Triangle Seminars

Abstract:
The decade 1963-1973 is sometimes referred to as the 'golden age' of black hole
research. Mathematical theorems proved in this period led to a complete
classical description of equilibrium black holes in four space-time dimensions.
More recently, string theory has forced us to take seriously the possibility of
extra spatial dimensions. Thinking about black holes in more than four
dimensions has led to spectacular advances in our understanding of quantum
gravity. In the last five years, we have learned that higher-dimensional black
holes exhibit much richer behaviour than four-dimensional ones, even
classically. I shall review the discoveries of this new 'silver age' of black
hole research. The talk should be accessible to MSc students.

Abstract:
In my talk, I shall present results that have been obtained in collaboration with Tini Garske, on mutation-selection models which describe the evolution of two- or four-letter sequences. Mutation is modelled as a Markov process, and selection is introduced via a fitness function, which assigns a reproductive fitness to each sequence. We consider permutation-invariand fitness functions, or, more generally, Hopfield-type fitness functions, where the fitness is determined by the overlap with a number of given reference sequences. For infinite sequence length, the equilibrium properties of the sequence space models can be determined from a simple maximum principle, which also proves to be a good approximation for the case of finite sequence length.