Seminars, for informal dissemination of research results, exploratory work by research teams, outreach activities, etc., constitute the simplest form of meetings at a Mathematics research centre.
CAMGSD has recorded the calendar of its seminars for a long time, this page serving both as a means of public announcement of forthcoming activities but also as a historic record.
The human brain exhibits cryptic spatiotemporal dynamics that can be investigated through the lens of coupled dynamical systems and spectral decomposition methods. In this talk, I will present how concepts from harmonic analysis, Markov processes, and oscillatory dynamics provide a rigorous mathematical framework for deciphering the hidden rules governing large-scale brain organisation.
More precisely, I will show how brain patterns switch as a Markov process; how eigenmodes exhibit damped oscillatory motion; and how collective rhythms emerge from metastable synchronisation. This work illustrates a bidirectional bridge: mathematical formalisms illuminate neuroscience phenomena, while brain data offers concrete applications for advancing theoretical frameworks—ultimately enabling us to understand the dynamical principles underlying cognitive function, consciousness and mental health.
I will first introduce the bigraded cohomology for real algebraic varieties developed by Johannes Huisman and Dewi Gleuher. This is a cohomology theory that refines the equivariant cohomology "à la Kahn-Krasnov" of the complex points of a real variety, the latter often being preferred (by the algebraic geometers) in the cohomological study of real algebraic varieties. Since the construction of this bigraded cohomology and its associated characteristic classes relies on the sheaf exponential morphism, I will explain how to produce an arithmetic (or algebraic) variant of these cohomology groups, whose main advantage is toeliminate topological or transcendental conditions. I will conclude by comparing these two versions of bigraded cohomology.
