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Leonidas Alaoglu Memorial Lecture 4:15 p.m. 151 Sloan Karen Vogtmann Geometries for automorphism groups of free groups Abstract: Finitely generated free groups are the simplest, most basic class of infinite groups, but their automorphism groups are remarkably complex, and many natural questions about their structure remain unanswered. There are a variety of beautiful geometric objects on which these groups act, but there are also rigidity phenomena which restrict the type of objects with any sort of nontrivial action by these groups. I will describe some of the spaces with nice actions and some with no actions, then show how this geometric information can be leveraged into algebraic information about automorphism groups of free groups.
Karen Vogtmann is a professor of mathematics at Cornell University, working in geometric group theory. Her main focus in recent years has been studying the group of outer automorphisms of a free group, via its action on a geometric object called Outer Space. This space has surprising connections with other areas of mathematics, from infinitedimensional Lie algebras to phylogenetic trees. Vogtmann has held research positions at the Mathematical Sciences Research Institute at Berkeley, the Institute for Advanced Study at Princeton and the Institut des Hautes Etudes Scientifique in France. She is currently a trustee of the American Mathematical Society, and previously served as Vice President of the Society. She has served on scientific advisory boards of the American Institute of Mathematics and the Mathematical Sciences Research Institute and the arXiv advisory board, as well as many other national and international committees. In 2006 she gave an invited address at the International Congress of Mathematicians in Madrid, and in 2007 gave the Emmy Noether Lecture at the annual meeting of the AMS in New Orleans.
Host bar 5:45 p.m. Reservations Required MENU Hearts of Romaine Classic CaesarMushroom and Truffle Chicken Breast Berries Athenaeum Please indicate if you require a vegetarian or kosher meal For reservations, please contact Stacey V. Croomes at 6263954336 or send payment by May 2, 2008 made out to Caltech for $35.00 per person to: Stacey V. Croomes Caltech 25337
The Leonidas Alaoglu Memorial Lecture was established by friends and family of the late Leonidas Alaoglu in recognition of his great talents, distinguished contributions to mathematics, and long friendship with Caltech. The Institute is privileged to honor his memory with a lecture each year by an outstanding mathematician. 
