ABSTRACT: The Reshetikhin-Turaev construction associated knot invariants to the data of a simple Lie algebra and a choice of irreducible representation. The Jones polynomial is the most famous example coming from the Lie algebra sl(2) and its two-dimensional representation. In this talk we will explain Cautis-Kamnitzer-Morrison’s novel new approach to studying RT invariants associated to the Lie algebra sl(n). Rather … Read More

ABSTRACT: Y-algebras form a four parameter family of vertex operator algebras associated to Y-shaped junctions of interfaces in N=4 super Yang-Mills theory. One can glue such Y-shaped junctions into the more complicated webs of interfaces. Corresponding vertex operator algebras can be identified with conformal extensions of tensor products of Y-algebras associated to the trivalent junctions of the web by fusions … Read More

ABSTRACT: I will present a surprising relation between knot invariants and quiver representation theory, motivated by various string theory constructions involving BPS states. Consequences of this relation include the proof of the famous Labastida-Marino-Ooguri-Vafa conjecture (at least for symmetric representations), explicit (and unknown before) formulas for colored HOMFLY polynomials for various knots, new viewpoint on knot homologies, a novel type … Read More

ABSTRACT: BPS quivers and Spectral Networks are two powerful tools for computing BPS spectra in 4d N=2 theories. On the Coulomb branches of these theories, the BPS spectrum is well-defined only away from walls of marginal stability, where wall-crossing phenomena take place. Surprisingly, while BPS spectra are ill-defined, there is a lot of information hidden in spectral networks at maximal … Read More