The picture you see on the left is a braid, which you can think of as strings of wire weaving around each other, without backing up.
Braids play an important role in our research.
Backing up a bit, the subject of our poster is the interplay between the topology, geometry, and combinatorics of subspace arrangements. Our research draws on a variety of techniques from algebraic and geometric topology, algebraic geometry, singularities, combinatorial group theory, and computational algebra. The emphasis is on finding effectively computable invariants of the complements of arrangements, with a view towards a complete homotopy classification. In the process, we discover subtle and varied differences between such arrangements and complex hyperplane arrangements. These phenomena may be thought of as manifestations of the non-complex nature of real arrangements, revealed through the geometry of the fundamental group of the complement.