University of Illinois at Chicago

Quasimiminimality, Categoricity, and Excellence in L_ω1,ω

We describe the connections between Zilber's work on categoricity in quasiminimal excellent classes, the general theory of excellence in L_ω1,ω, and Shelah's generalization of Morley's theorem to this context. If time permits we will discuss Zilber's analytic model for the green field and connections to quantum tori. Slides for this talk.

Oxford

Model theory of exponential maps of Abelian varieties

I will discuss the elementary and non-elementary classification theory of universal group covers of Abelian varieties, after Zilber and Gavrilovich. I will explain how the model theory is tightly connected to some well-studied and not-so-well-studied issues of arithmetic nature. This talk will in part report on recent joint work with Anand Pillay.

Bilgi University

How it started: early works of Zilber

I will speak on the development of ideas of geomeric stability theory in Boris' works of the seventies.

Paris

Model Theoretic Ranks and divisible groups in separably closed fields (joint with F.Benoist and A.Pillay)

Paris

Introduction to geometric stability

Slides for this talk.

Rutgers

Torsion in Connected Groups of Finite Morley rank

We will discuss some of the special properties of elements of finite order in groups of finite Morley rank. It is commonplace that the study of simple groups exploits the properties of involutions (elements of order 2), but there are also general results on torsion elements in connected groups which have some relationship with the unipotent/semisimple classification in algebraic group theory. These results have applications to permutation groups of finite Morley rank, and to some special configurations arising in connection with the classification of groups of odd type.

University of East Anglia

Covers

Questions about finite covers, particularly those with finite relative automorphism group, were studied 10 to 15 years ago. A more recent preprint of Hrushovski (`Groupoids, Imaginaries and Internal Covers') provides a new way of looking at some of these questions. The aim of this talk is to review some of the results in Hrushovski's preprint and relate some of the older results to them.

St. Petersburg

A set theoretic construction of a model category

Ben Gurion

Symmetric Indivisibility of model theoretic structures

In induced Ramsey theory a countable relational structure M is said to be indivisible if for any colouring of M in two colours there exists a monochromatic substructure N which is isomorphic to M. The structure M is said to be symmetrically indivisible if, in addition, one can require that any isomorphism of the monochromatic structure N can be extended to an automorphism of M. In the talk we will show that Rado's random graph is symmetrically indivisible (a result of Kojman and Geschke) and extend their proof to other structures such as dense linear orders, the random n-hyper graph and the colourful graph). We will introduce a seemingly more powerful new proof of these facts, and use it to prove the symmetric indivisibility of the triangle free random graph, and other structures. We will also present some simple model theoretic necessary conditions for a structure to be (symmetrically) indivisible, and conclude with a couple of intriguing open questions. This is a joint work with M. Kojman and A. Onshuus.

Jerusalem

The notion of a stabilizer

Abstract: In the late 1970's, Zilber's notion of a stabilizer, as it appeared for instance in his indecomposability theorem, had a profound effect on the young subject of groups of finite Morley rank. I will trace the development of this notion in stable group theory, simplicity, and a recent application to combinatorics.

Wrocław

Independence in positive characteristic

Several years ago Boris Zilber suggested to me to work on a positive characteristic version of Ax's theorem. In my talk I will discuss what happened next.

Queen Mary, London

The algebraic numbers definable in Zilber's fields

Leeds

Groups in stable and simple theories

This will be an introductory talk around stable group theory and related topics (such as groups in simple and o-minimal theories). I will discuss chain conditions in stable groups, groups of finite Morley rank (some of the earlier results), stabilisers in stable and simple theories, and 1- based groups.

University of Illinois at Chicago

An introduction to CIT

Leeds

Some model theory of covers

Lyon

One, two, three!

Once I wrote that the main argument in a famous paper published by Cherlin in 1979, "Groups of small Morley rank", is that the only positive integers smaller than three are one and two. I will produce a stronger illustration of this principle: with some supplementary work, the results of Cherlin can be obtained using the Cantor rank, which fails to have the paradisiac properties of the Morley rank. This shows that the meagre things that we know on the Zil'ber and Cherlin conjecture, more than thirty years after its formulation, does not depend on the deep properties of the groups of finite Morley rank.

Yeditepe University, Istanbul

On the automorphism groups of groups F/R'

Let F be an infinitely generated free group and R a fully invariant subgroup of F such that

• R is contained in the commutator subgroup F' of F;
• the quotient group F/R is residually torsion-free nilpotent.

Manchester

Same model theory for complex holomorphic functions definable in o-minimal structures

Oxford

On model theory of "new structures" from noncommutative geometry and physics

I am going to give more details on structures originating in noncommutative geometry and physics and give a link to old and recent developments in model theory proper.