This page contains abstracts from previous Calf seminars, listed alphabetically by speaker. Please contact one of the organisers if you spot any errors or dead links.
Mohammad Akhtar (Imperial College)
The contents of this talk are joint work with Tom Coates, Alexander Kasprzyk and Sergey Galkin.
Oliver E. Anderson (University of Liverpool)
Elizabeth Baldwin (University of Oxford)
Moduli of stable maps as a GIT quotient.
Federico Barbacovi (UCL)
SemiOrthogonal Decompositions, gluing, and spherical twists.
Marta Benozzo (University College London)
Gergely Berczi (University of Budapest)
Fabio Bernasconi (Imperial College)
Alberto Besana (University of Milan)
Valentin Boboc (University of Manchester)
Arkadij Bojko (University of Oxford)
Matt Booth (University of Edinburgh)
Pawel Borowka (University of Bath)
An easy exercise or an open problem?
Non-simple abelian varieties.
Nathan Broomhead (University of Bath)
The Dimer Model and Calabi-Yau Algebras.
Tim Browning (University of Oxford)
Jaroslaw Buczynski (University of Warsaw)
For more details see the preprint math.AG/0503528.
Vittoria Bussi (Oxford)
Paul Cadman (University of Warwick)
Livia Campo (University of Nottingham)
Francesca Carocci (Imperial College)
Gil Cavalcanti (University of Oxford)
Notes for this talk are available.
Examples of generalized complex structures.
Notes for this talk are available.
Andrew Chan (Warwick)
In this talk I shall introduce Gröbner bases and see the problems that arise when trying to adapt this theory to polynomial rings over fields with valuations. We shall discuss how these Gröbner bases are interesting to algebraic geometers and how they have important applications to tropical geometry.
Emily Cliff (Oxford)
Giulio Codogni (Cambridge)
Gaia Comaschi (Université des Sciences et Technologies de Lille 1)
Barrie Cooper (University of Bath)
An introduction to Derived Categories.
McKay Matrices, CFT Graphs, and Koszul Duality (Part I).
George Cooper (University of Oxford)
Stephen Coughlan (University of Warwick)
Alice Cuzzucoli (Warwick)
Dougal Davis (LSGNT)
Hannah Dell (University of Edinburgh)
Ruadhaí Dervan (Cambridge)
Carmelo Di Natale (Cambridge)
Will Donovan (Imperial College)
The McKay Correpsondence.
Bradley Doyle (UCL)
Vivien Easson (University of Oxford)
Notes for this talk are available.
Vladimir Eremichev (University of Warwick)
Erroxe Etxabarri Alberdi (University of Nottingham) Fano 3-folds with 1-dimentional K-moduli. We give a friendly introduction to K-stability, and the motivation behind it. We will see how to study and completely describe all one-dimensional components of the K-moduli of smooth Fano 3-folds. And we will finish giving some specific examples for family 3.12. This result is in collaboration with Abban, Cheltsov, Denisova, Kaloghiros, Jiao, Martinez-Garcia and Papazachariou.
Daniel Evans (University of Liverpool)
Andrea Fanelli (Imperial College London) Lifting Theorems in Birational Geometry. In this talk, I will try to convince you of how important lifting pluri-canonical sections is. Two main approaches can be used: the algebraic one, based on vanishing and injectivity theorems, and the analytic one, which relies on Ohsawa-Takegoshi type L^2-extension theorems. Bypassing as much as possible the birational mumbo jumbo, I will eventually discuss the Dlt Extension Conjecture proposed by Demailly, Hacon and Păun.
Enrico Fatighenti (University of Warwick) Hodge Theory via deformations of affine cones. Hodge Theory and Deformation Theory are known to be closely related: many example of this phenomenon occurs in the literature, such as the theory of Variation of Hodge Structure or the Griffiths Residues Calculus. In this talk we show in particular how part of the Hodge Theory of a smooth projective variety X with canonical bundle either ample, antiample or trivial can be reconstructed by looking at some specific graded component of the infinitesimal deformations module of its affine cone A. In an attempt of a global reconstruction theorem we then move to the study of the Derived deformations of the (punctured) affine cone, showing how to find amongst them the missing Hodge spaces.
Oscar Finegan (Cardiff University) Derived Intersection Products. The structure sheaf for an intersection of subschemes is given by taking the tensor product of the structure sheaves of the subschemes that you are intersecting. Derived algebraic geometry (more or less) says that if we replace all of our sheaves by complexes of sheaves, the derived structure complex of the intersection will be the derived tensor product of the original structure complexes. Morally speaking, this new complex "should" encode geometric information about the intersection, namely how badly and in which ways the intersection fails to be transverse, and the question is "What does this complex explicitly look like?" In this talk I will discuss some setup and existing results in this area, as well as my progress on the problem.
Aeran Fleming (University of Liverpool) Kähler packings of projective, complex manifolds. In this talk I will introduce the notion of Kähler packings and explore their connections to multipoint Seshadri constants and Nagata's conjecture. I will then briefly present a general strategy to explicitly construct Kähler packings on projective, complex manifolds and if time permits discuss some examples of blow ups of the complex projective plane.
Joel Fine (Imperial College London)
Peter Frenkel (Budapest University of Technology & Economics)
This talk is based on the preprint math.AT/0301159.
Tarig Abdel Gaidr (University of Glasgow)
Tim Grange (Loughborough)
Jacob Gross (Oxford)
Tiago Guerreiro (Loughborough University)
Giulia Gugiatti (LSGNT)
Pierre Guillot (University of Cambridge)
Eloïse Hamilton (University of Oxford)
Michael Hallam (University of Oxford)
Umar Hayat (University of Warwick)
Thomas Hawes (University of Oxford) GIT for non-reductive groups. Geometric invariant theory (GIT) is concerned with the question of constructing quotients of algebraic group actions within the category of varieties. This problem turns out to be sensitive to the kind of group being considered. When a reductive group G acts on a projective variety X, Mumford showed how to find an open subset X^s of X (depending on a linearisation of the action) that admits an honest orbit space variety X^s/G. Moreover, this admits a canonical compactification X//G, obtained by taking Proj of the finitely generated ring of invariant sections of the linearisation. This rather nice picture breaks down when the group G is not reductive, since there is the possibility of non-finitely generated rings of invariants. This talk will look at work being done to describe a similar Mumford-style picture for non-reductive group actions. After reviewing Mumford's result for reductive groups, we will look at the work done by Doran and Kirwan on GIT for unipotent group actions, which provide the key for formulating GIT for general algebraic groups. We will finish by looking at work in progress on how to extend the ideas of Doran and Kirwan to the case where the group is not unipotent.
David Holmes (University of Warwick)
Julian Holstein (University of Cambridge)
Vicky Hoskins (University of Oxford)
Daniel Hoyt (University of Cardiff)
Austin Hubbard (University of Bath) Hyperpolygon spaces and their crepant resolutions. Hyperpolygon spaces are algebraic symplectic varieties that arise in numerous contexts. We will discuss their construction as Nakajima quiver varieties and present results that describe the birational geometry of their crepant resolutions.
Anton Isopoussu (Cambridge) K-stability, convex cones and fibrations. Test configurations are a basic object in the study of canonical metrics and K-stability. We introduce two ideas into the theory. We extend the convex structure on the ample cone to the set of test configurations. The asymptotics of a filtration are described by a convex transform on the Okounkov body of a polarisation. We describe how these convex transforms change under a convex combination of test configurations. We also discuss the K-stability of varieties which have a natural projection to a base variety. Our construction appears to unify several known examples into a single framework where we can roughly classify degenerations of fibrations into three different types: degenerations of the cocycle, degenerations of the general fibre and degenerations of the base.
Shivang Jindal (University of Edinburgh)
Seung-Jo Jung (Warwick)
Anne-Sophie Kaloghiros (Cambridge)
Grzegorz Kapustka and Michal Kapustka (Jagiellonian University, Krakow)
Grzegorz Kapustka (Jagiellonian University, Krakow)
Michal Kapustka (Jagiellonian University, Krakow)
Alexander Kasprzyk (University of Bath)
Notes for the first talk are available.
Recognising toric Fano singularities.
What little I know about Fake Weighted Projective Space.
Jonathan Kirby (University of Oxford)
Weronika Krych (University of Warsaw)
Felix Küng (University of Liverpool)
Roberto Laface (Leibniz Universität Hannover) Decompositions of singular Abelian surfaces. Inspired by a work of Ma, in which he counts the number of decompositions of abelian surfaces by lattice-theoretical tools, we explicitly find all such decompositions in the case of singular abelian surfaces. This is done by computing the transcendental lattice of products of isogenous elliptic curves with complex multiplication, generalizing a technique of Shioda and Mitani, and by studying the action of a certain class group act on the factors of a given decomposition. Incidentally, our construction provides us with an alternative and simpler formula for the number of decompositions, which is obtained via an enumeration argument. Also, we give an application of this result to singular K3 surfaces.
Alyosha Latyntsev (University of Oxford)
In this talk, I will
Marco Lo Giudice (University of Bath, and University of Milan)
Introduction to schemes.
Detailed notes on scheme theory are available.
Artin level algebras.
Cormac Long (University of Southampton)
Andrew MacPherson (Imperial College London)
A non-archimedean analogue of the SYZ conjecture.
Joseph Malbon (University of Edinburgh)
Aimeric Malter (University of Birmingham)
Diletta Martinelli (Imperial College London)
Mirko Mauri (LSGNT)
Francesco Meazzini (Sapienza Università di Roma)
Caitlin McAuley (University of Sheffield)
Ciaran Meachan (University of Edinburgh)
Simen Moe (Imperial College London) Stable rationality of polytopes Stable rationality specializes in smooth families, as shown by Nicaise--Shinder. Using toric geometry to construct degenerations, Nicaise--Ottem provided new examples of stably irrational hypersurfaces in projective space, such as very general quartic fivefolds. Their strategy uses the motivic volume as a stable birational invariant. However, this requires controlling the stable birational type of the strata in the degeneration. This can be obtained, for example, if a stratum has a strong type of variation of stable birational type. In this context, I will describe a large class of hypersurfaces in algebraic tori that exhibit a strong type of variation of stable birational types. This leads to a purely combinatorial strategy for proving the non-stable rationality of hypersurfaces in tori. As an application, I will discuss many new examples of stably irrational hypersurfaces in projective space.
Siao Chi Mok (University of Cambridge
Ben Morley (University of Cambridge)
Jasbir Nagi (University of Cambridge)
This talk is based on the preprint hep-th/0309243.
Oliver Nash (University of Oxford)
Igor Netay (HSE, Moscow)
Alvaro Nolla de Celis (University of Warwick)
Claudio Onorati (University of Bath) Moduli spaces of generalised Kummer varieties are not connected. Using the recent computation of the monodromy group of irreducible holomorphic symplectic (IHS) manifolds deformation equivalent to generalised Kummer varieties, we count the number of connected components of the moduli space of both marked and polarised such manifolds. After recalling basic facts about IHS manifolds, their moduli spaces and parallel transport operators, we show how to construct a monodromy invariant which translates this problem in a combinatorial one and eventually solve this last problem.
Asymptotic cohomological functions..
Kyriakos Papadopoulos (University of Liverpool)
Notes for this talk are available.
Reflection groups of integral hyperbolic lattices.
Nebojsa Pavic (University of Sheffield)
Andrea Petracci (Imperial College London)
James Plowman (Warwick)
Flora Poon (University of Bath) Kuga-Satake varieties of families of K3 surfaces of Picard rank 14. In the 60s, Kuga and Satake constructed a weight one Hodge structure from a weight two Hodge structure of K3 type, which gives us a polarised abelian variety called the Kuga-Satake (KS) variety associated to a lattice polarised K3 surface. In the project, we study the KS varieties associated to K3 surfaces polarised by lattices of rank 14. Specifically, we have constructed the simple abelian subvarieties in the KS varieties associated to K3 surfaces in three special families, and discovered that they are dense in some moduli spaces of polarised abelian 8-folds of PEL type. We believe the dominant map we found from moduli spaces of K3 surfaces of Picard rank 14 to that of the simple factors of the associated KS varieties demonstrates how the type II_4 locally symmetric domains are associated to the type IV_6 ones.
Joseph Prebble (Loughborough University)
Matthew Pressland (University of Bath)
Ice Quivers with Potential and Internally 3CY Algebras.
Thomas Prince (Cambridge)
Qiu Yu (University of Bath)
Lisema Rammea (University of Bath)
Construction of Non-General Type surfaces in P^4_w.
Jorgen Rennemo (Imperial College)
Sönke Rollenske (Imperial College London)
Fredrik Vaeng Rotnes (Imperial College London)
Taro Sano (University of Warwick)
Deformations of weak Fano manifolds.
Shu Sasaki (Imperial College London)
Danny Scarponi (Oxford/Tolouse)
Sebastian Schlegel Mejia (University of Edinburgh)
Dirk Schlueter (University of Oxford)
Chris Seaman (Cardiff)
Ed Segal (Imperial College London)
Crepant resolutions and quiver algebras.
Superpotential algebras from three-fold singularities.
Lars Sektnan (Imperial College)
Yuhi Sekiya (University of Nagoya)
We use the following well-known graded ring construction: given a polarised variety (X,D), under certain assumptions the graded ring R(X,D) = ⊕ n≥0H0(X,nD) gives an embedding XProj(R(X,D)) ∈ wℙ. It is well known that the numerical data of (X,D) is encoded in the Hilbert series PX(t) := ∑ n≥0h0(X,nD)tn.
We aim to break down the Hilbert series into terms associated to the orbifold loci of X.
The talk should be fairly introductory. I will explain the ideas behind the work from scratch, exhibit some results in 3-D and explain some ideas for the 4-D case.
Orbifold Riemann-Roch and Hilbert Series.
Kenneth Shackleton (University of Southampton)
This talk is based on the preprint math.GT/0412078.
Alexander Shannon (University of Cambridge)
Geometry without geometry.
YongJoo Shin (Sogang University)
James Smith (University of Warwick)
Notes for the second part of this talk are available.
K3s as quotients of symmetric surfaces.
David Stern (University of Sheffield)
Vocabulary made easy.
Liam Stigant (Imperial College London)
In this talk I will present a conceptual overview of the MMP and its aims, before focusing on the mixed characteristic setting and some of the specific difficulties that arise here. I will also discuss some of the ways in which the study of threefolds in mixed characteristic is easier than for varieties of the same dimension over a field, in particular giving sketches of some relatively simple proofs of termination and abundance for threefolds. These results are traditionally very difficult even in dimension 3 over a field, in fact they remain unknown in full generality for positive characteristic threefolds. The proof of abundance is part of some joint work with Fabio Bernasconi and Iacopo Brivio.
Jacopo Stoppa (Imperial College)
Andrew Strangeway (Imperial College)
Tom Sutherland (University of Oxford)
Affine cubic surfaces and cluster varieties.
Rosemary Taylor (University of Warwick)
Elisa Tenni (University of Warwick)
Alan Thompson (University of Oxford)
Models for Threefolds Fibred by K3 surfaces of Degree Two.
Andrey Trepalin (HSE, Moscow)
Karoline van Gemst (University of Sheffield)
Jorge Vitoria (University of Warwick)
Thomas Wennink (University of Liverpool)
Anna Lena Winstel (TU Kaiserlautern)
John Wunderle (University of Liverpool)
Jacobians of hyperelliptic curves.
Christian Wuthrich (University of Cambridge)
Xiong Yirui (University of Sheffield)