Past Advanced Class Logic

22 May 2014
11:00
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.

  • Advanced Class Logic
8 May 2014
11:00
Kristian Strommen
Abstract
<p> <div>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.</div> <div></div> <div>Everyone welcome!&nbsp;</div> </p>
  • Advanced Class Logic
6 March 2014
11:00
Franziska Yahnke
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.

  • Advanced Class Logic
27 February 2014
11:00
Jonathan Kirby
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.

  • Advanced Class Logic
5 December 2013
11:00
Jamshid Derakhshan
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.

  • Advanced Class Logic

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