Geometric measure theory and harmonic analysis

Overview

Core fields of research

Basic natural phenomena and mathematical thinking

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

Félix Lequen

Postdoctoral Researcher

Aleksi Pyörälä

Postdoctoral Researcher

Hrit Roy

Postdoctoral Researcher

Alex Rutar

Postdoctoral Researcher

Yibo Chen

Doctoral Researcher

Guangzeng Yi

Doctoral Researcher

Publications

Publications

Publication

2025

Available through Open Access

A fractal local smoothing problem for the wave equation

Bulletin of the London Mathematical Society.

Beltran, David

Roos, Joris

Rutar, Alex

Seeger, Andreas

Publication

2025

Available through Open Access

Approximate incidence geometry in the plane

Research in the Mathematical Sciences.

Orponen, Tuomas

Publication

2025

Available through Open Access

Interpolating with generalized Assouad dimensions

Journal of Geometric Analysis.

Banaji, Amlan

Rutar, Alex

Troscheit, Sascha

Publication

2025

Available through Open Access

Large cliques in extremal incidence configurations

Revista Matematica Iberoamericana.

Orponen, Tuomas

Yi, Guangzeng

Publication

2025

Available through Open Access

On bounded energy of convolution of fractal measures

Annales Fennici Mathematici.

Yi, Guangzeng

Publication

2025

Available through Open Access

On Fourier transforms of fractal measures on the parabola

Transactions of the American Mathematical Society.

Orponen, Tuomas

Puliatti, Carmelo

Pyörälä, Aleksi

Publication

2025

Available through Open Access

On various Carleson-type geometric lemmas and uniform rectifiability in metric spaces: Part 1

Revista Matematica Iberoamericana.

Fässler, Katrin

Violo, Ivan Yuri

Publication

2025

Available through Open Access

Regularity of non-autonomous self-similar sets

Mathematical Proceedings of the Cambridge Philosophical Society.

Käenmäki, Antti

Rutar, Alex

Publication

2025

Available through Open Access

The dimension of projections of planar diagonal self-affine measures

Annales Fennici Mathematici.

Pyörälä, Aleksi

Publication

2025

Available through Open Access

The Kakeya conjecture in three dimensions

Arkhimedes.

Rutar, Alex

Publication

2024

Available through Open Access

Blow up analysis for a parabolic MEMS problem, I : Hölder estimate

Calculus of Variations and Partial Differential Equations.

Wang, Kelei

Yi, Guangzeng

Publication

2024

Available through Open Access

How much can heavy lines cover?

Journal of the London Mathematical Society.

Dąbrowski, Damian

Orponen, Tuomas

Wang, Hong

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