Forthcoming events in this series


Thu, 13 Nov 2014
11:00
C5

Convergence properties in Stone spaces

Robert Leek
((Oxford University)))
Abstract

In this talk, I will introduce an internal, structural 
characterisation of certain convergence properties (Fréchet-Urysohn, or 
more generally, radiality) and apply this structure to understand when 
Stone spaces have these properties. This work can be generalised to 
certain Zariski topologies and perhaps to larger classes of spaces 
obtained from other structures.

Thu, 30 Oct 2014
11:00
C5

"Decidability in extensions of F_p((t))";

Ben Rigler
(Oxford)
Abstract

"We consider certain distinguished extensions of the field F_p((t)) of formal Laurent series over F_p, and look at questions about their model theory and Galois theory, with a particular focus on decidability."

Thu, 29 May 2014
11:00
C5

"Specialisations of algebraically closed fields".

Ugur Efem
Abstract

Algebraically closed fields, and in general varieties are among the first examples
of Zariski Geometries.
I will consider specialisations of algebraically closed fields and varieties.
In the case of an algebraically closed field K, I will show that a specialisation
is essentially a residue map, res from K to a residue field k.  
In both cases I will show universality of the specialisation is controlled by the
transcendence degree of K over k.  

Thu, 22 May 2014
11:00
C5

"On the decidability of generalized power series fields"

Benjamin Rigler
Abstract

Given a field K and an ordered abelian group G, we can form the field K((G)) of generalised formal power series with coefficients in K and indices in G. When is this field decidable? In certain cases, decidability reduces to that of K and G. We survey some results in the area, particularly in the case char K > 0, where much is still unknown.

Thu, 22 May 2014
11:00
C5

"On the decidability of generalized power series fields"

Benjamin Rigler
Abstract

Given a field K and an ordered abelian group G, we can form the field K((G)) of generalised formal power series with coefficients in K and indices in G. When is this field decidable? In certain cases, decidability reduces to that of K and G. We survey some results in the area, particularly in the case char K > 0, where much is still unknown.

Thu, 08 May 2014
11:00
C5

Demushkin Fields and Valuations

Kristian Strommen
Abstract

I will give an outline of ongoing work with Jochen Koenigsmann on recovering valuations from Galois-theoretic data. In particular, I will sketch a proof of how to recover, from an isomorphism G_K(2) \simeq G_k(2) of maximal pro-2 quotients of absolute Galois groups, where k is the field of 2-adic numbers, a valuation with nice properties. The latter group is a natural example of a so-called Demushkin group.
Everyone welcome! 
Thu, 06 Mar 2014
11:00
C5

'Defining p-henselian valuations'

Franziska Yahnke
(Muenster)
Abstract

(Joint work with Jochen Koenigsmann) Admitting a p-henselian
valuation is a weaker assumption on a field than admitting a henselian
valuation. Unlike henselianity, p-henselianity is an elementary property
in the language of rings. We are interested in the question when a field
admits a non-trivial 0-definable p-henselian valuation (in the language
of rings). They often then give rise to 0-definable henselian
valuations. In this talk, we will give a classification of elementary
classes of fields in which the canonical p-henselian valuation is
uniformly 0-definable. This leads to the new phenomenon of p-adically
(pre-)Euclidean fields.

Thu, 27 Feb 2014
11:00
C5

'Counterexamples to a conjecture of Wilkie'

Jonathan Kirby
(UEA)
Abstract

In an o-minimal expansion of the real field, while few holomorphic functions are globally definable, many may be locally definable. Wilkie conjectured that a few basic operations suffice to obtain all of them from the basic functions in the language, and proved the conjecture at generic points. However, it is false in general. Using Ax's theorem, I will explain one counterexample. However, this is not the end of the story.
This is joint work with Jones and Servi.

Thu, 05 Dec 2013
11:00
C5

"Poincare series counting numbers of definable equivalence classes"

Jamshid Derakhshan
(Oxford)
Abstract

Hrushovski-Martin-Rideau have proved rationality of Poincare series counting 
numbers of equivalence classes of a definable equivalence relation on the p-adic field (in connection to a problem on counting representations of groups). For this they have proved 
uniform p-adic elimination of imaginaries. Their work implies that these Poincare series are 
motivic. I will talk about their work.

Thu, 28 Nov 2013
11:00
C5

'Model Theory of Adeles and Adelic Geometry'.

Dr Derakhshan
(Oxford)
Abstract

This is joint work with Angus Macintyre. I will discuss new developments in 
our work on the model theory of adeles concerning model theoretic 
properties of adeles and related issues on adelic geometry and number theory.