Speaker: Thomas Oliver
Title: Hyperbolic circles and non-trivial zeros
Abstract: L-functions can often be considered as generating series of arithmetic information. Their non-trivial zeros are the subject of many famous conjectures, which offer countless applications to number theory. Using simple geometric observations in the hyperbolic plane, we will study the relationship between the zeros of L-functions and their characterisation amongst more general Dirichlet series.
Speaker: Ebrahim Patel
Title: From trains to brains: Adventures in Tropical Mathematics.
Abstract: Tropical mathematics uses the max and plus operator to linearise discrete nonlinear systems; I will present its popular application to solve scheduling problems such as railway timetabling. Adding the min operator generalises the system to allow the modelling of processes on networks. Thus, I propose applications such as disease and rumour spreading as well as neuron firing behaviour.