Objective The theory of modular forms is a subject where the most diverse branches of mathematics come together: complex analysis, algebraic geometry, representation theory, number theory. The last decades have witnessed the emergence of deep connections between modular forms and the p-adic Hodge theory. These relations have been used in many of the recent most remarkable developments in Mathematics such a the proof of Fermat's last theorems. This advanced course will survey this circle of ideas, with a special emphasis on the recent comparison theorems of T. Tsuji and the generalizations, and so in the study of topics such as Serre's conjecture and the recent proof of the full modularity conjecture. The aim of the course is to provide young researchers with the necessary tools to tackle open problems in the subject are, giving them the opportunity to learn the most recent results on p-adic Hodge Theory and also their interpay with modular forms.ftp://ftp.cordis.lu/pub/improving/docs/HPCF-2000-00028-1.pdf Fields of science natural sciencesmathematicspure mathematicsarithmeticsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsmathematical analysiscomplex analysisnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Programme(s) FP5-HUMAN POTENTIAL - Programme for research, technological development and demonstration on "Improving the human research potential and the socio-economic knowledge base" (1998-2002) Topic(s) 1.4.1.-3.1S6 - Mathematical and Information Sciences Call for proposal Data not available Funding Scheme ACM - Preparatory, accompanying and support measures Coordinator Type of Event: Euro Summer School EU contribution No data Address This event takes place in Bellaterra (Barcelona) Spain See on map Total cost No data