Sheaves on Calabi-Yau 4-folds and Virtual Invariants - An Overview

Explore the enumerative geometry of Calabi-Yau 4-folds in this comprehensive 1-hour 7-minute lecture by Martinus Kool at BIMSA. Delve into the developments made possible by the Borisov-Joyce/Oh-Thomas virtual class, examining how these advancements extend beyond traditional Gromov-Witten and Donaldson-Thomas invariants of Calabi-Yau 3-folds. Discover how point counting on Calabi-Yau 4-folds relates to Nekrasov's Magnificent Four formula in physics, and learn about curve counting's connection to Gromov-Witten invariants. Investigate surface counting on both non-compact and compact Calabi-Yau 4-folds, exploring its links to Nekrasov's gauge origami and the variational Hodge conjecture. Gain insights from Kool's collaborative works with Arbesfeld-Lim, Bae-Park, Cao-Monavari, and Rennemo in this cutting-edge exploration of string theory and enumerative geometry.