Edinburgh

20-24 April 2026

K-Stability and Equivariant Birational Geometry

Organisers: Ivan Cheltsov and Robert Śmiech.

Venue: MacLaren Stuart Room, Old College, University of Edinburgh

Registration: the registration is now closed. If you still would like to participate, contact Robert Śmiech.

Timetable: the precise timetable will be published later, but we begin on Monday morning and have a full day of talks on Friday.

ATTENTION: we would like to warn you against scamming attempts that often target conferences with public speaker/participant list. Do not trust and do not answer to any correspondence that claims to be related to our event that does not come from the official (i.e. associated to the University of Edinburgh) e-mail addresses of the organizers.

Speakers

Hamid Abban
Paolo Cascini
Livia Campo
Thibaut Delcroix
Elena Denisova
Ruadhaí Dervan
Kristin DeVleming
Alexander Duncan
Maksym Fedorchuk
Andreas Höring
Dasol Jeong
Anne-Sophie Kaloghiros
Ludmil Katzarkov
Frédéric Mangolte
Jesús Martínez-García
Antoine Pinardin
Piotr Pokora
Eleonora Romano
Luis Solá Conde
Julia Schneider
Yuri Tschinkel
Jarosław Wiśniewski
Egor Yasinsky
Susanna Zimmermann

Abstracts

Hamid Abban

TBA

Paolo Cascini

TBA

Livia Campo

TBA

Thibaut Delcroix

TBA

Elena Denisova

TBA

Ruadhaí Dervan

TBA

Kristin DeVleming

TBA

Alexander Duncan

Title: Amitsur Subgroups in Arithmetic and Equivariant Geometry

Abstract: For a variety defined over a field, a line bundle over the algebraic closure may fail to descend to a line bundle on the original variety. Similarly, if there is a group action, that action may fail to lift to certain line bundles. The Amitsur subgroup precisely measures this failure, taking values in the Brauer group of the field (or in an equivariant analog). A key property of the Amitsur subgroup is that it is an (equivariant) birational invariant. When all overfields and subgroups are considered, it is fine enough to completely distinguish between varieties in several interesting classes. I will discuss how the language of Mackey functors can be used to describe and compute the Amitsur subgroup, especially in the cases of Fano varieties, toric varieties, and torsors of tori.

Maksym Fedorchuk

TBA

Andreas Höring

Title: Intersection of two quadrics: modular interpretation and Hitchin morphism

Abstract: Let X be a smooth complete intersection of two quadrics in a projective space. The manifold X does not have any non-zero vector fields, but in earlier work with Beauville, Etesse, Liu and Voisin we showed that the symmetric tensors of the tangent bundle define a Lagrangian fibration on the total space of the cotangent bundle. By a result of Ramanan the complete intersection also has a modular interpretation, i.e. is isomorphic to a moduli space of “Spin bundles”. This allows to define a Hitchin morphism on the total space of the cotangent bundle. I will present all these constructions and show that the two fibrations coincide. This is joint work with Vladimiro Benedetti and Jie Liu.

Dasol Jeong

Title: Conical Kähler-Einstein metrics on K-unstable del Pezzo surfaces

Abstract: For a Fano manifold X, the greatest Ricci lower bound R(X), arising from the continuity method, plays a key role for the study of Kähler-Einstein metrics. In particular, the existence of Kähler-Einstein metric implies that R(X)=1.

On the other hand, Yau-Tian-Donaldson conjecture was solved using Kähler-Einstein metric with singularities along (pluri)anticanonical divisor D. Motivated by the formal similarity between the equations arising in the continuity method and those defining conical Kähler–Einstein metrics, Donaldson conjectured that R(X) coincides with the supremum R(X,D) of cone angles along anticanonical divisors D on X.

However, Székelyhidi provided counterexamples in the surface cases. Note that there are only two K-unstable smooth del Pezzo surfaces S_1 and S_2, that are blowups of P^2 at one point and two points, respectively.

In this talk, I will briefly review the history and introduce several tools such as K-stability and delta invariants. Then, I will explain how to find R(S_i,C_i) for i=1,2 using delta invariant, where C_i are smooth anticanonical curves on S_i.

Anne-Sophie Kaloghiros

TBA

Ludmil Katzarkov

TBA

Frédéric Mangolte

TBA

Jesus Martinez-Garcia

TBA

Antoine Pinardin

Title : Finite simple subgroups of the real Cremona group of rank three.

Abstract : In a joint work with Ivan Cheltsov and Yuri Prokhorov, we prove that the only non cyclic finite subgroups of Cr(3,R) are A5 and A6.

Piotr Pokora

Title: Geometry of lines on smooth quartic surfaces

Abstract: We study the geometry of arrangements of rational curves on smooth quartic surfaces over the complex numbers, using methods from logarithmic geometry. In particular, we investigate pairs of the form (smooth quartic surface, arrangement of lines) and analyze their Chern slopes. Our results show that the highest Chern slope currently known for such pairs is achieved by the Fermat quartic surface.

Eleonora Romano

Title: K-polystability of Fano 4-folds with large Lefschetz defect

Abstract: We investigate the K-polystability of smooth complex Fano 4-folds with Lefschetz defect at least 2, with particular emphasis on the cases of Lefschetz defect 3 and on Casagrande–Druel Fano 4-folds with Lefschetz defect 2. After recalling the classification of Fano 4-folds with Lefschetz defect 3, we show that exactly five of the corresponding deformation families are K-polystable. We then discuss K-polystability within the class of Casagrande–Druel Fano 4-folds with Lefschetz defect 2, where K-polystability occurs only in very few cases. The results presented in this talk are joint work with S. A. Secci.

Luis Solá Conde

Title: Chow quotients of flag varieties

Abstract: In this talk I will present a construction of the Chow quotient of the complete flag variety of C^4 by the action of a maximal torus in its automorphism group, and its birational properties. We will also discuss how to extend this construction to other rational homogeneous spaces.

Julia Schneider

Title: Atomic semi-orthogonal decompositions for derived categories of G-surfaces.

Abstract: In this talk, I discuss a joint work with Alexey Elagin and Evgeny Shinder that lies at the intersection of birational and derived geometry. What kind of geometric information is encoded in the derived category of a variety, and how does this information behave under birational maps? We consider the case of surfaces equipped with a group action, and show that their derived categories admit a canonical (mutation-equivalence class of) semi-orthogonaldecompositionthat “behaves well” with respect to birational geometry. We call such decompositions “atomic”. If time permits, I will discuss applications to (bi-)rationality questions.

Yuri Tschinkel

Title: Equivariant birational geometry

Abstract: I will discuss some new results and constructions in equivariant birational geometry.

Jarosław Wiśniewski

Title: Graphs with translations and compasses, upgrading torus action.

Abstract: Given an algebraic torus action on a smooth projective variety
with a finite number of fixed points and 1-dimensional orbits we describe
it in terms of a GKM graph (GKM=Goresky-Kottwitz-MacPherson) with extra
features. There are natural questions about recovering the geometry of the
variety in question from the graph of the torus action. For example: is
the variety toric and the torus action is a downgrading of the big torus
action? I will report on the joint work with Maria Donten-Bury.

Egor Yasinsky

TBA

Susanna Zimmermann

TBA