Conference: L2-Invariants and their Analogues in Positive Characteristic

Vanderbilt University, Nashville TN

Investigators

Abstract

This National Science Foundation award provides partial funding for U.S. based researchers to participate in a mathematical research and training program that will take place at Instituto de Ciencias Matematicas (ICMAT) in Madrid, Spain, from February 19, 2018 to June 15, 2018. This is a well-timed and ambitious program to bring together specialists as well as beginning researchers to study objects known as L2 invariants and their applications. These invariants draw on many areas of mathematics, such as Algebra, Analysis, Geometry and Topology, and in turn provide extremely useful tools to study unsolved problems in these areas. The objective of the program is two-fold: to train a new generation of leading researchers, and to facilitate advanced research. In order to achieve these goals, the program will begin with a two-week long introductory school aimed at early career researchers, such as graduate students and postdoctoral fellows, followed by several week-long advanced courses, and end with a closing workshop. Throughout, it will include weakly research and study seminars. Priority for funding is given to early career researchers. Historically, the theory of L2-invariants has its origin in the works of M. Atiyah, in which he proposed an extension of the Atiyah-Singer index theory of elliptic differential operators on compact manifolds to the non-compact case. The modern definition of these invariants is more algebraic and uses the language of CW-complexes. The analogue of the first L2-Betti number in positive characteristic, the p-gradient, was introduced by M. Lackenby in his study of hyperbolic 3-manifold groups. The study of L2-invariants is linked to topology, geometry, global analysis, operator theory, ring theory, group theory and K-theory. This program aims to reunite leading specialists in these areas in an exciting research environment at the ICMAT. It is a great opportunity to train young researchers in an area which has been successful in addressing important problems, such as the Baum-Connes conjecture and the Hanna Neumann conjecture, and is an important source of tools and ideas for attacking intriguing open problems in many areas of mathematics. More information is available at the program website at: https://www.icmat.es/rt/l2invariants2018/