### Research interests

**Electronic and magnetic properties of quasicrystals**

Atoms in a quasicrystal are highly organized, with motifs that repeat albeit without a fixed period, in such a way that they give rise to sharp diffraction pattern. Unlike crystals, quasicrystals can have, for example, 5-fold or 8-fold axes of symmetry, which are forbidden for periodic solids. Lacking translational invariance, quasicrystals do have discrete scale invariance. The Penrose tiling for example, is invariant under a scale change corresponding to the golden mean. My research activities concern finding the solutions for the energy of an electron propagating in such a solid, for the typical form of wavefunctions and how a wave packet spreads as a function of time.

In a recent collaboration, I consider the fate of an impurity spin which is placed in a quasiperiodic environment. The calculations indicate that magnetic screening (the Kondo effect) occurs at different temperatures, depending on the nature of the environment and the chemical potential,. This may furnish an explanation for the exotic behavior at low temperature observed recently in the heavy fermion quasicrystal alloy AlAuYb.

**Disordered and aperiodic quantum antiferromagnets**

In the antiferromagnetic Heisenberg model one considers pairwise interactions between spins on lattice sites. In the simplest situations, where only nearest neighbor interactions are allowed, and when the structure of the solid permits, the minimal energy configuration of spins is an alternating up-down-up-…Neel state. Although this state is easy to describe in the classical magnet, its quantum equivalent is a highly complex correlated state of matter. Frustrated and disordered antiferromagnets are still very poorly understood. A large part of my research has been concerned with the spatial structure of the local magnetizations in the ground state of 2D tilings, and the study of the magnetic excitations (magnons) in such aperiodic antiferromagnets. The methods used include linear spin wave theory, renormalization group, and classical and quantum Monte Carlo simulations.