Uploaded April 2026 | Updated September 2026, 2 weeks ago
Speaker: Sachin Chauhan (Uppsala University)
Abstract: In joint work with Tobias Ekholm and Pietro Longhi, we study open topological strings with branes wrapping knot complements. Using skein-valued holomorphic curve counting, we show that the corresponding partition function can be organised in terms of flow loops in the knot complement, giving a flow-loop formula in both T*S^3 and the resolved conifold. For torus knots, this simplifies dramatically: the full partition function localizes to contributions from only two or three holomorphic annuli, which in turn leads to a generalized quiver description. We also show how this construction is tied to the augmentation curve through a quantized augmentation polynomial that annihilates the gl_1-skein partition function. This provides a new geometric coordinate chart on the corresponding D-module.
Speaker: Sachin Chauhan (Uppsala University)
Abstract: In joint work with Tobias Ekholm and Pietro Longhi, we study open topological strings with branes wrapping knot complements. Using skein-valued holomorphic curve counting, we show that the corresponding partition function can be organised in terms of flow loops in the knot complement, giving a flow-loop formula in both T*S^3 and the resolved conifold. For torus knots, this simplifies dramatically: the full partition function localizes to contributions from only two or three holomorphic annuli, which in turn leads to a generalized quiver description. We also show how this construction is tied to the augmentation curve through a quantized augmentation polynomial that annihilates the gl_1-skein partition function. This provides a new geometric coordinate chart on the corresponding D-module.
