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)
Gergely Berczi (University of Budapest)
Fabio Bernasconi (Imperial College)
Alberto Besana (University of Milan)
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.
Gröbner bases have several nice properties that mean that certain problems in algebraic geometry can be reduced to the construction of a Gröbner basis. For example Gröbner bases allows us to easily determine whether a polynomial lives in some ideal, find the solutions to systems of polynomial equations, as well as having applications in robotics.
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).
Stephen Coughlan (University of Warwick)
Alice Cuzzucoli (Warwick)
Dougal Davis (LSGNT)
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)
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.
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.
Tim Grange (Loughborough)
Jacob Gross (Oxford)
Giulia Gugiatti (LSGNT)
Pierre Guillot (University of Cambridge)
Eloïse Hamilton (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)
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.
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)
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.
Marco Lo Giudice (University of Bath, and University of Milan)
Introduction to schemes.
Detailed notes on scheme theory are available.
Cormac Long (University of Southampton)
Andrew MacPherson (Imperial College London)
A non-archimedean analogue of the SYZ conjecture
Diletta Martinelli (Imperial College London)
Mirko Mauri (LSGNT)
Francesco Meazzini (Sapienza Università di Roma)
Caitlin McAuley (University of Sheffield)
Ciaran Meachan (University of Edinburgh)
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)
On A-infinity algebras of highest weight orbits
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.
John Christian Ottem (University of Cambridge)
We discuss how various notions of positivity of vector bundles is related to the geometry of subschemes.
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)
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)
Taro Sano (University of Warwick)
Deformations of weak Fano manifolds
Shu Sasaki (Imperial College London)
Danny Scarponi (Oxford/Tolouse)
Chris Seaman (Cardiff)
Ed Segal (Imperial College London)
Crepant resolutions and quiver algebras
Superpotential algebras from three-fold singularities. The orbifold X = C^3 / Z_3 is a simple but interesting example of a (non-compact) Calabi-Yau threefold. Physicists predict that type II string theory on X reduces in the low-energy limit to a gauge theory, which is described by a quiver and a superpotential. We'll discuss how these objects arise mathematically.
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.
Dirk Schlueter (University of Oxford)
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.
Jacopo Stoppa (Imperial College)
Andrew Strangeway (Imperial College)
Tom Sutherland (University of Oxford)
Affine cubic surfaces and cluster varieties In this talk we will consider affine cubic surfaces obtained as the complement of three lines in a cubic surface where it intersects a tritangent plane. We will interpret certain families of these affine cubic surfaces as moduli spaces of local systems on the punctured Riemann sphere. We will see how to draw quivers on the sphere so that the associated cluster variety is related to the total space of these families.
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)
Jorge Vitoria (University of Warwick)
Anna Lena Winstel (TU Kaiserlautern)
John Wunderle (University of Liverpool)
Jacobians of hyperelliptic curves.
Christian Wuthrich (University of Cambridge)