18 citations · 64 across the 9 of their papers we have counts for
9 papers
Direct proof of one-hook scaling property for Alexander polynomial from Reshetikhin-Turaev formalism
Andrey Morozov, Aleksandr Popolitov, Alexei Sleptsov
We prove that normalized colored Alexander polynomial (the limit of colored HOMFLY-PT polynomial) evaluated for one-hook (L-shape) representation R possesses scal…
On an alternative stratification of knots
E. Lanina, A. Popolitov, N. Tselousov
We introduce an alternative stratification of knots: by the size of lattice on which a knot can be first met. Using this classification, we find ratio of unknots and knots with mor…
Harer-Zagier formulas for knot matrix models
Alexei Morozov, Aleksandr Popolitov, Shamil Shakirov
Knot matrix models are defined so that the averages of characters are equal to knot polynomials. From this definition one can extract single trace averages and generation functions…
Topological Recursion for the extended Ooguri-Vafa partition function of colored HOMFLY-PT polynomials of torus knots
Petr Dunin-Barkowski, Maxim Kazarian, Aleksandr Popolitov +2
We prove that topological recursion applied to the spectral curve of colored HOMFLY-PT polynomials of torus knots reproduces the n-point functions of a particular partition functio…
Exact SUSY Wilson loops on from -Virasoro constraints
Luca Cassia, Rebecca Lodin, Aleksandr Popolitov +1
Using the ideas from the BPS/CFT correspondence, we give an explicit recursive formula for computing supersymmetric Wilson loop averages in 3d Yang-Mills-Chern-Simo…
Evolution for Khovanov polynomials for figure-eight-like family of knots
Petr Dunin-Barkowski, Aleksandr Popolitov, Svetlana Popolitova
We look at how evolution method deforms, when one considers Khovanov polynomials instead of Jones polynomials. We do this for the figure-eight-like knots (also known as 'double bra…
Solving q-Virasoro constraints
Rebecca Lodin, Aleksandr Popolitov, Shamil Shakirov +1
We show how q-Virasoro constraints can be derived for a large class of (q,t)-deformed eigenvalue matrix models by an elementary trick of inserting certain q-difference operators un…
Combinatorial structure of colored HOMFLY-PT polynomials for torus knots
Petr Dunin-Barkowski, Aleksandr Popolitov, Sergey Shadrin +1
We rewrite the (extended) Ooguri-Vafa partition function for colored HOMFLY-PT polynomials for torus knots in terms of the free-fermion (semi-infinite wedge) formalism, making it v…
On Undulation Invariants of Plane Curves
A. Popolitov, Sh. Shakirov
One of the general problems in algebraic geometry is to determine algorithmically whether or not a given geometric object, defined by explicit polynomial equations (e.g. a curve or…