Talks

Hopf algebra lattice models are related to certain topological quantum field theories and give rise to topological invariants of oriented surfaces. Examples are the combinatorial quantisation of Chern-Simons theory and the Kitaev model.
Our main result is the construction of a mapping class group action on these models, formulated under weaker assumptions than the associated topological quantum field theories, namely for pivotal Hopf algebras in symmetric monoidal categories. This description also yields new structures for semisimple finite-dimensional Hopf algebras. The action of the mapping class group is defined in terms of simple graph transformations and allows one to compute quantum Dehn twists explicitly.

With the detection of GW170817 we have observed the first multi messenger signal from two merging neutron stars. This signal carried a multitude of information about the underlying equation of state (EOS) of nuclear matter, which so far is not known for densities above nuclear saturation. In particular it is not known if exotic states or even a phase transition to quark matter can occur at densities so extreme that they can't be probed by any current experiment.

I will show how the information carried in the gravitational wave signal of GW170817 can be used to constrain the EOS at densities above saturation and what we can learn about the possible existence of phase transitions. I will
also comment on how we can improve on those limits with upcoming observations of the NICER mission.In the second part of the talk I will focus on what we can learn about exotic states of matter from neutron star mergers.I will comment briefly on the impact of high spins in mergers and the importance of accurate numerical modelling in the context of these studies.Finally I will show how neutron star mergers can be used to study quark phase transitions and the phase diagram of QCD.