Lower Dimensional Betti Numbers of Homogeneous Spaces of Lie Groups

Explore the intricacies of lower dimensional Betti numbers in homogeneous spaces of Lie groups in this 26-minute lecture by Pralay Chatterjee. Part of the "Zariski Dense Subgroups, Number Theory and Geometric Applications" program at the International Centre for Theoretical Sciences, this talk delves into advanced mathematical concepts at the intersection of algebraic topology and Lie theory. Gain insights into how Betti numbers characterize the topological structure of these spaces and their significance in understanding the geometry of Lie groups. Suitable for graduate students and researchers in mathematics, this lecture contributes to the broader program's goal of surveying recent progress in arithmetic and Zariski-dense subgroups, with applications to various areas of mathematics including algebraic and differential geometry.