The proposal is asking for travel support for US based graduate students and postdoctoral mathematicians to attend a major conference in geometric group theory. This is a great opportunity for these junior mathematicians to familiarize themselves with the frontiers of research in this very active subject and in the future contribute to it. In addition, many of the participants (e.g. two of the main speakers) are anticipated to be women. Based on initial inquiries, it is also likely that several of US based mathematicians that will be supported on this grant, if funded, will be women.
Geometric group theory is a relatively new area of mathematics whose object is study groups by first constructing a geometric object whose symmetries form the given group and then to analyze the geometry of this object. An important example of this is the group of symmetries of a free group, realized geometrically as the so called "Outer space", constructed by Culler and Vogtmann.
This award was used to fund travel of junior US-based mathematicians to a conference in geometric group theory at Luminy, France in June 2010. The subject of the conference is a relatively new area of mathematics that belongs to both algebra and geometry. It studies symmetries (the collection of all of them is called the symmetry group) of geometric shapes, and most notably, frequently reverses this process and constructs a geometric shape with prescribed symmetry groups. Symmetry groups are ubiquitous in mathematics, physics and other sciences, and the field of geometric group theory studies them systematically and for their own sake. The conference featured 23 talks by top experts in this field and had 98 participants from many countries. The list of talks and participants can be found at the conference web page www.math.utah.edu/vogtmannfest The award was used to partially support junior US-based mathematicians. They benefited from interaction with the top experts in the field. The talks covered a wide range of topics within the field, and many new results were presented. For example, one of the lectures was on "distortion" of one symmetry group within another and the consequences this has for the original geometric shapes. Another discussed symmetry groups associated with a system of mirrors, for example arising in rooms with all four walls mirrors, where an observer sees an infinite collection of his own images arranged in a particular pattern.
