Geometric measure theory and harmonic analysis

Overview

Research group type

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

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

Publication

2024

Available through Open Access

Kaufman and Falconer Estimates for Radial Projections and a Continuum Version of Beck’s Theorem

Geometric and Functional Analysis.

Orponen, Tuomas

Shmerkin, Pablo

Wang, Hong

Publication

2024

Available through Open Access

On the discretised ABC sum-product problem

Transactions of the American Mathematical Society.

Orponen, Tuomas

Publication

2024

Available through Open Access

On the Hausdorff dimension of radial slices

Annales Fennici Mathematici.

Orponen, Tuomas

Publication

2024

Available through Open Access

Resonance between planar self-affine measures

Advances in Mathematics.

Pyörälä, Aleksi

Publication

2024

Available through Open Access

Ricci curvature bounded below and uniform rectifiability

Annales Fennici Mathematici.

Hyde, Matthew

Villa, Michele

Violo, Ivan Yuri

Publication

2024

Available through Open Access

Structure of sets with nearly maximal Favard length

Analysis and PDE.

Chang, Alan

Dąbrowski, Damian

Orponen, Tuomas

Villa, Michele

Publication

2023

Available through Open Access

A note on Kakeya sets of horizontal and SL(2) lines

Bulletin of the London Mathematical Society.

Fässler, Katrin

Orponen, Tuomas

Publication

2023

Available through Open Access

Additive properties of fractal sets on the parabola

Annales Fennici mathematici.

Orponen, Tuomas

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