Universally Counting Curves in Calabi-Yau Threefolds - ICBS 2024

Explore a groundbreaking lecture on enumerative geometry and curve counting in complex threefolds. Delve into the foundations of modern enumerative geometry, from basic concepts like unique lines between points to more complex ideas such as the 27 lines on smooth cubic surfaces. Discover a novel approach to enumerative invariants based on the "Grothendieck group of 1-cycles" and a universal curve enumeration invariant. Learn how this new perspective simplifies the structure of curve counting in complex threefolds with nef anticanonical bundle, revealing that the group is generated by "local curves". Understand the implications of this generation result, including new cases of the MNOP conjecture that relates Gromov-Witten and Donaldson-Pandharipande-Thomas invariants. Gain insights into cutting-edge mathematical research presented by John Vincent Pardon at the International Congress of Basic Science 2024, offering a fresh perspective on curve counting in Calabi-Yau threefolds.