Karen Vogtmann
University of Warwick
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Primary Section: 11, Mathematics Membership Type:
Member
(elected 2022)
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Biosketch
Karen Vogtmann is a mathematician working in topology and algebra. She is known for introducing new topological and geometric models for the study of infinite discrete groups and has had a particularly strong influence on the modern approach to automorphism groups of free groups. Born in California, Vogtmann lived in Washington state and Chicago before returning to California for college. She received a B.A. in 1971 and a Ph.D. in 1977, both in mathematics from the University of California at Berkeley. After positions at Michigan, Brandeis, and Columbia she took a tenure-track position at Cornell University. In 2011 she become the Goldwin Smith Professor of Mathematics at Cornell. She moved to the University of Warwick in 2014. Vogtmann has served as Vice President of the American Mathematical Society and as chair of its Board of Trustees. She was awarded the Polya Prize of the London Mathematical Society and the Humboldt Forschungspreis. She is a Fellow of the Royal Society and was an inaugural Fellow of the American Mathematical Society, as well as a member of the National Academy of Sciences.
Research Interests
Karen Vogtmann is interested in constructing geometric objects on which various infinite discrete groups act as symmetries. She then studies the geometry and topology of these spaces to obtain structural information about the groups. She has had notable success in this direction with an object now known as Outer space, whose symmetries encode the group of outer automorphisms of a free group. Points in Outer space correspond to finite metric graphs. This leads to connections with many areas of mathematics and science, including the study of phylogenetic trees, perturbative quantum theory and tropical algebraic geometry. Vogtmann is exploring these connections as well as continuing to derive applications to group theory. She is also developing analogous spaces for other automorphism groups, most recently for outer automorphism groups of right-angled Artin groups.
