Final Activity Report Summary - BUDALGGEO (Algebraic Geometry)
Algebraic geometry and geometric topology are among the prestigious fields in mathematics. However in Hungary, the study of these subjects has been not part of the country's strong mathematical tradition. The main goal of the project has been fully achieved; namely, the progressing algebraic geometry and geometric topology group at the Alfred Renyi Institute of Mathematics in Budapest has been developed into a mature centre. In particular, the project contributed to the cohesion of the European research area.
Substantial results have been obtained in the main themes of the project: 1) Arithmetic geometry: The theory of algebraic cycles and motivic cohomology 2) Singularity theory 3) Invariants of low dimensional manifolds. In addition many important results connect two topics from the above list. The various backgrounds of the members of research group have been effectively amalgamated, thereby providing fruitful cross-fertilization. How high the quality of these results is shown by the fact that many of them appears in top mathematical journals, like Duke Mathematical Journal or Crelle's journal. All together the project has substantially increased the potential of the European Research Area.
Substantial results have been obtained in the main themes of the project: 1) Arithmetic geometry: The theory of algebraic cycles and motivic cohomology 2) Singularity theory 3) Invariants of low dimensional manifolds. In addition many important results connect two topics from the above list. The various backgrounds of the members of research group have been effectively amalgamated, thereby providing fruitful cross-fertilization. How high the quality of these results is shown by the fact that many of them appears in top mathematical journals, like Duke Mathematical Journal or Crelle's journal. All together the project has substantially increased the potential of the European Research Area.