Universally Counting Curves in Calabi-Yau Threefolds

Explore the cutting-edge developments in enumerative geometry through this 57-minute lecture by John Pardon from Stony Brook University. Delve into a new perspective on enumerative invariants based on the "Grothendieck group of 1-cycles" and the "universal" curve enumeration invariant. Discover how this approach simplifies the structure of complex threefolds with nef anticanonical bundle, revealing that it is generated by "local curves." Learn about the implications of this generation result, including new cases of the MNOP conjecture relating Gromov--Witten and Donaldson--Pandharipande--Thomas invariants of complex threefolds. Gain insights into the evolution of enumerative geometry from classical statements to modern theories, and understand the challenges in defining curve counts in general settings.

John Pardon, Stony Brook: Universally counting curves in Calabi--Yau threefolds