Monday, April 24, 2023 - 3:45pm to 4:45pm
École Polytechnique Fédérale de Lausanne
In this lecture, I will take you on a mathematical mystery tour of the marvelous intricacy of the brain, during which you will see that applying the tools of that part of pure mathematics known as algebraic topology to neuroscientific data reveals fascinating, complex structures in the brain, enabling us moreover to start to understand the role that these structures play in brain function. I will focus on explaining how topology enables us to discern meaningful patterns in the incredibly intricate network of cells of which the brain is composed, not to mention the highly complex network of blood vessels that provide oxygen and nutrients to the cells. To avoid being overwhelmed by the complexity of the fully detailed network, we will apply a trick familiar to all mathematicians, often known as dimensionality reduction. We will choose to focus on only certain key elements of the networks, obtaining thus a highly simplified representation of the full structure. Most of the work I will describe has been carried out in cooperation with the Blue Brain Project at EPFL.