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.
This grant reimbursed some travel expenses for participants of the conference "Ramification in algebra and geometry" held at Emory University during 16-20 May 2011. The subject of the conference was linear algebraic groups and their related algebraic, number theoretic, and geometric structures. The unifying theme in these areas 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. In this example, the ramification distinguishes a screw (helicoid) from a spring (helix). Abstractions of this concept have proved fundamental in many branches of mathematics. There has been a recent explosion of research activity centered around ramification in the context of linear algebraic groups and their related structures. The conference captured the current state of the art and connected researchers pursuing different threads in this subject. Built on a series of previous successful conferences in Canada and Europe, this was one of the only conferences in the US dedicated to this subject. More than 100 mathematicians (representing 10 countries and 16 US states) attended the conference to share their knowledge and discuss their latest research advances, with 51 participants giving presentations. Some of the lectures were recorded and can be downloaded for free from iTunesU at http://itunes.apple.com/us/itunes-u/ramification-in-algebra-geometry/id443224115 In addition to showcasing new research by established experts, the conference also promoted talented graduate students by offering them the opportunity to give brief plenary lectures. The conference also offered unique networking opportunities for young predoctoral and postdoctoral researchers to establish contacts with international experts and amongst themselves.
