Past Logic Seminar

23 May 2013
17:00
Andrew Lewis
Abstract
The Schelling segregation model has been extensively studied, by researchers in fields as diverse as economics, physics and computer science. While the explicit concern when the model was first introduced back in 1969, was to model the kind for racial segregation observed in large American cities, the model is sufficiently abstract to apply to almost situation in which agents or nodes arrange themselves geographically according to a preference not to be of a minority type within their own neighbourhhood. Kirman and Vinkovik have established, for example, that Schelling's model is a finite difference version of a differential equation describing interparticle forces (and applied in the modelling of cluster formation). Despite the large literature relating to the model, however, it has largely resisted rigorous analysis -- it has not been possible to prove the segregation behaviour easily observed when running simulations. For the first time we have now been able to rigorously analyse the model, and have also established some rather surprising threshold behaviour. This talk will require no specialist background knowledge.
16 May 2013
17:00
Tom Leinster
Abstract
It has long been a challenge to synthesize the complementary insights offered by model theory and category theory. A small fragment of that challenge is to understand ultraproducts categorically. I will show that, granted some general categorical machinery, the notions of ultrafilter and ultraproduct follow inexorably from the notion of finiteness of a set. The machine in question, known as the codensity monad, has existed in an underexploited state for nearly fifty years. To emphasize that it was not constructed specifically for this purpose, I will mention some of its other applications. This talk represents joint work with an anonymous referee. Little knowledge of category theory will be assumed.
7 March 2013
17:00
Jeff Paris
Abstract
I shall give a non-technical survey of Pure Inductive Logic, a branch of Carnap's Inductive Logic which was anticipated early on in that subject but has only recently begun to be developed as an area of Mathematical Logic. My intention is to cover its origins and aims, and to pick out some of the key concepts which have emerged in the last decade or so.
28 February 2013
17:00
Gareth Jones
Abstract
Masser recently proved a bound on the number of rational points of bounded height on the graph of the zeta function restricted to the interval [2,3]. Masser's bound substantially improves on bounds obtained by Bombieri-Pila-Wilkie. I'll discuss some results obtained in joint work with Gareth Boxall in which we prove bounds only slightly weaker than Masser's for several more natural analytic functions.
21 February 2013
17:00
Ivan Tomasic
Abstract
The study of difference algebraic geometry stems from the efforts of Macintyre and Hrushovski to count the number of solutions to difference polynomial equations over fields with powers of Frobenius. We propose a notion of multiplicity in the context of difference algebraic schemes and prove a first principle of preservation of multiplicity. We shall also discuss how to formulate a suitable intersection theory of difference schemes.
7 February 2013
17:00
Peter Holy
Abstract
<p>The Outer Model Programme investigates L-like forcing &nbsp;extensions of the universe, where we say that a model of Set Theory &nbsp;is L-like if it satisfies properties of Goedel's constructible&nbsp;universe of sets L. I will introduce the Outer Model Programme, talk &nbsp;about its history, motivations, recent results and applications. I &nbsp;will be presenting joint work with Sy Friedman and Philipp Luecke.</p>

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