About me

I am a postdoctoral research fellow based at the University of Warwick, working with David Bate. I obtained my PhD in 2021 at the University of Edinburgh, under the supervision of Jonas Azzam.

My main area of interest is geometric measure theory. More specifically, I'm interested in quantitative aspects of rectifiability in both Euclidean and non-Euclidean settings.

Published articles

• A d-dimensional analyst’s travelling salesman theorem for subsets of Hilbert space. Math. Ann. 388 (2024), 108-189. (Article, arXiv)
• The restricted content and the d-dimensional Analyst's Travelling Salesman Theorem for general sets. Adv. Math. 397 (2022), 108-189. (Article, arXiv)
• The weak lower density condition and uniform rectifiability, with Jonas Azzam. Ann. Fenn. Math. 47 (2022), 791–819. (Article, arXiv)



Preprints

• Ricci curvature bounded below and uniform rectifiability, with Michele Villa and Ivan Violo (2023, arXiv).
• Uniformly rectifiable metric spaces: Lipschitz images, Bi-Lateral Weak Geometric Lemma and Corona Decompositions, with David Bate and Raanan Schul (2023, arXiv).
• Cone and paraboloid points of arbitrary subsets of Euclidean space, with Michele Villa (2021, arXiv).

Talks

• (Scheduled) Geometry of measures and free boundaries. A conference in honour of Tatiana Toro. University of Washington, Seattle. (July 2024)
• (Scheduled) Analysis seminar, University of Connecticut, Connecticut. (April 2024)
• (Scheduled) Analysis seminar, SUNY Stony Brook, New York. (April 2024)
• (Scheduled) Analysis seminar, Essex University, UK. (March 2024)
• Harmonic analysis, PDEs and GMT, University of the Basque Country, Bilbao, Spain. (June 2023)
• Analysis seminar, University of Bristol, UK. (May 2023)
• LMS Harmonic analysis and PDE research network, University of Warwick, UK. (February 2023)
• Analysis seminar, Universitat Autònoma de Barcelona, Spain. (February 2023)
• Workshop on geometric measure theory and analysis on metric spaces, University of Warwick, UK. (August 2022)
• Analysis seminar, University of Warwick, UK. (June 2022)
• Analysis seminar during HIM research trimester on PDEs, harmonic analysis and geometric measure theory, Hausdorff research institute for mathematics, Bonn, Germany. (March 2022)
• Analysis seminar, University of Edinburgh, UK. (March 2021)



Conferences

• Jyväskylä Summer School, University of Jyväskylä, Finland. (August 2023)
• Harmonic analysis, PDEs and GMT, University of the Basque Country, Bilbao, Spain. (June 2023)
• Geometric measure theory and analysis on metric spaces, University of Warwick, UK. (August 2022)
• Fourier @ 200, University of Edinburgh, UK (June 2022)
• HIM research trimester on PDEs, harmonic analysis and geometric measure theory, Hausdorff research institute for mathematics, Bonn, Germany. (Spring 2022)
• Harmonic analysis in non-homogeneous spaces, University of Birmingham, UK. (June 2019)
• Radamacher’s theorem in metric measure spaces and Alberti representations, University of Edinburgh, UK (October 2018).
• Calculus of variation and geometric measure theory, University of Sussex, UK. (July 2018)

Teaching

• Autumn 2023:
• (UoW) Graduate real analysis (MA947 - Lecturer)
• Spring 2020:
• (UoE) Workshops for Calculus and its Applications (CAP, MATH08058)
• Autum 2019:
• (UoE) Workshops for Introduction to Linear Algebra (ILA, MATH08057)
• (UoE) Workshops for Accelerated Proofs and Problem Solving (APPS, MATH08071)
• Spring 2019:
• (UoE) Workshops for Proofs and Problem Solving (PPS, MATH08059)
• Autumn 2018:
• (UoE) Workshops for Honours Analysis (HAna, MATH10068)
• (UoE) Workshops for Accelerated Proofs and Problem Solving (APPS, MATH08071)