*Quasiconformal methods in analysis and applications* (QUAMAP) is an ERC project developing mathematical models to explain diverse natural phenomena, such as tomography, turbulence and random geometry.

Scaling invariance occurs in different forms in many natural phenomena. A wellknown example of a rough scale invariance is the fractal nature of a shoreline. From a mathematical point, explaining and making use of the scale invariance leads to the method of conformal (shape preserving) and quasiconformal mappings (that preserve shapes only roughly). Fourier analysis, where one decomposes a signal into its constituent frequencies, provides a related approach to analyse complicated natural phenomena.

QUAMAP is devoted to applying aspects of modern mathematical analysis, from quasiconformal mappings to Fourier analysis, to problems including the geometry of energy minimisers, scaling limits in random geometry, an imaging technique based on electrical surface measurements, as well as the behaviour of fluids in turbulent regimes.