**Abstract** : The main objective of the field of Computational Neuroscience is to understand how the brain works through mathematical models (numerical and analytical works). Some of these models are described by neural fields equations. Neural fields are integro-differential equations that describe the spatiotemporal dynamics of the activity of a piece of neocortical tissue. Neural fields equations emerge when one assimilates the high number of neurons of the selected piece of brain tissue in its continuum limit. Neural fields have been studied both analytically and numerically by many researchers. They can model many different and interesting biological phenomena such as attention, working memory, self-organization, or synaptic depression. The seminar consists of two parts. The first part is a brief introduction to neuroscience and the second part is dedicated to neural fields. We will review how neural fields equations can be derived, how the steady-state solution can be computed, and its stability can be insured. Finally, some cognitive models that are based on neural fields will be presented.

__Bio__ : Georgios Detorakis has studied Applied Mathematics and Neuroscience. He did his PhD on cortical plasticity, self-organization and neural fields. During his PhD, he studied the formation of topographic maps in area 3b of the primary somatosensory cortex and the multimodal problem of “Touch and the body”. He is now a postdoc fellow at L2S working with Antoine Chaillet on Parkinson’s disease in the ANR project "SynchNeuro". He uses delayed neural fields in order to model some brain areas that play a crucial role in Parkinson’s disease motor symptoms.