Daniele CAPPELLETTI - Visiting Assistant Professor, University of Wisconsin–Madison - APPROXIMATIONS OF STOCHASTIC MODELS FOR REACTION NETWORKS.

Abstract
Stochastic reaction networks are mathematical models mainly used to describe the time evolution of a system of chemical species undergoing chemical transformations. Despite this being the main application, the models are also fruitfully used in Ecology and Epidemiology. In particular, stochastic reaction networks are continuous time Markov chains whose allowed transitions (potentially infinitely many) are described by a finite set of reactions, or a finite graph. A central part of research in the field concerns linking properties of this graph with dynamical features of the model.
In this seminar, Dr. Cappelletti will formally describe stochastic reaction networks and discuss different possible approximations thereof when the number of molecules is so high that model simulations become cumbersome. He will explain in which sense these approximations hold and what they fail to capture, describe some of his contributions in this setting and illustrate some open problems in the field.

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