Past Junior Logic Seminar

1 March 2016
15:00
Kesavan Thanagopal
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.

  • Junior Logic Seminar
16 February 2016
15:00
Felix Weitkamper
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.
 
  • Junior Logic Seminar
2 February 2016
15:00
Sebastian Eterovic
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. 

  • Junior Logic Seminar
30 November 2015
17:00
Haden Spence
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.

  • Junior Logic Seminar
23 November 2015
17:00
Alexander Betts
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.

  • Junior Logic Seminar
9 November 2015
16:00
Philip Dittmann
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.

  • Junior Logic Seminar

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