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.

Wed, 24 Feb 2016

16:00 - 17:00
C3

CAT(0) Boundaries

Robert Kropholler
(Oxford University)
Abstract

I will talk about the boundaries of CAT(0) groups giving definitions, some examples and will state some theorems. I may even prove something if there is time. 

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. 

Wed, 10 Feb 2016
16:00
C3

Quasi-isometric rigidity and higher-rank symmetric spaces

Elia Fioravanti
(Oxford University)
Abstract

I will discuss a couple of techniques often useful to prove quasi-isometric rigidity results for isometry groups. I will then sketch how these were used by B. Kleiner and B. Leeb to obtain quasi-isometric rigidity for the class of fundamental groups of closed locally symmetric spaces of noncompact type.

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