Geometric and dyadic harmonic analysis: general measures and rectifiability

The project "Geometric and dyadic harmonic analysis: general measures and rectifiability" studies geometric notions, like rectifiability, and analytic objects, like singular integrals. This is a five-year Academy Research Fellow project in mathematics at the University of Helsinki. The unified theme between the geometric and analytic fronts is the usage of general measures. This so called non-homogeneous analysis has been an active topic since the breakthroughs in the early 2000. However, in the specific area of rectifiability this is a new trend. The studied research problems are related to these new non-homogeneous rectifiability results. Also other related geometric problems are studied, especially their connection to the analytic part i.e. to the singular integral theory. The boundedness theory of singular integrals is developed as an independent subject, too. The research problems are of high international interest.