Explore the fascinating world of infinite groups, their ℓ2-homology, and boundaries in this comprehensive lecture by Genevieve Walsh from Tufts University. Delve into the first part of a minicourse presented at the International Centre for Theoretical Sciences as part of the "Geometry in Groups" program. Gain insights into active areas of geometric group theory, strengthening your understanding of this rapidly growing field. Learn from an eminent researcher known for her exposition, and discover connections between geometry, topology, dynamics, analysis, and probability. Engage with complex mathematical concepts and expand your knowledge of infinite groups and their properties in this 1-hour 18-minute session, designed to increase exposure to cutting-edge research in geometric group theory.