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

Explore Donaldson-Thomas invariants of torsion sheaves in a lecture on Atiyah Class and Sheaf Counting on Local Calabi-Yau 4 Folds. Delve into the study of sheaves with 2-dimensional support on smooth projective surfaces within non-compact Calabi-Yau fourfolds. Examine cases where the universal truncated Atiyah class of codimension 2 sheaves reduces to one defined over the moduli space of torsion codimension 1 sheaves in embedded noncompact divisors. Discover how this reduction property relates fourfold Donaldson-Thomas theory to reduced threefold Donaldson-Thomas theory and moduli spaces of sheaves on base surfaces. Investigate predictions about the modularity of fourfold invariants when the base surface is an elliptic K3. Gain insights from Harvard University CMSA/University of Miami/IMSA affiliated speaker Artan Sheshmani in this 69-minute advanced mathematics presentation.