Graph Braid Groups Exterior Face Algebras and Differential Forms

I am a geometric group theorist. Geometric group theory is a highly interdisciplinary field focusing on the study of groups via their actions on geometric spaces. Geometric group theory uses the tools and approaches of algebraic topology, commutative algebra, semigroup theory, hyperbolic geometry, geometric analysis, combinatorics, computational group theory, computational complexity theory, logic, dynamical systems, probability theory, and other areas. It is a young and fast-growing field, with much of the work in the area accomplished within the past 30 years.