**abstract:**
Volume transmission is a fundamental neural communication
mechanism in which neurons in one brain nucleus modulate the
neurotransmitter concentration in the extracellular space of a second
nucleus. In this talk, we will describe a mathematical model of volume
transmission involving the diffusion equation in a bounded
three-dimensional domain with a set of interior holes that randomly switch
between being either sources or sinks. The interior holes represent nerve
varicosities that are sources of neurotransmitter when firing an action
potential and are sinks otherwise. To analyze this random PDE, we will show
that its solution can be represented as a certain local time of a Brownian
particle in a random environment, and that this representation can be used
to prove surprising properties of the solution.

More broadly, we will explain how this probabilistic perspective on Brownian functionals relates to recent results on escape problems involving mean first passage times of diffusion and asymptotic analysis of PDEs.

Wed 26 Sep, 9:30 - 10:35, Aula Dini

<< Go back