As a distinct area, geometric group theory is relatively new, and became an identifiable branch of mathematics in the early 1990's. Geometric group theory closely interacts with low-dimensional topology, hyperbolic geometry, Lie groups and homogeneous spaces, algebraic topology, computational group theory, and differential geometry. There are also substantial connections with complexity theory, mathematical logic, dynamical systems, probability theory, K-theory, and other areas of mathematics.
Group theory is an abstract subject, but it is also the mathematical way to investigate symmetry. Thus many problems from various areas of mathematics which involve some sort of symmetry are susceptible to the application of group theory. In this proposal we plan to cover three main areas: the abstract structure of finite groups; some geometrical aspects of group theory; and several recent applications of group theory to other areas of mathematics.
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