Anyon superconductivity and the fractional quantum Hall effect

• Interactions of anyonic quasi-particles (vortices) in the Chern-Simons extension of the Ginzburg-Landau model

States of matter in ferromagnetic superconductors:

• Interactions of compostie magnetic skyrmion-superconducting vortex pairs (SVPs)
• Effects of spin-flip scattering on composite SVPs
• Coexistence of mixed magnetic skyrmion and fractional vortex states in two-band ferromagnetic superconductors with equal spin-triplet pairing

Probing states of matter in superconducting condensed matter systems:

• Ultrasound response to time-reversal symmetry breaking in a superconducting phase

Electrostatic self-interactions of topological textures in condensed matter systems:

• Flexoelectric polarization effect on hopfions and skyrmions in liquid crystals
• Magnetostatic self-interactions of bulk magnetic skyrmion textures in chiral ferromagnets

Magnetic skyrmion quasi-particles in condensed matter systems:

• Effect of the dipolar interaction on bulk magnetic skyrmions in chiral ferromagnets
• Trapping and manipulation of magnetic skyrmions with domain walls in chiral magnetic thin films

Nuclear matter as a crystal of topological solitons:

• Quantized and gravitating skyrmion crystals as a model of isospin asymmetric nuclear matter with applications to neutron stars
• Resolving the incompressibility of infinitely dense nuclear matter via soliton crystals stabilized by vector mesons
• Predicting the Bethe-Weizsacker semi-empirical mass formula coefficients using non-linear \(\sigma\)-model crystals coupled to \(\omega\)-mesons
• Proving the existence and uniqueness of energy minimizing lattices for a variety of generalized skyrmion models

Topological solitons in the presence of a strong background magnetic field:

• Reduction of the chiral soliton lattice in quantum chromodynamics to a gauged \(\mathbb{C}P^1\) model with a constant background gauge
• Crystalline structure of gauged lumps in an applied magnetic field