Miasnikov, Alexei Ushakov, Alexander

Stevens Institute of Technology, Hoboken, NJ, United States

Kervaire Seminar: Geometry of groups 2013 (Swiss Doctoral Program in Mathematics), Les Diablerets, Switzerland, 10-15 March, 2013. The conference covers several branches of modern group theory: geometric group theory, asymptotic behavior of infinite groups, group actions and dynamical systems. Research one-hour talks are complemented by several mini-courses given by the leading experts in the field.

Geometric group theory is a relatively young field with roots in combinatorial group theory and topology. In the mid 1980's, spurred by ideas of Gromov, group theorists began to pay attention to the geometric structures which cell complexes can carry. This attention shed a great deal of light on the earlier combinatorial and topological investigations and stimulated other innovative ideas which have been developing at a rapid pace. As it has grown over the past 20 years, geometric group theory has developed many different facets, including geometry, topology, analysis, logic. Asymptotic behavior of infinite groups has been one of the main themes in geometric group theory since the early nineties. The asymptotic invariants of a group reflect the large-scale geometry of the group, they paly an important part in theory and applications. Interplay between group actions and dynamical systems is a new area of group theory. On the one hand, conformal dynamical systems yield a rich source of such groups with interesting algebraic, geometric, and spectral properties. On the other hand, such groups can be shown to yield conformal dynamical systems with remarkable geometric and measure-theoretic regularity.

www.unige.ch/~tatiana/Diablerets/Diablerets/home.html

Geometric group theory is a relatively young field with roots in combinatorial group theory and topology. Combinatorial group theory traces back to work of Max Dehn at the beginning of the twentieth century, and focuses on the combinatorial nature of cell complexes associated to groups. In the mid 1980's, spurred by ideas of Gromov, group theorists began to pay attention to the geometric structures which cell complexes can carry. This attention shed a great deal of light on the earlier combinatorial and topological investigations into group theory, and stimulated other innovative ideas which have been developing at a rapid pace. As it has grown over the past 20 years, geometric group theory has developed many different facets, including geometry, topology, analysis, logic. The new, more geometric, perspectives have enabled rapid progress on many of these fronts. A tremendous solidification of previously disparate results has also occurred. Asymptotic behavior of infinite groups has been one of the main themes in geometric group theory since the early nineties. The asymptotic invariants of a group reflect the large-scale geometry of the group. The study of asymptotic properties of groups, inspired by asymptotic geometry, has proved itself to be very profitable for group theory and its applications. Interest in the asymptotic behavior of infinite groups is motivated by numerous applications of the group theory. For a given group, the large-scale approach allows one to distinguish between the typical properties of large subsets of the group and exceptional cases which one can disregard in many applications. Group actions and dynamical systems is a new area of group theory based on recently discovered connections between the theory of groups acting on rooted trees and dynamical systems. On the one hand, conformal dynamical systems yield a rich source of such groups with interesting algebraic, geometric, and spectral properties. On the other hand, such groups can be shown to yield conformal dynamical systems with remarkable geometric and measure-theoretic regularity. This connection is established by means of the theory of Gromov hyperbolic spaces. Partial results suggest a deep relationship between algebraic properties of groups and geometric properties of dynamical systems. In the past several years there have been dramatic achievements in these areas, representing progress on a number of the most basic and difficult questions in this field. The event gathered more than 70 researchers from all around the world including such renowned group theorists like: Martin Bridson (Oxford), Rostislav Grigorchuk (Texas A&M), Pierre de la Harpe (Geneva), Olga Kharlampovich (CUNY), Alexei Miasnikov (Stevens Insitute of Technology), Paul Schupp (UI Urbana-Champaign), Dan Segal (Oxford).

- Agency
- National Science Foundation (NSF)
- Institute
- Division of Mathematical Sciences (DMS)
- Type
- Standard Grant (Standard)
- Application #
- 1265642
- Program Officer
- Shuguang Wang

- Project Start
- Project End
- Budget Start
- 2013-01-15
- Budget End
- 2014-06-30
- Support Year
- Fiscal Year
- 2012
- Total Cost
- $25,200
- Indirect Cost

- Name
- Stevens Institute of Technology
- Department
- Type
- DUNS #

- City
- Hoboken
- State
- NJ
- Country
- United States
- Zip Code
- 07030