Atiyah Class and Sheaf Counting on Local Calabi-Yau 4 Folds

This course covers the learning outcomes and goals of understanding Donaldson-Thomas invariants of torsion sheaves with 2-dimensional support on a smooth projective surface within a non-compact Calabi Yau fourfold. The course aims to demonstrate how the universal truncated Atiyah class of these codimension 2 sheaves can be reduced to one in specific cases, leading to a connection between fourfold DT theory, reduced DT theory of a threefold, and moduli spaces of sheaves on the base surface. The course teaches the skills of analyzing and relating Atiyah classes, sheaf counting, and moduli spaces in the context of local Calabi-Yau 4-folds. The teaching method involves theoretical discussions and proofs presented by the speaker. This course is intended for individuals interested in advanced topics in algebraic geometry, particularly those focusing on sheaf theory and Calabi-Yau manifolds.