkähler manifolds deformation equivalent to a generalized Kummer variety is not yet available.

In this talk we will construct non-commutative abelian surfaces as equivariant categories of the derived category of K3 surfaces which specialize to Kummer K3 surfaces. Then we will explain how to realize all hyperkähler manifolds of Kummer type as moduli spaces of stable objects on non-commutative abelian surfaces. Applications to algebraic cycles and abelian fourfolds of Weil type will be discussed.

This is joint work in preparation with Arend Bayer, Alex Perry and Laura Pertusi.

Wednesday 24 Jun 2026, 3pm. Speaker: Asher Auel (Dartmouth)

Title: Rationality in arithmetic families

Abstract: It has been known for a decade that rationality is not a deformation invariant in smooth families of complex fourfolds. The situation for arithmetic families, namely the relationship between the rationality of a variety defined over Q and of its reductions modulo primes p, is much less understood. In this talk, I'll discuss work in progress with Sarah Frei and Alena Pirutka on constructing fourfolds over Q that are not stably rational over the complex numbers but are rational modulo p for infinitely many primes p. Our construction involves Reid's list of “famous 95” K3 surfaces in weighted projective space as well as arithmetic work on reduction of Brauer classes.

Wednesday 1 Jul 2026, 3pm. Speaker:

Title:

Abstract: