Disputation Maximilian Schimpf On the enumerative geometry of local curves

Modern enumerative geometry studies the number of solutions to geometric problems, often employing techniques that trace back to string theory. This thesis focuses on curve counting on threefolds, particularly local curves, which serve as a representative class. The two primary approaches to counting curves—Gromov-Witten theory and stable pair theory—are conjecturally equivalent (known in many cases), and we investigate both for local curves. For stable pairs, we derive fully explicit formulas for all descendent invariants, expressed in terms of the Bethe roots of the quantum intermediate long wave system. On the Gromov-Witten side, we propose a connection between curve counts and quasi-Jacobi forms and provide supporting evidence for this conjecture.