Homological Mirror Symmetry - Counting Curves on Calabi-Yau Threefolds

Explore the intricacies of counting curves in Calabi-Yau threefolds in this 54-minute lecture by John Pardon from the Simons Center at Stony Brook. Delve into the Grothendieck group of Calabi-Yau 1-cycles on almost complex threefolds, understanding its role as the "universal" method for curve counting. Examine recent advancements in the Gopakumar-Vafa conjecture by Ionel-Parker and Doan-Ionel-Walpuski, and learn how to adapt these concepts to complex threefolds. Discover how the MNOP conjecture, linking Gromov-Witten and Donaldson-Thomas/Pandharipande-Thomas invariants of complex Calabi-Yau threefolds, can be derived from local Calabi-Yau cases, as demonstrated by Bryan-Pandharipande and Okounkov-Pandharipande. Gain insights into this ongoing research in the field of Homological Mirror Symmetry.