Quiver Structures of Knot Invariants, Open Strings, and Recursion

Explore the intricate connections between knot theory, string theory, and quiver structures in this advanced mathematics lecture. Delve into the fascinating relationship between generating series of HOMFLY-PT polynomials and partition functions of motivic Donaldson-Thomas invariants of symmetric quivers. Examine the string theory interpretation of this correspondence, focusing on M2 brane interactions mediated by an M5 brane. Investigate how invariance under deformations leads to a generalization of the knots-quivers correspondence, supported by wall-crossing phenomena associated with skein relations. Learn about potential extensions to multiple M5 branes, based on collaborative research with Ekholm, Kucharski, and Nakamura. This hour-long talk by Pietro Longhi from Uppsala University offers a deep dive into cutting-edge mathematical concepts at the intersection of knot theory and string theory.