DESCRIPTION
Venue: International Centre, Goa
One of the basic problems in mathematics is the description of the absolute Galois group G of the field Q of rational numbers. This group is so large and complicated that conjecturally all finite groups can be realized as its quotients. Arguments in Galois cohomology reduce many of the fundamental questions of arithmetic geometry to the study of G.
A fruitful approach to understanding this group is through its representations; the study of one-dimensional representations constitutes global class field theory. Some forty years ago, a vast program aimed at understanding all representations of G was advanced. More recently, some very precise conjectures about the 2-dimensional representations of G were put forward. Major success has been achieved in the past decades in proving these conjectures through the combined efforts of several mathematicians. This conference will bring together some of the people who have made seminal contributions to these developments.