It is shown that Kazama-Suzuki conditions for the denominator subgroup of N=2 superconformal G/H coset model determine Generalized K¨ahler geometry on the target space of the corresponding N=2 supersymmetric σ-model.

We compute the absolute Poisson's ratio $\nu$ and the bending rigidity exponent $\eta$ of a free-standing two-dimensional crystalline membrane embedded into a space of large dimensionality $d = 2 + d_c$, $d_c \gg 1$. We demonstrate that, in the regime of anomalous Hooke's law, the absolute Poisson's ratio approaches material independent value determined solely by the spatial dimensionality $d_c$: $\nu = -1 +2/d_c-a/d_c^2+\dots$ where $a\approx 1.76\pm 0.02$. Also, we find the following expression for the exponent of the bending rigidity: $\eta = 2/d_c+(73-68\zeta(3))/(27 d_c^2)+\dots$. These results cannot be captured by self-consistent screening approximation.

It is shown that the anomalous elasticity of membranes affects the profile and thermodynamics of a bubble in van der Waals heterostructures. Our theory generalizes the non-linear plate theory as well as membrane theory of the pressurised blister test to incorporate the power-law scale dependence of the bending rigidity and Young's modulus of a two-dimensional crystalline membrane. This scale dependence caused by long-ranged interaction of relevant thermal fluctuations (flexural phonons), is responsible for the anomalous Hooke's law observed recently in graphene. It is shown that this anomalous elasticity affects dependence of the maximal height of the bubble on its radius and temperature. We identify the characteristic temperature above which the anomalous elasticity is important. It is suggested that for graphene-based van der Waals heterostructures the predicted anomalous regime is experimentally accessible at the room temperature.

Quantized vortices in a complex wave field described by a defocusing nonlinear Schrödinger equation witha space-varying dispersion coefficient are studied theoretically and compared to vortices in the Gross-Pitaevskii model with external potential. A discrete variant of the equation is used to demonstrate numerically that vortex knots in three-dimensional arrays of oscillators coupled by specially tuned weak links can exist for as long times as many tens of typical vortex turnover periods. [PRE 100, 012205 (2019)].

Due to the development of the chromosome conformation capture (Hi-C) method, it has become possible to get insight into the chromatin organization by measuring the frequency of physical contacts between different parts of genome. The mechanism of active loop extrusion holds great promise for explaining the key features of the contact maps obtained from the Hi-C data. The loop extrusion model assumes that ATP-dependent process allows nanometer-size molecular machines to organize chromosomes by producing dynamically expanding chromatin loops. In this talk I will give a brief introduction into the loop extrusion model and demonstrate that analytical predictions extracted from this model in its simplest version, where chromatin fiber is treated as an ideal Gaussian chain, are in agreement with experimentally measured statistics of contacts in the interphase chromosomes.

The weakly dissipating dielectric spheres (glass, quartz, etc.) permit to realize high order Fano resonances for internal Mie modes. These resonances for specific values of the size parameter yield field-intensity enhancement factors on the order of 10⁴–10⁷, which can be directly obtained from analytical calculations. These “super-resonances” provides magnetic nanojets with giant magnetic fields, which is attractive for many applications.

I will briefly discuss some aspects of the phenomenon of string breaking in QCD. Such a phenomenon is responsible for strong decays of hadrons. Mainly, I focus on what happens at finite baryon density.

We study the properties of Markov chain Monte Carlo simulations of classical spin models with local updates. We derive analytic expressions for the mean value of the acceptance rate of the single-spin-flip algorithms for the one-dimensional Ising model. We find that for the Metropolis algorithm the average acceptance rate is a linear function of energy. We further provide numerical results for the energy dependence of the average acceptance rate for the 3- and 4-state Potts model, and the XY model in one and two spatial dimensions. In all cases, the acceptance rate is an almost linear function of the energy in the critical region. The variance of the acceptance rate is studied as a function of the specific heat.