Junior Algebraic geometry Warwick Seminar (JAWS)

Junior Algebraic geometry Warwick Seminar (JAWS) 2026-27

Seminar organisers: Shing Tak Lam, Chunkai Xu, Yaoqi Yang

Time: Thursdays 3-4pm

Location: D1.07 (Terms 1 and 2), MS04 (Term 3)

Term 1

Week 1 (October 8th) - Zac Su'a (Warwick)

Quantum cohomology and atoms

In recent work, Katzarkov–Kontsevich–Pantev–Yu introduced the theory of Hodge atoms, combining quantum cohomology and Hodge theory to construct new invariants in birational geometry. As a headline application, they proved that a very general cubic fourfold is irrational. In the year following, the theory has developed rapidly, with further applications to rationality problems and equivariant birational geometry. In this talk, I will give an introduction to this theory, motivated by rationality problems for cubic hypersurfaces but also by conjectural `canonical' semiorthogonal decompositions of the derived category of a smooth complex projective variety. I will then explain a simplified but more computable version of the theory and discuss some explicit computations for Fano varieties and blowups.

Week 2 (October 15th) - Noah Dizep (Heriot-Watt)

ADHM Bundles and counting surfaces in Calabi--Yau fourfolds

The recent seminal work "Foundations of surface counting in CY4" by Bae, Kool and Park establishes a Donaldson--Thomas type theory, counting surfaces in Calabi--Yau fourfolds. I will present joint work with Richard Szabo on computing a variant of surface counts on CY4s using Diaconescu's technology of ADHM Bundles on a toric, projective surface. The enumerative invariants we compute have a natural interpretation as the index of a topological theory, which we will discuss.

Week 3 (October 22nd)- Calum Crossley (UCL)

That time a Hirzebruch surface grew out of my umbrella

Starting from a way to visualize the homological algebra of a singularity, I will talk about how to relate noncommutative resolutions of singularities to certain partial compactifications of a variety with a function. Using this, basic birational geometry of rational surfaces leads to a family of noncommutative resolutions for a doubled Whitney umbrella singularity, with implications for what a minimal model theory for noncommutative resolutions can look like.

Week 4 (October 29th)- Robert Rogers (Sheffield)

Reduced Gromov-Witten Invariants

One of the defects of usual Gromov-Witten theory is the presence of degenerate maps that factor through curves of lower genus. Reduced Gromov-Witten invariants aim to take these contributions into account to construct a more enumerative theory but have only been constructed in some cases. In this talk we will explore some historical constructions of reduced invariants and describe some current work in progress joint with Cristina Manolache.

Week 5 (November 5th) - Heath Pearson (Nottingham)

Week 6 (November 12th) - Joseph Malbon (Imperial)

Week 7 (November 19th) - Roktim Mascharak (LSGNT)

Week 8 (November 26th) - Cat Rust (QMUL)

Week 9 (December 3rd) - Charalampos (Harry) Evangelatos (University of Southern Denmark)

Week 10 (December 10th)