During Fall 2012 there will be a semester-long special program entitled "Free Groups: Algorithms, Geometry and Dynamics" held at the Centre de Recerca Matemà tica (CRM) in Barcelona, Spain. There will be two focused events, (1) a series of advanced courses primarily aimed at graduate students and postdocs tentatively set for the week of September 17-21 and (2) an international conference tentatively set for the week of November 26-30. There has been lately a flurry of activity surrounding the group of outer automorphisms of a free group. During this exciting time in its development, the advanced courses will be aimed to attract future researchers, and to prepare them to attend the subsequent international conference. Postdocs and more advanced graduate students will also be invited to give presentations on their own work. The international conference will bring together many of the top experts, primarily from North America and Europe, to give talks on their research, to share ideas, and to initiate new projects.
Humans are naturally attracted to symmetry, be it a regular hexagonal pattern in a honeycomb, a clever rhyme scheme of a poem or the beautiful tilings in the Alhambra. The symmetries of an object are often the first properties we look for when we encounter something for the first time and try to understand it. A group is a mathematician?s way of defining and thinking about symmetry. Just as a thorough investigation of the integers is important to understand the rational numbers because every rational number is the quotient of two integers, a thorough investigation of free groups is important to understand groups because every group is the quotient of two free groups. Symmetries of free groups are the focus of this international conference and the of advanced courses. Leading mathematicians will be at the conference to discuss current progress in this area and to train younger researchers. Instructors for the advanced courses will prepare notes that will be bounded and subsequently published. More information can be found at the website for the CRM http://www.crm.es and at the conference webiste www.crm.es/Activitats/Activitats/2012-2013/Automorphisms/default.htm
Automorphisms of free groups is a very active research area with active researchers both in the United States and Europe among other places as well. There are many interesting facets regarding automorphisms: Algorithms Dynamics Geometry During fall 2012, a special thematic program was planned at the Centre de Recerca Matemàtica (CRM) in Barcelona, Spain that brought together specialists from around the world to discuss open problems and recently developed tools and techniques for understanding automorphisms of free groups. The thematic program included two focused events: Summer School on Automorphisms of Free Groups: (September 25-29, 2012) Five courses were presented with topic primarily aimed towards algorithmic questions. Instructors and topics: Javier Aramayona and Christopher J. Leininger: Geometric structures on surfaces and geodesic currents Ruth Charney: Automorphisms of right-angled Artin groups Volker Diekert: Locally finite graphs of finite tree width and virtually free groups Saul Schleimer: Hyperbolic groups and straight-line progams Pedro Venture Alves da Silva: Fixed points of virtually free group homomorphisms Conference of Automorphisms of Free Groups: (November 12-16, 2012) Twenty lectures were presented; speaker, titles and abstracts can be found on the conference webpage. This award funded the participation of twenty United States mathematicians. Seven were funded to attend the Summer School program. Of these six were graduate students and one was recent PhD graduate. Thirteen were funded to attend the Conference. Of these, three were graduate students and seven were recent PhD graduates. The remaining were either speakers at the conference or during one of the surrounding activities. Seven of the funded participants were women. This award has helped to initiate new projects including trans-Atlantic collaborations and established connections between junior researchers located in the United States with their European counterparts.
