Karen Vogtmann FRS (born July 13, 1949 in Pittsburg, California[1]) is an American mathematician working primarily in the area of geometric group theory.

Vogtmann was inspired to pursue mathematics by a National Science Foundation summer program for high school students at the University of California, Berkeley.

[4][7] She has been elected to serve as a member of the board of trustees of the American Mathematical Society for the period February 2008 – January 2018.

[8][9] Vogtmann is a former editorial board member (2006–2016) of the journal Algebraic and Geometric Topology and a former associate editor of Bulletin of the American Mathematical Society.

[18] On June 21–25, 2010 a 'VOGTMANNFEST' Geometric Group Theory conference in honor of Vogtmann's birthday was held in Luminy, France.

[32] Vogtmann's early work concerned homological properties of orthogonal groups associated to quadratic forms over various fields.

[33][34] Vogtmann's most important contribution came in a 1986 paper with Marc Culler called "Moduli of graphs and automorphisms of free groups".

Points of Xn can also be thought of as free and discrete minimal isometric actions Fn on real trees where the quotient graph has volume one.

By construction the Outer space Xn is a finite-dimensional simplicial complex equipped with a natural action of Out(Fn) which is properly discontinuous and has finite simplex stabilizers.

[37][38][39][40] Much of Vogtmann's subsequent work concerned the study of the Outer space Xn, particularly its homotopy, homological and cohomological properties, and related questions for Out(Fn).

In her papers with Conant,[43][44][45] Vogtmann explored the connection found by Maxim Kontsevich between the cohomology of certain infinite-dimensional Lie algebras and the homology of Out(Fn).

The paper of Billera, Vogtmann and Holmes produced a method for quantifying the difference between two evolutionary trees, effectively determining the distance between them.