Workshop on mapping class groups of surfaces and outer automorphism groups of free groups

University Of Texas At Austin, Austin TX

Investigators

Abstract

The "Workshop on Mapping Class Groups and Out(F_N)" will be held at the University of Texas, Austin, May 25-30, 2015. This conference brings together experts studying two of the cornerstones of modern geometric group theory and low-dimensional topology: mapping class groups of surfaces and outer automorphism groups of free groups. The ubiquity of these groups throughout mathematics has motivated their study from many perspectives, drawing on and contributing to the development of numerous diverse fields. The workshop will feature six introductory mini-course lectures and 16 research talks by the world's leading experts, describing cutting edge techniques and the latest results in the field. This award partially supports workshop speakers and early career mathematicians. Mapping class groups and outer automorphism groups of free groups have evolved hand-in-hand throughout their long and rich history because of the similarities in their definitions and structure, and because they share much of the same robustness in their individual elements. The imperfect analogy between the two groups has led to many striking developments on one side, which in turn motivate problems on the other. In addition, abstracting the ideas and techniques from the setting of these groups has led to generalizations with applications in many other classes of groups and geometric situations. The lectures will cover a wide array of topics, such as hyperbolicity of associated complexes, quasi-isometric embeddings and distance formulas, connections to right-angled Artin groups and to outer automorphism group of other groups, and algebraic and homological properties, to name a few. Speakers and conference participants will be asked to provide links to topics related to the conference, which will be posted to the website: http://www.math.uiuc.edu/~clein/modoutsched.html