MATHLOGAPS (Marie Curie Framework 6 Early Stage Training Site) University of Leeds (UK) University of Manchester (UK) Universit? de Lyon 1 (France) Ecole Normale Sup?rieure de Lyon (France) Ludwig Maximilians Universitaet Muenchen (Germany) The Early Stage Training Site offers funding for PhD studentships, including short term visits between Sep 1, 2004 and Aug 31, 2008 at one of the five organizing institutions in the following research areas (see eligibility criteria below): Research areas covered Model Theory (Leeds, Manchester, Lyon): Geometric stability and simplicity theory, and partial stability in unstable structures; extensions and variations on minimality (e.g. weak o-minimality), model theory of valued fields, stable and simple fields, model theory of groups (especially groups of finite Morley rank), automorphism groups of first order structures; the interaction of model theory and representation theory, and functorial model theory; model theory of finite structures; non-standard analysis (infinite dimensional stochastic analysis; malliavin calculus). Set Theory (Leeds, Manchester, Munich): Fine structure, core models, large cardinals, generalized set theory, constructive set theory, hyperset theory, set theory without the axiom of choice, and connections with model theory. Proof Theory and Applications to Theoretical Computer Science (Leeds, Manchester, Munich, Lyon): Ordinal analysis of strong subsystems of analysis and related constructive type theories; subrecursive hierarchy classifications of provably recursive functions; weak systems and implicit complexity theory; lambda-calculus; program synthesis; program and proof development systems; realisability; formalisation of proof checking; automated deduction; corecursion and coinduction; logic of streams. Computability Theory (Leeds): Turing degrees, other forms of reducibility and relative computability, local and global definability in degree structures Complexity Theory (Lyon): Models of computation; automata theory; tilings of finite regions of the plane by polygonal pieces. Reasoning under Uncertainty and Non-monotonic Logic (Manchester): Default reasoning, probability logic, many-valued logics, rationality principles, maximum entropy, consequence, inductive logic. Leeds: http://www.maths.leeds.ac.uk/Pure/logic: H.D. Macpherson, Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, England Manchester: http://www.maths.man.ac.uk/logic: G. Wilmers, Department of Mathematics, Manchester University, Oxford Rd, Manchester M13 9PL, England Lyon 1: http://igd.univ-lyon1.fr/home/blossier/logique: F. Wagner, Institut Girard Desargues, 21 Avenue Claude Bernard, 69622 Villeurbanne cedex, France. Lyon ENS: http://www.ens-lyon.fr/LIP: P. Koiran, Laboratoire de L'Informatique du Parallelisme (LIP), 46 Allee d'Italie, 69364 Lyon, France. Munich: http://www.mathematik.uni-muenchen.de/~logik: H. Schwichtenberg, Mathematisches Institut LMU M?nchen, Theresienstrasse 39, M?nchen 80333, Germany, Eligibility This scheme is for Early Stage Researchers. Roughly speaking, those funded should be within 4 years of having achieved a degree which, in their own country, would allow them to qualify for a doctoral programme. Appointments are also subject to mobility restrictions. These mean, again only roughly, that an appointment cannot be made at a centre in the candidates country. For the precise and full details on eligibility, see the Handbook on Marie Curie Host Fellowships For Early Stage Training, dowloadable from http://europa.eu.int/comm/research/fp6/mariecurie-actions/action/stage_en.h tml