Explore the intricacies of Heegaard Floer homology and its applications in topology across dimensions 3.5 to 1 in this comprehensive lecture from the Frontiers in Geometry and Topology Summer School. Delivered by renowned speaker Jen HOM from Georgia Tech, USA, this 1 hour and 35 minute presentation delves deep into the mathematical concepts and their implications in the field. Gain valuable insights into this advanced topic and its relevance in modern topology research.