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

2023

Available through Open Access

Cheeger's differentiation theorem via the multilinear Kakeya inequality

Pure and Applied Functional Analysis.

Bate, David

Kangasniemi, Ilmari

Orponen, Tuomas

Publication

2023

Available through Open Access

Hardy spaces and quasiconformal maps in the Heisenberg group

Journal of Functional Analysis.

Adamowicz, Tomasz

Fässler, Katrin

Publication

2023

Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory

Oberwolfach Reports.

Orponen, Tuomas

Shmerkin, Pablo

Wang, Hong

Publication

2023

Available through Open Access

On a Continuous Sárközy-Type Problem

International Mathematics Research Notices.

Kuca, Borys

Orponen, Tuomas

Sahlsten, Tuomas

Publication

2023

Available through Open Access

On the dimension of visible parts

Journal of the European Mathematical Society.

Orponen, Tuomas

Publication

2023

Available through Open Access

On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane

Duke Mathematical Journal.

Orponen, Tuomas

Shmerkin, Pablo

Publication

2023

Available through Open Access

Riesz transform and vertical oscillation in the Heisenberg group

Analysis and PDE.

Fässler, Katrin

Orponen, Tuomas

Publication

2023

Available through Open Access

Vertical projections in the Heisenberg group via cinematic functions and point-plate incidences

Advances in Mathematics.

Fässler, Katrin

Orponen, Tuomas

Publication

2022

Available through Open Access

Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups

Annali di Matematica Pura ed Applicata.

Di Donato, Daniela

Fässler, Katrin

Publication

2022

Available through Open Access

Integrability of orthogonal projections, and applications to Furstenberg sets

Advances in Mathematics.

Dąbrowski, Damian

Orponen, Tuomas

Villa, Michele

Publication

2022

Available through Open Access

Loomis-Whitney inequalities in Heisenberg groups

Mathematische Zeitschrift.

Fässler, Katrin

Pinamonti, Andrea

Publication

2022

Available through Open Access

Metric Rectifiability of H-regular Surfaces with Hölder Continuous Horizontal Normal

International Mathematics Research Notices.

Di Donato, Daniela

Fässler, Katrin

Orponen, Tuomas

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