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Colored HOMFLY polynomials for the pretzel knots and links
A. Mironov, A. Morozov, A. Sleptsov
With the help of the evolution method we calculate all HOMFLY polynomials in all symmetric representations [r] for a huge family of (generalized) pretzel links, which are made from…
Wall Crossing Invariants: from quantum mechanics to knots
D. Galakhov, A. Mironov, A. Morozov
We offer a pedestrian level review of the wall-crossing invariants. The story begins from the scattering theory in quantum mechanics where the spectrum reshuffling can be related t…
Seiberg-Witten curves and double-elliptic integrable systems
G. Aminov, H. W. Braden, A. Mironov +2
An old conjecture claims that commuting Hamiltonians of the double-elliptic integrable system are constructed from the theta-functions associated with Riemann surfaces from the Sei…
On colored HOMFLY polynomials for twist knots
A. Mironov, A. Morozov, An. Morozov
Recent results of J.Gu and H.Jockers provide the lacking initial conditions for the evolution method in the case of the first non-trivially colored HOMFLY polynomials H_{[21]} for…
Matching branches of non-perturbative conformal block at its singularity divisor
H. Itoyama, A. Mironov, A. Morozov
Conformal block is a function of many variables, usually represented as a formal series, with coefficients which are certain matrix elements in the chiral (e.g. Virasoro) algebra.…
On KP-integrable Hurwitz functions
A. Alexandrov, A. Mironov, A. Morozov +1
There is now a renewed interest to the Hurwitz tau-function, counting the isomorphism classes of Belyi pairs, arising in the study of equilateral triangulations and Grothiendicks's…