School and Workshop on Geometry Discrete Actions - ICTP

Howard University, Washington DC

Investigators

Abstract

The School and Workshop on the Geometry of Discrete Group Actions will be held at the International Centre for Theoretical Physics from 24 August to 4 September, 2015 in Trieste, Italy. Discrete group actions can be thought of as extensions of tilings that you might see on walkways or the configurations of molecules found in crystals. This field of mathematics continues to evolve and surprise. During he first week of the activity (the school), international experts in the field will give several mini-courses for young researchers from across the globe. The workshop, held during the second week, will be where established researchers will exchange their newest results in this field. Both activities will enhance communication between researchers from the U.S. and the rest of the world, especially young researchers from historically underrepresented groups and countries. The Abdus Salam International Centre for Theoretical Physics will host the School and Workshop on Geometry Discrete Actions from 24 August to 4 September 2015 in Trieste, Italy. The organizers of the school and workshop are Bertran Deroin (Ecole Normale Superieure, France), Todd A. Drumm (Howard University, DC, USA), John Parker (University of Durham, UK), and Jose Seade (Universidad Nacional Autonoma de Mexico, Mexico). Discrete actions on geometric spaces are of historic and current interest in mathematics. Students of mathematics are often first introduced these ideas with tilings of the plane, but the complexity of the actions and the geometries considered have been expanded on many times over. The interconnections between seemingly disparate schools of thought are a hallmark of this field, as is the interaction between the geometric and more dynamical properties of the discrete actions. The relatively newer studies of Character Varieties and Higher Teichmuller Theory are a natural and fertile continuation of this tradition. The general themes for this activity were inspired by the Sullivan-McMullen dictionary in complex dimension 2. This school and workshop will be a unique blend of complex geometry, hyperbolic geometry, and Lorentzian geometry. The purpose of this activity is to introduce young mathematicians to the themes of this activity and present some of recent developments in these fields of study. The school will consist of 5 short courses will include courses on Hyperbolic Surfaces, Lorentzian Geometry, Complex Hyperbolic Geometry< Kleinian Groups, and Character Varieties. These courses will be aimed at the upper graduate student level and will serve as an introduction to current research. The workshop, held during the second week of the activity, will concentrate on new results by invited researchers. Young mathematicians and established researchers will benefit from seeing presentation on the latest results. At the end of the conference, a session will be devoted to open problems related to the themes of the activity. The interaction between researchers working in developing countries, European researchers and U.S.-based researchers is an especially important part of activity. The location of the school at workshop at ICTP, whose website <www.ictp.it> contains additional information about the institute, plays a vital role in this mission.