Conformal blocks in any CFT are eigenfunctions of Casimir operator. We will show how to reformulate this problem as harmonic analysis on the appropriate vector bundle. The fiber is built from the representations of operators in four-point correlation function and the base is a double factor of conformal group. Surprisingly the resulting equations come in the form of matrix version of (super) integrable Calogero-Sutherland model. I will illustrate the correspondence through the nontrivial example of 3D seed conformal blocks introduced in 1511.01497.

Raman spectroscopy is one of the key experimental methods for the structural analysis of glasses, thanks to its simple application and its sensitivity to variations of composition or atomic-scale order. However, the inherent disorder of the glassy structure results to broad and overlapping peaks in the spectra, rendering their quantitative analysis a challenging task and resulting in a mostly phenomenological interpretation. This drawback can be addressed by the use of modern and accurate theoretical tools, such as ab-initio vibrational spectroscopies. In this work we have studied some simple sodosilicate glasses and we have used density functional theory (DFT) to calculate their vibrational density of states, as well as their Raman and IR spectra. The main advantage of the DFT calculations is that the resulting spectra can be directly correlated with the structural models and, most importantly, the vibrational spectrum can be decomposed into exact contributions arising from individual structural units. In the case of the sodosilicate glasses, we have identified correlations between spectral characteristics and stoichiometry, the effect of the presence of bridging and non-bridging oxygens, the contributions of smaller or larger Si-O-Si angles, as well as the ones arising from the presence of the so-called Q-species. These results open the way for the study of even more complex glasses and aid in the interpretation of experimental spectra.

Use of polymer electrolytes instead of traditional liquid electrolytes offers elegant solutions to many problems in current battery technology. However, a major obstacle in use of polymer electrolytes is their low ionic conductivity. Classical theories suggest that structural (segmental) relaxation controls ionic conductivity in polymers. This is indeed observed in materials such as polyethylene oxide (PEO), the classical polymer electrolyte. However, the mechanism of ionic conductivity in polymers remains poorly understood. In this talk we present an overview of traditional mechanisms of ionic conductivity with emphasis on ‘superionic’ behavior in some materials. Based on this understanding we demonstrate that only strong decoupling of ionic conductivity from segmental dynamics can lead to a ‘superionic’ behavior of a polymer and might provide sufficiently high conductivity required for many applications at ambient temperature. Using the knowledge on diffusion and decoupling phenomena developed in the field of soft materials we suggest the way to design of polymeric structures with strongly decoupled ionic conductivity [1,2]. Our experimental studies demonstrate feasibility of the proposed approach and reveal ‘superionic’ behavior in several new polymers. The polymer specific decoupling of ionic conductivity is especially well illustrated by a comparison of ionic liquids with their polymerized analogs [3,4]. Our detailed studies of polymerized ionic liquids (PolyILs) helped to unravel mechanisms controlling ion diffusion in this promising class of polymer electrolytes [3-5]. We present a model that predicts the glass transition temperature and decoupling of ion conductivity from segmental dynamics in PolyILs based on knowledge of their chemical structure. Ways to further enhancement of ionic conductivity in PolyILs and their possible limitations are discussed at the end.

References
[1] Y. Wang, et al., Phys. Rev. Letters 108, 088303 (2012).
[2] Y. Wang, et al., Polymer 55, 4067 (2014).
[3] J. R. Sangoro, et al., Soft Matter 10, 3536 (2014).
[4] F. Fan, et al. Macromolecules 49, 4557 (2016)
[5] F. Fan, et al., Macromolecules 48, 4461 (2015).

Ionic liquids are an emerging class of solvents with an appealing set of physical attributes. These include negligible vapor pressure, impressive chemical and thermal stability, tunable solvation properties, high ionic conductivity, and wide electrochemical windows. In particular, the non-volatility renders ionic liquids practical components of devices, but they require structure-directing agents to become functional materials. Block polymers provide a convenient platform for achieving desirable nanostructures by self-assembly, with lengthscales varying from a few nanometers up to several hundred nanometers. Furthermore, ionic liquids and polymer blocks can be selected to impart exquisitely tunable thermosensitivity, by exploiting either upper or lower critical solution transitions (UCSTs and LCSTs). In selected cases, it is also possible to prepare photoreversible and photopatternable systems. Overall, by combining designed block polymers and ionic liquids we have demonstrated materials with superior performance for a remarkably diverse set of applications. These include micelles for extraction, nanoreactors for catalysis, gate dielectrics in organic transistors, electrochromic and electroluminescent gels, and membranes for gas separation, ion batteries, and fuel cells.

The observation of Higgs decays into heavy neutrinos would be evidence for new physics associated to neutrino masses. We study such decays within the type I seesaw mechanism in the GeV mass range via displaced vertices and explore the region of parameter space where they can be measured at the LHC. We show that, after imposing pseudorapidity cuts, there is a region where the number of events is larger than O(10).