Conference: Ramification in algebra and geometry

Emory University, Atlanta GA

Investigators

Abstract

This grant provides support for the conference "Ramification in Algebra and Geometry" to be held at Emory University, 16-20 May 2011. This conference is primarily focused on the interaction between algebra, geometry, and number theory within the following thematic areas: the arithmetic of linear algebraic groups and homogeneous spaces, cohomological invariants, essential dimension, division algebras and the Brauer group, Chow groups and motivic decomposition, generic Galois extensions, and Brauer-Manin obstructions. This conference brings together international experts and junior researchers working in these areas. The unifying theme is ramification. The geometric notion of ramification is familiar to anyone who has seen a screw (helicoid): looking along the length of a screw, the central axis--where all the threads meet--is where the screw is "ramified." Off the central axis, the screw is not ramified: a laser beam passing through the threads parallel to the central axis pierces only distinct sheets of metal. Here, the ramification distinguishes a screw (helicoid) from a spring (helix). Abstractions of this concept have proved fundamental in many areas of mathematics; this conference will focus on some of the recent applications in algebra and geometry.