Martedi' 13 novembre alle 9,30 in Aula Buzano (Politecnico di Torino, DISMA) il prof Badal Joshi (California State University San Marcos) terrà un seminario dal titolo Graphical symmetries of reaction networks and their stationary measures Abstract: Reaction networks are used to model chemical reactions, biochemical reactions, interacting populations in ecology, genetics and infectious disease dynamics among many other systems. Depending on the system scale, three most commonly used models are continuous-time Markov chain (CTMC), stochastic differential equations and ordinary differential equations (ODE). With increased data and scientific focus shifting towards biochemistry which often involves populations as small as few tens of molecules, CTMC models have seen dramatic increase in relevance. The long-term dynamics of a continuous-time Markov chain model are described by its stationary distribution. In general, the explicit form of the stationary distribution is impossible to obtain even for very small networks. However, when the network has some natural symmetries, we can obtain the explicit stationary distribution and it can be connected with the equilibria of the corresponding ODE system. We will discuss the symmetries of reaction balance, complex balance, reaction vector balance, and cycle balance and their properties in both the deterministic (ODE) setting and stochastic (CTMC) setting. We will also discuss the relations between the various forms of balance and the connection with existence and form of the stationary distribution. Cordialmente, Enrico Bibbona Probability, Statistics and Optimization group Department of Mathematical Sciences "G. L Lagrange" Politecnico di Torino