North meets South colloquium

9 November 2018
Cristina Palmer-Anghel and Francis Woodhouse

Cristina Palmer-Anghel: Quantum invariants via topological intersection pairings
The world of quantum invariants for knots started in 1984 with the discovery of a strong link invariant, namely the Jones polynomial. Then, Reshetikhin and Turaev developed a conceptual algebraic method that, starting with any quantum group, produces invariants for knots. The question that we have in mind is to find topological models for certain types of quantum invariants. On the topological side, in 2000, Bigelow, building on earlier work of Lawrence,
interpreted the original Jones polynomial in a homological manner- as a graded intersection pairing in a covering of a configuration space of the punctured disc. On the quantum side of the story, the coloured Jones polynomials are a sequence of quantum invariants constructed through the Reshetikhin-Turaev recipe from the quantum group Uq(sl(2)). The first invariant of this sequence is the original Jones polynomial. In this talk we will present how one can use topological intersection pairings in order to describe a topological model for all coloured Jones polynomials.

Francis Woodhouse: Autonomous mechanisms inspired by biology

Unlike the air around us, biological systems are not in equilibrium: cells consume chemical energy to keep growing and moving, forming a clear arrow of time. The recent creation of artificial versions of these ‘active’ materials suggests that these concepts can be harnessed to power new soft robotic systems fuelled by as simple a source as oxygen. After an introduction to the physics of natural and artificial active systems, we will see how endowing a mechanical network with activity can create an intricate self-actuating mechanism.