Amorphous spatial structures appear ubiquitously in nature from hetereogeneous materials or cell packings to nuclear matter in supernova explosions or the distribution of galaxies in the universe.
My research aims to combine surprising physical phenomena with rigorous mathematics. In particular, I am committed to combine the techniques from statistical physics, stochastic geometry, and spatial statistics. Using a rigorous spatial characterization, I study the formation mechanisms of amorphous spatial structures as well as structure-property relationships of heterogeneous materials and, albeit with less intensity, their uses as future material designs.
Examples that I have worked on include random tessellations and sphere packings
with a hidden long-range order, as well as ordered networks that appear both in butterfly wing scales and in nuclear matter.
From disordered point patterns to amorphous tessellations, unique geometric and stochastic properties, like hidden order in amorphous structures, can define new “Geometric states of matter” that are endowed with unique physical properties.
A prominent example is disordered hyperuniformity with an anomalous suppression of large-scale density fluctuations in a system which can be locally amorphous and isotropic like a liquid but at the same time macroscopically uniform like a crystal.
- Random spatial structures from nuclear physics to gamma-ray astronomy
- Statistical physics and physics of condensed matter
- Geometric states of matter
- Random tessellations, hyperuniformity and hyperfluctuating structures
- Interplay between physics and geometry of complex structures
- Stochastic geometry from random fields to porous media, from analytics to numerics
- Sensitive and robust shape descriptors derived from integral geometry
- Statistical methods for spatial data analyses
- Percolation; fractal percolation; topology
- Biological tissues and nanostructures; random foam; anisotropy; quasicrystals
- Disordered photonic networks