Higher Rank DT/PT Wall-Crossing in Bridgeland Stability

Explore higher rank Donaldson-Thomas/Pandharipande-Thomas wall-crossing phenomena through Bridgeland stability conditions in this mathematical seminar lecture. Discover how the Gieseker moduli space of stable sheaves on smooth projective threefolds with Picard rank 1 relates to PT stable objects through a single wall separation in Bridgeland stability space. Learn about the theoretical framework that realizes the higher rank DT/PT correspondence as a wall-crossing phenomenon, examining the mathematical structures and proofs that establish this connection. Gain insights into advanced topics in algebraic geometry including moduli spaces, stability conditions, and their applications to understanding geometric invariants and their relationships.