Starting with a gentle approach to the Alday–Gaiotto–Tachikawa (AGT) correspondence
from its 6d origin, these notes provide a wide (albeit shallow) survey of the literature on …

If a knot is represented by an m‐strand braid, then HOMFLY polynomial in representation R
is a sum over characters in all representations Q∈ R⊗ m. Coefficients in this sum are traces …

A bstract The colored HOMFLY polynomials, which describe Wilson loop averages in Chern-
Simons theory, possess an especially simple representation for torus knots, which begins …

A bstract Character expansion is introduced and explicitly constructed for the (noncolored)
HOMFLY polynomials of the simplest knots. Expansion coefficients are not the knot …

A bstract Explicit answer is given for the HOMFLY polynomial of the figure eight knot 4 1 in
arbitrary symmetric representation R=[p]. It generalizes the old answers for p= 1 and 2 and …

We study the connection between topological strings and contact homology recently
proposed in the context of knot invariants. In particular, we establish the proposed relation …

A bstract We discuss the notion of renormalization group (RG) completion of non-Gaussian
Lagrangians and its treatment within the framework of Bogoliubov-Zimmermann theory in …

A bstract\(\mathrm {\mathcal {R}}\)-matrix is explicitly constructed for simplest representations
of the Ding-Iohara-Miki algebra. Calculation is straightforward and significantly simpler than …

We discuss using the cabling procedure to calculate colored HOMFLY polynomials. We
describe how it can be used and how the projectors and R-matrices needed for this …

We consider braids with repeating patterns inside arbitrary knots which provides a multi-
parametric family of knots, depending on the “evolution” parameter, which controls the …