Teaching

 

Undergraduate courses (BP Physics):

 

• Symmetry and group theory in physics
• Methods of mathematical physics
• Theory of functions of one complex variables
• Differential and Integral equations
• Differential and Integral calculus
• Quantum Theory
• Classical Mechanics
• General Physics

 

Graduate courses (MP Theoretical Physics):

 

• Lie groups in physics
• Theory of solitons (Theory of integrable systems)
• Quantum Field Theory

 

 

Scientific interests

 

Mathematical and theoretical physics, including but not limited to

• theory of integrable systems
• finite gap integration
• representation theory of Lie groups and algebras,
• uniformisation of plane algebraic curves,
• theory of Abelian functions.

Publications

 

Papers

 

Bernatska J. General derivative Thomae formula for singular half-periods, Letters in Mathematical Physics, accepted (2020), doi:10.1007/s11005-020-01315-8, arXiv:1904.09333

 

Bernatska J., Kopeliovich Y. Addition of divisors on hyperelliptic curves via interpolation polynomials, SIGMA, Vol.16 (2020), 053, 21 pages, doi:10.3842/SIGMA.2020.053, arXiv:1912.13277

 

Bernatska J., Enolski V., Nakayashiki A. Sato Grassmannian and degenerate sigma function, Communications in Mathematical Physics, Vol.374 (2020), pp.627-660, doi:10.1007/s00220-020-03704-5, arXiv:1810.01224

 

Bernatska J., Leykin D. On degenerate sigma-functions of genus two, Glasgow Mathematical Journal, Vol.61 (2019), pp.169-193, doi:10.1017/S0017089518000162, arXiv:1509.01490.

 

Bernatska J., Leykin D. On regularization of second kind integrals, SIGMA, Vol.14 (2018), 074, 28 pages, doi:10.3842/SIGMA.2018.074, arXiv:1709.10167

 

Bernatska J., Holod P. Orbit approach to separation of variables in 𝔰𝔩(3)-related integrable systems, Communications in Mathematical Physics, Vol.333 (2015), pp.905-929, doi:10.1007/s00220-014-2176-9, arXiv:1402.6730

 

Bernatska J., Holod P. SU(3) magnet: finite-gap integration on the lowest genus curve, Journal of Physics: Conference Series Vol.482 (2014) 012004 (10pp), Physics and Mathematics of Nonlinear Phenomena 2013 (PMNP2013), doi:10.1088/1742-6596/482/1/012004, arXiv:1312.2421

 

BernatskaJ., Holod P. Harmonic analysis on Lagrangian manifolds of integrable Hamiltonian systems, Journal of Geometry and Symmetry in Physics, Vol.29 (2013), pp.39-51, doi:10.7546/jgsp-29-2013-39-51, arXiv:1307.1785

 

Bernatska J., Messina A. Reconstruction of hamiltonians from given time evolutions, Physica Scripta, Vol.85 (2012), 015001 8 pages, doi:10.1088/0031-8949/85/01/015001, arXiv:1006.5183

 

Bernatska J., Holod P. Topological excitations in a two-dimensional spin system with high spin s ≥ 1, Theoretical and Mathematical Physics, Vol.160 (2009), No.1, pp.879-887, doi:10.1007/s11232-009-0077-4, arXiv:1001.0375

 

Bernatska J., Holod P. A generalized Landau-Lifshitz equation for an isotropic SU(3) magnet , Journal of Physics A: Math. Theor., Vol.42 (2009), 075401 14 pages, doi:10.1088/1751-8113/42/7/075401, arXiv:1001.0372

 

Bernatska J., Holod P. Ordered states and nonlinear large-scale exitations in a planar magnet of spin s = 1, Ukrainian Journal of Physics, Vol.53 (2008), No.12, pp.1208-1219, link, arXiv:1001.0373

 

Bernatska J. On the behavior of a simple-layer potential for a parabolic equation on a Riemannian manifold, Ukrainian Mathematical Journal, Vol.60 (2008), No.7, pp.1028-1044, doi:10.1007/s11253-008-0110-z

 

Bernatska J., Holod P. Geometry and topology of coadjoint orbits of semisimple Lie groups, Proceedings of International Conference `Geometry, Integrability and Quantization' (2008), pp.146--166, doi:10.7546/giq-9-2008-146-166, arXiv:0801.2913

 

Bernatska J., Holod P. On Separation of variables for integrable equations of soliton type, Journal of Nonlinear Mathematical Physics, Vol.14 (2007), No.3, pp.353-374, doi:10.2991/jnmp.2007.14.3.5, arXiv:1001.0376

 

Holod P.I., Bernatska J.N., Kutniy S.V. Parameterization for complex Liouville tori of integrable Hamiltonians system on loop group orbits, Naukovi Zapysky NaUKMA, Vol.51 (2006), pp.25-34 (in Ukrainian), link

 

Bernatska Yu. N. The first boundary value problem for a parabolic equation on a manifold, Differental Equations, Vol.41 (2005), No.6, pp.840-851, doi:10.1007/s10625-005-0223-1

 

Holod P.I., Bernatska Yu. M. Nonlinear Alfven waves and solitons in cold plasma, Ukrainian Journal of Physics, Vol.49 (2004), No.3, pp.236-247, link

 

Bernatska J. Perturbation method for a parabolic equation with drift on a Riemannian manifold, Ukrainian Mathematical Journal, Vol.56 (2004), No.2, pp.183-197, doi:10.1023/B:UKMA.0000036095.72970.58

 

Bernatska J. The logarithmic gradient of the kernel of the heat equation with drift on a Riemannian manifold, Siberian Mathematical Journal, Vol.45 (2004), No.1, pp.11-18, doi:10.1023/B:SIMJ.0000013010.71915.85

 

Bernatska J. Behavior of the double-layer potential for a parabolic equation on a manifold, Ukrainian Mathematical Journal, Vol.55 (2003), No.5, pp.712-728, doi:10.1023/B:UKMA.0000010251.45236.9b

 

Bernatska J. An estimate for a fundamental solution of a parabolic equation with drift on a Riemannian manifold, Siberian Mathematical Journal, Vol.44 (2003), No.3, pp.387-404, doi:10.1023/A:1023800411968

 

Bernatska J., Holod P. Canonic coordinates of soliton type nonlinear equations in finite gap sector, Naukovi Zapysky NaUKMA, Vol.19 (2001), pp.31-42 (in Ukrainian), link

 

Bondarenko V., Bidyuk P., Bernatska J. Solving parabolic equation by using the method of fast convergent iterations, Int. J. Appl. Math. and Comp. Sci., Vol.10 (2000), No.2, pp.333-344, link

 

Bernatska J., Kachkovski A. A quantum-chemical study on the structures of linear conjugated systems that absorb in the near IR range, Theoretical and Experimental Chemistry, Vol.35 (1999), No.3, pp.142-145, doi:10.1007/BF02513031

 

Textbooks and Monographs

 

Bernatska J., Holod P. Classical Mechanics, 2014 (in Ukrainian, e-format)

 

Bernatska J. Methods of Mathematical Physics, 2012 (in Ukrainian, e-format)

 

Bernatska J. M. Elements of the theory of functions of a complex variable, Kyiv, 2008, 144 pages. (in Ukrainian)

 

Bernatska J. N. Some problems for a parabolic equation on a Riemannian manifold, Candidate's Degree thesis. Kyiv National Taras Shevchenko University, Kyiv, 2004. (in Ukrainian)

 

Preprints

 

Bernatska J. New generalisation of Jacobi derivative formula, arXiv:2007.05531

 

Bernatska J., Kopeliovich Y., Addition of divisors on trigonal curves, arXiv:2006.11838

 

Bernatska J. Addition law on Jacobian of genus two curve for cryptography, in Special Session on Mathematical Cryptology, AMS Sectional Meeting, University of Connecticut, Hartford, CT, April 13-14, 2019, manuscript