Forthcoming events in this series


Tue, 01 Mar 2016

15:00 - 16:00
L1

A "Simple" Answer to a "Not Quite Simple" Problem - The Prequel to A "Simple" Question

Kesavan Thanagopal
(Oxford University)
Abstract

In this seminar, I aim to go through the "main prequel" of the talk I gave during the first Advanced Class of this term, and provide a "simple" answer to Abraham Robinson's original question that he posed in 1973 regarding the (un)decidability of finitely generated extensions of undecidable fields. I will provide a quick introduction to, and some classical results from, the mathematical discipline of Field Arithmetic, and using these results show that one can construct undecidable (large) fields that have finitely generated extensions which are decidable. Of course, as I had mentioned in the advanced class, a counterexample to the "simple" question that I have been working on unfortunately does not seem to lie within this class of large fields. If time permits, I will provide a sneak peek into the possible "sequel" by briefly talking about what the main issue of solving the "simple" problem is, and how a "hide-and-seek" method might come in handy in tackling that problem.

Tue, 23 Feb 2016

15:00 - 16:00
C4

Galois Characterization of Henselian Fields

Chenkai Wang
(Oxford University)
Abstract

 I will talk about Jochen’s theorem about the existence of some non-trivial Henselian valuation given by investigating the absolute Galois group.

Tue, 16 Feb 2016

15:00 - 16:00
L5

Hrushovski's construction

Felix Weitkamper
(Oxford University)
Abstract
I will give a general overview of the versatile method behind Hrushovski's construction and then sketch the proof that the original strongly minimal set considered by him does not interpret an infinite group using a group configuration.
 
Tue, 02 Feb 2016

15:00 - 16:00
L5

The Manin-Mumford Conjecture via O-minimality

Sebastian Eterovic
(Oxford University)
Abstract

In the talk I will give an introduction to the Manin-Mumford conjecture and to the Pila-Zannier strategy for attacking it in the case of products of elliptic curves. if the permits it, I will also speak about how this same strategy has allowed to attack the analogous André-Oort conjecture for Shimura Varieties of abelian type. 

Mon, 30 Nov 2015

17:00 - 18:00
L1

Slightly Rubbish Modular Ax-Lindemann

Haden Spence
(Oxford University)
Abstract

In quite an elementary, hands-on talk, I will discuss some Ax-Lindemann type results in the setting of modular functions.  There are some very powerful results in this area due to Pila, but in nonclassical variants we have only quite weak results, for a rather silly reason to be discussed in the talk.

Mon, 23 Nov 2015

17:00 - 18:00
L3

Functors of points and moduli problems

Alexander Betts
(Oxford University)
Abstract

In algebraic and arithmetic geometry, there is the ubiquitous notion of a moduli space, which informally is a variety (or scheme) parametrising a class of objects of interest. My aim in this talk is to explain concretely what we mean by a moduli space, going through the functor-of-points formalism of Grothendieck. Time permitting, I may also discuss (informally!) a natural obstruction to the existence of moduli schemes, and how one can get around this problem by taking a 2-categorical point of view.

Mon, 09 Nov 2015

16:00 - 17:00
C2

Characterising the integers in the rationals

Philip Dittmann
(Oxford University)
Abstract

Starting from Hilbert's 10th problem, I will explain how to characterise the set of integers by non-solubility of a set of polynomial equations and discuss related challenges. The methods needed are almost entirely elementary; ingredients from algebraic number theory will be explained as we go along. No knowledge of first-order logic is necessary.

Mon, 02 Nov 2015
17:00
L3

Non-Archimedean Analytic Geometry..etc.

Nicholas Wentzlaff
Abstract

I want to give an introduction into non-Archimedean Geometry, and show how Model Theory was used to prove the recent results of Hrushovski-Loeser on topological properties of analytic spaces. This may also be of interest with view towards Zilber's programme for syntax-semantics dualities.