Interaction with homological and quantum algebra, representation theory, geometry, and computation has led to great leaps in low-dimensional topology over recent years. Examples include the program aimed at disproving the smooth four-dimensional Poincare conjecture; the emergence of polynomial-time computable knot polynomials; and topological approaches to problems in Lie theory. The synthesis of breakthrough ideas that led to these advances demonstrates the need for close collaboration between the adjacent research communities. This conference will bring together Swiss and international mathematicians to facilitate exchange and build new connections between researchers in low-dimensional topology and related fields.
