Claire Guerrier - Mathematical modeling and multiscale simulations for vesicular release at neuronal synapses Synaptic microdomains are underlying fundamental and yet not completely understood functions, such as learning and memory, breathing, sleeping, and many more. Motivated by understanding and analyzing these neuronal structures, we built a model to study vesicular release at synapses. As a first step, we computed the mean time for a Brownian particle to arrive at a narrow opening defined as the small cylinder joining two tangent spheres. The method relies on Möbius conformal transformation applied to the Laplace equation. We also estimated, when the particle starts inside a boundary layer near the hole, the splitting probability to reach the hole before leaving the boundary layer, which is also expressed using a mixed boundary-value Laplace equation. Using these results, we developed model equations and their corresponding stochastic simulations to study vesicular release at neuronal synapses, taking into account their specific geometry.