Homology Planes and Fundamental Groups

Explore the intricacies of homology planes and fundamental groups in this hour-long lecture by Rodolfo Aguilar from the University of Miami. Delve into the results surrounding the fundamental group of homology planes, focusing on smooth, affine complex surfaces with trivial reduced homology. Learn about an algorithm for computing a presentation of the fundamental group when homology planes arise from line arrangements. Discover potentially groundbreaking examples of homology planes of log-general type with infinite fundamental groups. The lecture covers topics such as introduction, cancellation, analytic Ramanujan surface, classification, countable number, fundamental group, applications, and concludes with a Q&A session.