AGGITatE 2023

An opportunity for researchers to broaden their mathematical horizons. This year's theme focuses on aspects of linear algebraic groups and the Cremona group.

  • Mon 19 - Wed 21 Jun 23


  • Colchester Campus

    CTC 3.05

  • Event type

    Workshops, training and support

  • Event organiser

    Mathematics, Statistics and Actuarial Science, School of

  • Contact details

    Dr Alastair Litterick

AGGITatE 2023: Algebras, Groups, Geometry, Invariants and related Topics at Essex


AGGITatE is an excellent opportunity for early- and mid-career researchers in algebra, geometry, and related areas to broaden their mathematical horizons and establish new collaborative networks. This year's theme focuses on aspects of linear algebraic groups and the Cremona group.



Thanks to our sponsors, the London Mathematical Society, the Foundation Compositio Mathematica, the Department of Mathematical Sciences and Overleaf, we can cover partial expenses of participants based at UK universities (travel and accommodation). Priority will be given to PhD students and early-career mathematicians. If you have such a request, please, indicate so in your registration. Other participants who can find their own support are welcome to come.

London Mathematical Society
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Composition Mathematica



10am: Morning talk 1

Mima Stanojkovski: Smooth cuboids in group theory 

A smooth cuboid can be identified with a 3x3 matrix of linear forms, with coefficients in a field K, whose determinant describes a smooth cubic in the projective plane. To each such matrix, one can associate a group scheme G over K. In particular, when K is the field of rationals and F is the field of p elements, the F-points G(F) of G form a finite p-group, and, as p varies, one obtains an infinite family of groups. In this talk, I will present joint work with Josh Maglione and Christopher Voll on the geometric study of automorphisms and isomorphism types of groups defined from smooth cuboids. I will also explain a connection with Higman's PORC conjecture and show that our geometric approach yields faster isomorphism testing of groups in this context.




11:30am: Morning talk 2

Susanna Zimmermann: Real birational involutions of rational conic fibrations

It is an old problem to classify the finite subgroups of Cremona groups. It was initiated by Bertini, and the most complete classification so far has been achieved by Dolgachev-Iskovskikh and Blanc over an algebraically closed field. Over the field of real numbers, the classification is almost complete, with a large part completed by Robayo and Yasinsky in 2017. In this talk, we will focus on birational involutions of the real plane; we will discuss the general attack to the classification and then focus on a particular subclassification - one of the birational involutions of the plane preserving a pencil of rational curves. This is joint work with I. Cheltsov, F. Mangolte and E. Yasinsky.


12:30pmLunch break 


2pm: Afternoon talk 1

Michael Bate: Edifices

Jacques Tits established the theory of buildings about fifty years ago as a way to bring combinatorial and geometric techniques to the study of semisimple algebraic groups (especially exceptional groups, where no "obvious" geometry immediately presents itself). In this talk I will report on some recent work which shows how to attach a building-like structure to an arbitrary smooth connected algebraic group over a field; we have christened these new structures "edifices". Edifices share some, but not all, of the nice geometric and combinatorial properties of spherical buildings - they are complete metric spaces, for example, but may not be simplicial complexes - and are well-behaved with respect to natural operations on algebraic groups, like homomorphisms and base change.

In this talk, I'll discuss how to construct an edifice, some basic properties and examples, and some of the motivation for studying them.




3:30pm: Afternoon talk 2

Christian Urech: Representation dimension of finite subgroups of Cremona groups

Studying finite subgroups of Cremona groups is a very rich subject with a long history. Already in rank two there is no complete classification of finite subgroups of Cremona groups. Instead of giving a complete classification, one can try to find bounds on the complexity of these subgroups. In this talk, we will consider the minimal dimension of faithful representations of finite groups as a measure for their complexity. This is joint work with A. Duncan and B. Heath.

7pmConference dinner (Brook Red Lion Hotel)


09:30am: Morning talk 1

Andrea Fanelli: On the Cremona group over imperfect fields

In this talk I will present an ongoing joint project with Fabio Bernasconi, Julia Schneider and Susanna Zimmermann aimed to extend some structural results on the rank-two Cremona group to the case of imperfect fields. Our motivation comes from the study of algebraic subgroups of the rank-three Cremona group over algebraically closed fields and our approach is birational geometric: our strategy requires a careful study of the Sarkisov program for rational surfaces over imperfect fields.


10:30am: Morning talk 2

Anne Lonjou: Regularisable subgroups of the Cremona group

The Cremona group, the group of birational transformations of the projective plane is a group which is nowadays well understood. A birational transformation is said regularisable if it is conjugated to an automorphism of a projective surface. Such elements are classified but the following natural question about regularisation is still open: Consider a finitely generated subgroup G of the Cremona group such that any element is regularisable. Is G conjugated to a subgroup of an automorphism of a projective surface ? In this talk, we will see how this question is related to understand elliptic elements and subgroups for the action of the Cremona group on some CAT(0) cube complexes and in which cases we are able to solve this question. This talk is based on several works with C. Urech, A. Genevois and P. Przytycki.


11:30am: Break


12pm: Morning talk 3

Frédéric Mangolte: Comessatti’s Theorem on Rational Surfaces and Real Fano threefolds

From the classification of real rational surfaces worked out by Comessatti at the beginning of the 20th century we get the following striking characterization of real rational surfaces: a geometrically rational real surface is rational if and only if its real locus is non-empty and connected. In a work in progress with Andrea Fanelli, we explore real loci of geometrically rational Fano threefolds and study the rationality of these.


2pm: Afternoon talk 1

David Stewart: Absolute rigidity of simple modules for algebraic groups (Joint work with Michael Bate)

Let k be a field and G be a smooth affine k-group of finite type. We show that the simple G-modules are absolutely rigid; that is, if V is a simple G-module, then the socle and radical series for VE as a GE-module coincide for any field extension E/k. Central to the proof is the authors’ recent classification of simple modules for connected G by highest weight. We use this to describe the endomorphism ring of simple G-modules and thereby give a dimension formula. For most of our results, the key case to consider is when G is a pseudo-split pseudo-reductive group and E/k is finite and purely inseparable.




3:30pm: Afternoon talk 2

Anna Bot: Realisation of birational maps

Given an invertible matrix F, we investigate under which conditions it can be realized as a birational map f of ℙ2, meaning if there exists a blow-up to a rational surface X on which f lifts to an automorphism whose action on the Picard group of f is precisely F. Based on ideas by McMullen and Uehara, we give sufficient conditions on points on a cuspidal cubic, and indicate how this can be used to prove that the ordinal of all dynamical degrees of all birational maps of ℙ2 is ωω.


5-7pm: Drinks reception


10am: Morning talk 1

Paula Lins: Bivariate zeta functions and twisted conjugacy  

In this talk we will discuss bivariate zeta functions of a large class of finitely generated nilpotent groups encoding numbers of (twisted-)conjugacy classes of each cardinality of congruence quotients of the associated groups.

Twisted conjugacy is a generalisation of usual conjugacy in which one considers a group automorphism φ of Γ and the action g · x = gxφ(g)-1 on Γ. The orbits of such action are called twisted conjugacy classes (also known as Reidemeister classes). We will discuss how bivariate zeta functions can be used to determine the possible sizes of twisted-conjugacy classes of finite nilpotent groups.


10:30am: Morning talk 2

Sokratis Zikas: Equivariant geometry of quadric bundles and maximal subgroups of Cremona groups

Maximal connected algebraic subgroups of the group of birational transformations Bir(X) of a variety X appear as automorphism groups of Mori fiber spaces birational to X. When X = ℙn for n = 2, 3 we have a classification of such groups and the models they act on, while in dimension 4 and more this is an open problem. In this talk we will explore the equivariant geometry of a class of quadric fibrations over ℙ1. As a result, we will see how their automorphism groups gives us families of maximal subgroups of Bir(ℙn) for any n at least 4. This is work in progress, joint with Enrica Floris.


11:30am: Break


12:00pm: Afternoon Talk 1

Ivan Cheltsov: Equivariant birational geometry of the three-dimensional projective space

In this talk, we will discuss G-equivariant birational geometry of the three-dimensional projective space for a finite group G acting biregularly on the projective space. In particular, we will describe all possibilities for the group G such that the projective space is not G-equivariantly birational to fibrations into rational curves or surfaces.



A workshop dinner will be held on Monday evening at The Red Lion Hotel in Colchester. Please indicate when registering if you wish to attend.



Department of Mathematics, University of York

Michael's work focuses on affine algebraic groups and their interaction with other mathematical structures. In particular, he is interested in Geometric Invariant Theory, Representation Theory and the theory of Spherical Buildings.

PhD student

Mathematics and Computer Science, University of Basel

I am interested in birational geometry; my first projects were on real forms on rational surfaces, now I'm studying Coble surfaces, and also dynamical degrees of birational maps.


School of Mathematics, University of Edinburgh

Ivan is an algebraic geometer, and a bi-rationalist in particular.


Department of Mathematics, Université de Bordeaux

Andrea's interests are in birational geometry, especially Fano varieties and fibrations; Mori fibre spaces and the minimal model program; rationally simply connected varieties; surfaces in positive characteristic; and algebraic subgroups of the Cremona group.

Research Fellow

Department of Mathematics, University of Basque County

Anne's research line is in birational geometry and geometric group theory.


School of Mathematics and Physics, University of Lincoln

Paula's research interests are in asymptotic group theory (in particular arithmetic and analytical properties of zeta functions associated to groups), and twisted conjugacy classes and the R-infinity property of groups. 


University of Angers

Frédéric is a specialist of real algebraic varieties, in particular their topology and their geometry.

Assistant Professor

Department of Mathematics, Università di Trento

Mima's main research is in the realm of group theory, specialising in p-groups.


Department of Mathematics, University of Manchester

David is a reader of Pure Mathematics. His research is concentrated on various aspects of Lie Theory, including the subgroup structure of algebraic groups, representation and cohomology theory of algebraic groups, and subalgebra structure of modular Lie algebras.   

Bernoulli Instructor

Institute of Mathematics, École Polytechnique Fédérale de Lausanne

Christian’s research lies at the intersection of algebraic geometry, geometric group theory, and dynamics, applying tools from geometric group theory to study Cremona groups.

Full Professor 

Institut de Mathématique d'Orsay, University of Paris-Saclay

Susanna's research interests are in birational geometry, Cremona groups, algebraic groups and real algebraic geometry. 

Teaching Assistant

Departement of Mathematics and Computer Science , University of Poiters

My main area of research is Birational Geometry; more specifically, I have worked on birational relations among Mori fibre spaces via the Sarkisov Program, with applications to Cremona groups.


Participants and affiliations 

 Participant  Affiliation
 Michael Bate  University of York
 Marta Benozzo  LSGNT
 Anna Bot  University of Basel
 Tiago Duarte Guerreiro  University of Essex
 Erroxe Etxabarri Alberdi  University of Nottingham
 Andrea Fanelli  Université de Bordeaux
 Simon Hart  University of York
 Liana Heuberger  University of Bath
 Paula Lins de Araujo  University of Lincoln
 Alastair Litterick  University of Essex
 Anne Lonjou  UPV & Ikerbasque
 Jesus Martinez Garcia  University of Essex
 Mima Stanojkovski  Università di Trento
 David Stewart  University of Manchester
 Harvey Sykes  Durham University / University of Essex
 Adam Thomas  University of Warwick
 Marc Truter  University of Warwick
 Christian Urech  EPFL
 Gerald Williams  University of Essex
 Elena Denisova   University of Edinburgh
 Sokratis Zikas  University of Poitiers
 Susanna Zimmermann

 Université Paris-Saclay

 Arman Sarikyan  University of Edinburgh
 Ivan Cheltsov  University of Edinburgh
 Mangolte  Aix-Marseille Université
 Alexandra Ciotau  University of Manchester
 Xuantong Qu  University of Nottingham
 Joseph Malbon  University of Edinburgh
 Antoine Pinardin  University of Edinburgh
 Michael Chitayat  University of Ottowa

How to get here

The workshop will take place at the Colchester Campus of the University of Essex. You can find directions to make your travel arrangements to Colchester. FindYourWay is a useful resource to find your way around the maze of rooms of the University. You can also download the app for Android and Apple devices.

Local amenities

If your accommodation is paid by the organisers, we will be in touch with details.

If you are self-funded, the following are good options for accommodation in Colchester:

All are in the route of buses 62 and 62B which take you directly to Campus in about 20 minutes. You can also walk to campus in 40-60 minutes, depending on the hotel.

Register for AGGITatE 2023

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