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NA61/SHINE at the CERN SPS is a fixed-target experiment pursuing a rich physics program including measurements for heavy ion, neutrino and cosmic ray physics. The main goal of the ion program is to study the properties of the onset of deconfinement and to search for the signatures of the critical point. A specific property of the critical point, the increase in the correlation length, makes fluctuations its basic signal. Higher order moments of suitable observables are of special interest as they are more sensitive to the correlation length than typically studied second order moments. In this contribution preliminary results on higher order fluctuations of negatively charged hadron multiplicity and net-charge in p+p interactions are shown. The new data are compared with model predictions.

We prove the existence of at least two solutions for a fourth order equation, which includes the vortex equations for the U(1) and CP(1) self-dual Maxwell-Chern-Simons models as special cases. Our method is variational, and it relies on an "asymptotic maximum principle" property for a special class of supersolutions to this fourth order equation.

We investigate the measurement of the sixth order cumulant and its ratio to the second order cumulant ($C_6/C_2$) in relativistic heavy-ion collisions. The influence of statistics and different methods of centrality bin width correction on $C_6/C_2$ of net-proton multiplicity distributions is demonstrated. There is no satisfactory method to extract $C_6/C_2$ with the current statistics recorded at lower energies by STAR at RHIC. With statistics comparable to the expected statistics at the planned future RHIC Beam Energy Scan II (BES II), no energy dependence of $C_6/C_2$ is observed in central collisions using the UrQMD model. We find if the transition signal is as strong as predicted by the PQM model, then it is hopefully observed at the upcoming RHIC BES II.

The equation of gluodynamics with modified integral kernel is solved up to 2NLO (next-to-next-to-leading order) and 3NLO (next-to-next-to-next-to-leading order) in perturbative QCD. A relationship between the nuclear factor Ns and the ratio of the cumulant and factorial moments of the multiplicity distribution is examined. A comparison of theoretical results and experimental data in p-Pb and Pb-Pb collisions at 200A GeV and 546A GeV is carried out.

The "in-situ" formation of very wide binaries is hard to explain as their physical separations are beyond the typical size of a collapsing cloud core ($\approx$5000-10,000 au). Here we investigate the formation process of such systems. We compute population statistics such as the multiplicity fraction (MF), companion-star fraction (CSF) and physical separation distribution of companions in the $\beta$-Pictoris moving group (BPMG). We compare previous multiplicity studies in younger and older regions and show that the dynamic evolution of a young population with a high degree of primordial multiplicity can lead to a processed separation distribution, similar to the field population. The evolution of outer components is attributed to the dynamical unfolding of higher-order (triple) systems; a natural consequence of which is the formation of wide binaries. We find a strong preference for wide systems to contain three or more components ($>$1000 au: 11 / 14, 10,000 au: 6 / 7). We argue that the majority of wide binaries identified in young moving groups are primordial. Under the assumption that stellar populations, within our galaxy, have statistically similar primordial multiplicity, we can infer that the paucity of wide binaries in the field is the result of dynamical evolution.

We use the generalized squeezed state description in the framework of the Ginzburg-Landau theory. Multiplicity distributions of the squeezed states are studied at second-order phase transition at different squeeze factors. It is shown that the normalized factorial moments exhibit a specific behaviour as functions of the resolution scale. We obtain the values of the scaling exponent which coincides with experimental data at small squeeze factor.

We collected the multiplicity data of stars in Taurus to build an up-to-date stellar/multiplicity catalog. After a general study of nearest-neighbor statistics on spatial random distribution, we introduce the one-point correlation $\Psi$ function to complement the pair correlation function and define the spatial regimes departing from randomness in Taurus. We then perform a set of statistical studies to characterize the binary regime that prevails in Taurus. The $\Psi$ function in Taurus has a scale-free trend with a similar exponent as the correlation function at small scale. It extends almost 3 decades up to $\sim 60$ kAU showing a potential extended wide binary regime. This was hidden in the correlation function due to the clustering pattern blending. Distinguishing two stellar populations, single stars versus multiple systems (separation $ \leq 1$ kAU), within Class II/III stars observed at high angular resolution, we highlight a major spatial neighborhood difference between the two populations using nearest-neighbor statistics. The multiple systems are three times more likely to have a distant companion within 10 kAU when compared to single stars. We show that this is due to the presence of most probable physical ultra-wide pairs. These UWPs are biased towards high multiplicity and higher-stellar-mass components at shorter separations. The multiplicity fraction per ultra-wide pair with separation less than 10 kAU may be as high as 83.5 $\pm$ 19.6\%. We suggest that these young pre-main sequence UWPs may be pristine imprints of their spatial configuration at birth resulting from a cascade fragmentation scenario of the natal molecular core. They could be the older counterparts, at least for those separated by less than 10 kAU, to the $\le$ 0.5 Myr prestellar cores/Class 0 multiple objects observed at radio/mm wavelengths.