## Conference on reaction networks and population dynamics in Oberwolfach

This is a belated report on a conference in Oberwolfach I attended a couple of weeks ago. The title includes two elements. The first held no suprises for me but the second was rather different from what I had expected. My expectation was that it would be about the evolution of populations of organisms. In fact it was rather focussed on models related to genetics, in other words with the question of how certain genetic traits spread through a population.

I want to mention one statement made in the talk of Gheorghe Craciun in Oberwolfach which I found intriguing. I might have heard this before but it did not stick in my mind properly. The statement is that the set of dynamical systems which possess a complex balanced steady state is a variety of codimension $\delta$, where $\delta$ is the deficiency. There seemed to be some belief in the audience that this variety is actually a smooth manifold. On one afternoon we had something similar to the breakout sessions in Banff. I suggested the topic for one of these, which was Lyapunov functions. The idea was to compare classes of Lyapunov functions which people working on different classes of dynamical systems knew. This certainly did not lead to any breakthrough but I think it did lead to a useful exchange of information. I documented the discussion for my own use and I think I could profit by following some of the leads there.
To finish I want to mention a claim made by Ankit Gupta in his talk. It did not sound very plausible to me but I expect that it at least contains a grain of truth. He said that these days more papers are published on $NF\kappa B$ than on all of mathematics.