Abstract: Topology is one of the oldest and more relevant branches of mathematics, and it has provided an expressive and affordable language which is progressively pervading many areas of mathematics, computer science and physics.
Using examples taken from work drug-altered brain functional networks, I will illustrate the type of novel insights that algebraic topological tools are providing in the context of neuroimaging.
I will then show how the comparison of homological features of structural and functional brain networks across a large age span highlights the presence of a globally conserved topological skeletons and of a compensation mechanism modulating the localization of functional homological features. Finally, with an eye to altered cognitive control in disease and early ageing, I will introduce preliminary theoretical results on the modelization of multitasking capacities from a statistical mechanical perspective and show that even a small overlap between tasks strongly limits overall parallel capacity to a degree that substantially outpaces gains by increasing network size.
This is a joint talk with the "Complex systems" seminar series.