My research combines surprising physical phenomena with rigorous mathematics.
Therefore, I use techniques from statistical physics, stochastic geometry, and spatial statistics.
Unique geometric and stochastic properties, like a 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.
Using a rigorous spatial characterization, I study the formation mechanisms of amorphous spatial structures as well as structure-property relationships of heterogeneous materials and their uses as future material designs.
Complex 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.
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.
- Geometric states of matter with unique probabilistic or geometric features
- Hyperuniformity in point processes and random media
- Quasicrystals and aperiodic order
- Stable matchings and random transport
- Photonic networks
- Biological tissues and nanostructures; foams and random tessellations;
- Percolation; fractal percolation; topology
- Physics of amorphous geometries from nuclear physics to soft matter and gamma-ray astronomy
- 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