Quantitative rectifiability in Euclidean and non-Euclidean spaces
Main funder
Funder's project number: 335479
Funds granted by main funder (€)
- 159 869,00
Funding program
Project timetable
Project start date: 01/09/2020
Project end date: 31/08/2022
Summary
This funding application, for the Finnish Academy, covers the research costs of the final two years of the Academy Fellowship project "Quantitative rectifiability in Euclidean and non-Euclidean spaces". The applied funding from the Finnish Academy is 159 869 euros. It would be used to hire a postdoc (12.5 months) and a PhD student (12 months), to organise an international conference on GMT and HA in 2021 or 2022, and to support the international mobility of my research group in 2020-2022.
Here is the public description:
The 5-year Academy Research Fellowship project "Quantitative rectifiability in Euclidean and non-Euclidean spaces" studies sets with integer dimension. A basic result in geometric measure theory (GMT) says that these sets fall essentially into two classes: rectifiable, and unrectifiable. A large amount of GMT deals with the question: how do analytic and geometric properties of sets from the two classes differ? For example, it is known that rectifiable sets are "visible" and unrectifiable sets are "invisible".
The current project continues research in this tradition, attempting to answer some notable open problems. The precise connection between visibility and rectifiability is one of them. Also, the theory of rectifiability will be developed in the Heisenberg group, which is the three-dimensional space equipped with a "non-Euclidean" geometry.
Here is the public description:
The 5-year Academy Research Fellowship project "Quantitative rectifiability in Euclidean and non-Euclidean spaces" studies sets with integer dimension. A basic result in geometric measure theory (GMT) says that these sets fall essentially into two classes: rectifiable, and unrectifiable. A large amount of GMT deals with the question: how do analytic and geometric properties of sets from the two classes differ? For example, it is known that rectifiable sets are "visible" and unrectifiable sets are "invisible".
The current project continues research in this tradition, attempting to answer some notable open problems. The precise connection between visibility and rectifiability is one of them. Also, the theory of rectifiability will be developed in the Heisenberg group, which is the three-dimensional space equipped with a "non-Euclidean" geometry.
