Donaldson-Thomas and Gromov-Witten Theories

Explore advanced mathematical theories through this comprehensive lecture series covering Donaldson-Thomas and Gromov-Witten invariants across various geometric contexts. Delve into the modularity properties of DT invariants on smooth K3 fibrations through detailed two-part presentations, then examine how these concepts extend to nodal fibrations and conifold transitions. Study stable pair PT invariants on both smooth and nodal fibrations, gaining insight into their computational methods and theoretical foundations. Investigate the relationship between DT and MNOP invariants, understanding their connections and differences in algebraic geometry. Conclude with an in-depth exploration of the S-duality conjecture on quintic threefolds, including rigorous proof techniques presented across two comprehensive sessions, providing essential knowledge for researchers and advanced students in algebraic geometry and mathematical physics.