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# Applied Mathematics Colloquium – Gadi Fibich (School of Mathematical Sciences, Tel Aviv University)

## March 19 @ 3:30 pm - 4:30 pm

**Spreading of Innovations on Networks**

**Abstract**. Spreading (diffusion) of new products is a classical problem. Traditionally, it has been analyzed using the compartmental Bass model, which implicitly assumes that all individuals are homogeneous and connected to each other. To relax these assumptions, research has gradually shifted to the more fundamental Bass model on networks, which is a particle model for the stochastic adoption by each individual.

In this talk I will review the emerging mathematical theory for the Bass model on networks. I will present analytic tools that enable us to obtain explicit expressions for the expected adoption level on various networks (complete, circular, d-regular, Erdos-Renyi, …), without employing mean-field type approximations. The main focus of the talk will be on the effect of network structure. For example, which networks yield the slowest and fastest adoption? What is the effect of boundaries? Of heterogeneity among individuals?