Quasiconformal Methods in Analysis and Applications
Principal investigator: Keith Rogers and Daniel Faraco
Project reference: 834728
Start Date: 2019-09-01
End Date: 2024-08-31
Abstract: Scaling invariance occurs in different forms in many natural phenomena. A well known 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 several problems arising in mathematical physics. Using these tools, along with nonlinear analogues, the project hopes to shed light on diverse challenging 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.
This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 834728.