Geometric measure theory and harmonic analysis

Overview

Core fields of research

Basic natural phenomena and mathematical thinking

Research areas

Geometry and Analysis

Faculty

Faculty of Mathematics and Science

Department

Department of Mathematics and Statistics

Research group description

We are interested in fractals and rectifiability, singular integrals, and more generally harmonic analysis with a geometric flavour, on Euclidean and non-Euclidean spaces.

Current

Projects

Related projects

Project

Multi-scale incidence geometry

Multi-scale incidence geometry

Project

Approximate incidence geometry

Approximate incidence geometry

Members

Members

Katrin Fässler

Associate professor

Tuomas Orponen

Associate professor

Matthew Hyde

Academy Research Fellow

Amlan Banaji

Postdoctoral Researcher

Hrit Roy

Postdoctoral Researcher

Alex Rutar

Postdoctoral Researcher

Yibo Chen

Doctoral Researcher

Guangzeng Yi

Doctoral Researcher

Publications

Publications

Publication

2022

Available through Open Access

Sub-elliptic boundary value problems in flag domains

Advances in Calculus of Variations.

Orponen, Tuomas

Villa, Michele

Publication

2021

Available through Open Access

Combinatorial proofs of two theorems of Lutz and Stull

Mathematical proceedings of the Cambridge Philosophical Society.

Orponen, Tuomas

Publication

2021

Available through Open Access

Plenty of big projections imply big pieces of Lipschitz graphs

Inventiones Mathematicae.

Orponen, Tuomas

Publication

2021

Available through Open Access

Singular integrals on regular curves in the Heisenberg group

Journal de Mathematiques Pures et Appliquees.

Fässler, Katrin

Orponen, Tuomas

Publication

2020

Available through Open Access

A Koebe distortion theorem for quasiconformal mappings in the Heisenberg group

Annali di Matematica Pura ed Applicata.

Adamowicz, Tomasz

Fässler, Katrin

Warhurst, Ben

Publication

2020

Available through Open Access

Dorronsoro's theorem in Heisenberg groups

Bulletin of the London Mathematical Society.

Fässler, Katrin

Orponen, Tuomas

Publication

2020

Available through Open Access

Semmes surfaces and intrinsic Lipschitz graphs in the Heisenberg group

Transactions of the American Mathematical Society.

Fässler, Katrin

Orponen, Tuomas

Rigot, Séverine

Publication

2020

Available through Open Access

Vertical versus horizontal Sobolev spaces

Journal of Functional Analysis.

Fässler, Katrin

Orponen, Tuomas

Publication

2019

Available through Open Access

Heisenberg quasiregular ellipticity

Revista Matemática Iberoamericana.

Fässler, Katrin

Lukyanenko, Anton

Tyson, Jeremy T.

Publication

2019

Available through Open Access

Intrinsic Lipschitz graphs and vertical β-numbers in the Heisenberg group

American Journal of Mathematics.

Chousionis, Vasileios

Fässler, Katrin

Orponen, Tuomas

Publication

2018

Available through Open Access

Curve packing and modulus estimates

Transactions of the American Mathematical Society.

Fässler, Katrin

Orponen, Tuomas

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