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Second MALOA Training Workshop
University of Leeds
Sunday June 26 to Saturday July 2 2011

Abstracts and Titles of lectures

Titles

  • Romain Kervarc, Onera (4 lectures) - Temporal logic and its application to the modelling and assessment of aerospace systems
  • Ben Miller, Westfälische Wilhelms-Universität Münster (4 lectures)- A graph-theoretic approach to descriptive set theory and structural dichotomy theorems
  • Michael Rathjen, The University of Leeds - Metamathematics of axiom systems for Constructive Set Theory
  • Peter Aczel, University of Manchester - Introduction to Constructive Set Theory
  • Nicola Gambino, Università degli Studi di Palermo - Constructive mathematics in Constructive Set Theory
  • Charles Steinhorn,Vassar College - Vapnik-Chervonenkis classes: model theory and applications
  • Ben Azvine, BT - Industrial Innovation – case studies from BT
  • Anand Pillay, The University of Leeds - The VC theorem and Keisler measures
  • Jennifer Rivas Perez, David Bond, University of Leeds - Designing posters and slides for greater impact
  • Michael Pinsker, Équipe de Logique Mathématique de l'Université Denis-Diderot Paris 7 - Constraint satisfaction with homogeneous templates: Applications of model theory and Ramsey theory in theoretical computer science
Towards the end of the week there will be the following two 4-5 lecture sessions in parallel:
  • Constructive set theory by P Aczel, N Gambino, M Rathjen
  • Constraint satisfaction with homogeneous domains by M Pinsker

Abstracts of courses

Ben Miller, Westfälische Wilhelms-Universität Münster - A graph-theoretic approach to descriptive set theory and structural dichotomy theorems. A course of 4 lectures.
We will review the main notions of definability central to descriptive set theory (analytic, Borel, etc.), as well as basic Baire category techniques. We will then move on to explore a variety of dichotomy theorems which give a sense of the difference between Borel structures and their more abstract counterparts.
Peter Aczel, Nicola Gambino, Michael Rathjen - A course of lectures on Constructive Set Theory
Constructive Set Theory provides a setting for the development of extensional constructive mathematics in the same first order language as classical set theory, but uses intuitionistic logic and only has axioms that can be constructively justified.
The course of 5 or 6 lectures will be given by Peter Aczel, Nicola Gambino and Michael Rathjen. Their titles and abstracts are given below.
If you wish to attend the lectures you may find it useful to read the first few chapters of the following pdf file of a draft book.
http://www.maths.manchester.ac.uk/logic/mathlogaps/workshop/CST-book-June-08.pdf
Introduction to Constructive Set Theory: Peter Aczel
I will introduce some of the axiom systems used in Constructive Set Theory and outline an explanation of the constructive concept of set that can be used to interpret the axiom systems, but cannot be used to justify some of the axioms of classical set theory, such as the powerset axiom and the full separation scheme.
Constructive mathematics in Constructive Set Theory: Nicola Gambino
I will explain how constructive mathematics can be developed in Constructive Set Theory. The focus will be on constructive topology, an important area of current research which illustrates well the main features of the development of mathematics in Constructive Set Theory.
Metamathematics of axiom systems for Constructive Set Theory: Michael Rathjen
I will situate the proof-theoretic strength of various constructive and intuitionistic set theories in a landscape of more familiar classical theories (e.g. from reverse mathematics). I will also discuss various independence results and then proceed onwards to discuss a metamathematical property, the existence property, EP, which is a hallmark of many intuitionistic theories. A theory has the EP if whenever it proves an existential statement then there is a provably definable witness for it.

Abstracts of lectures

Anand Pillay, The University of Leeds - The VC theorem and Keisler measures
Recent years have seen the discovery of widespread ``stable-like" behaviour in first order theories which are unstable but do not have the "independence theorem". However the stability-like behaviour tends to be at the level of measures rather than types. I will try to explain something of the role of the Vapnik-Chervonenkis inequality and theorem, from probability theory, in these developments.

Charles Steinhorn,Vassar College - Vapnik-Chervonenkis classes: model theory and applications
Vapnik-Chervonenkis classes, which have their origin in combinatorics, probability, and (perhaps surprisingly) model theory, all dating back about 40 years, have been applied in a wide variety of contexts in mathematics, computer science, and statistics. We discuss their relation to model theory and describe (in some depth) some of these applications.

Michael Pinsker, Équipe de Logique Mathématique de l'Université Denis-Diderot Paris 7 - Constraint satisfaction with homogeneous templates: Applications of model theory and Ramsey theory in theoretical computer science
Constraint Satisfaction Problems are fundamental computational problems that appear in many areas of theoretical computer science. For a fixed relational structure B, the constraint satisfaction problem for B, CSP(B), is the problem to decide whether a given finite structure A homomorphically maps to B. In the last 10 years it has been discovered that the question for which structures B CSP(B) can be solved in polynomial time is intimately related to central questions in universal algebra.

For *finite* structures B, this universal-algebraic approach lead to a conjecture, the tractability conjecture, that exactly describes those structures B for which CSP(B) is polynomial-time tractable, and those where CSP(B) is NP-hard. It turns out that the same universal-algebraic approach can be applied to study the complexity of CSP(B) for *omega-categorical* structures B. Surprisingly many problems that have been studied in the literature can be formulated as CSP(B) for an omega-categorical structure B.

I will introduce the universal-algebraic approach to constraint satisfaction, and then discuss the following specialized situation: We are given a countable structure S which is homogeneous in a finite language, ordered, and has the Ramsey property; we wish to determine the complexity of CSP(B), for all structures definable in B. Recently, model-theoretic and combinatorial methods have been developed to deal with this situation, and have been applied to obtain classifications of the compexity of CSP(B) for all B definable in the dense linear order and the random graph (it turns out that CSP(B) is either NP-complete or in P, for all such B).

Jennifer Rivas Perez, David Bond (University of Leeds)
Having great content is important when delivering a talk or poster. But presenting that content well is essential if your audience is going to get the most from your research. In this short session we will explore ways of presenting your research, so that next time you present at a conference or seminar, you'll really reach your audience. What is good design? Using hands-on examples, we'll examine the best (and worst!) ways to lay out your posters and slides, from the basics of colour, font, images, and space, up to the final presentation itself.

Ben Azvine, BT - Industrial Innovation – case studies from BT
Industrial innovation is the process of creating and exploiting new technologies to generate business benefit. There are many factors that determine whether a new technology will end up as a successful innovation. In this lecture I'll share my insight on what the process of industrial innovation consists of, what are the potential pitfalls, and how we can maximise the chances of success. I'll be sharing my experience using a number of case studies in the areas of performance and risk management, customer relationship management and data mining to demonstrate how novel applications are developed and used in an industrial environment.

Romain Kervarc (Onera) - Temporal logic and its application to the modelling and assessment of aerospace systems (4 hour course)
Aerospace is a sector where people have to deal with very large, complex systems involving numerous agents. Besides, real experimentation, common in other industrial sectors, is here impossible due to the cost and criticity of the involved systems. Hence, aerospace system study heavily relies on simulation and modelling. A paramount aspect in the study of such a system consists in the interactions between components and agents and the evolution of their relationships throughout time. Temporal logic is a natural framework for the description and modelling of this aspect, and this series of lectures will focus on how it may be used for the assessment or analysis of aerospace systems.