## Gareth Speight

Associate Professor

Department of Mathematical Sciences

University of Cincinnati

### General Information:

I enjoy mathematical analysis that has a geometric flavour, particularly real analysis, geometric measure theory, analysis on metric spaces, metric geometry and sub-Riemannian geometry.

My university profile is here. You can contact me at Gareth.Speight at uc.edu.

I organize the UC Analysis Seminar. If you are interested in giving a talk do let me know.

I am a co-organizer of the Ohio River Analysis Meeting, a yearly conference which alternates between the University of Cincinnati and the University of Kentucky. ORAM 14 will be held at the University of Cincinnati during March 29-30, 2025 (dates tentative).

My research is supported by Simons Collaboration Grant #576219 "Geometry of Lipschitz Maps and Carnot Groups" from 2018 to 2023 (extended to 2024).

### Papers and Preprints:

25. Universal Differentiability Sets in Laakso Space (with S. Eriksson-Bique and A. Pinamonti; arXiv)

24. Higher Order Whitney Extension and Lusin Approximation for Horizontal Curves in the Heisenberg Group (with A. Pinamonti and S. Zimerman; to appear in Journal de Mathématiques Pures et Appliquées; arXiv)

23. Maximal Directional Derivatives in Laakso Space (with M. Capolli and A. Pinamonti; to appear in Communications in Contemporary Mathematics; arXiv)

22. A C^(m,w) Whitney Extension Theorem for Horizontal Curves in the Heisenberg Group (with S. Zimmerman; Journal of Geometric Analysis 33(6), (2023); arXiv)

21. A C^k Lusin Approximation Theorem for Real-Valued Functions on Carnot Groups (with M. Capolli and A. Pinamonti; Indiana University Mathematics Journal 72(4) (2023); arXiv)

20. Regularity of Solutions to the Fractional Cheeger-Laplacian on Domains in Metric Spaces of Bounded Geometry (with S. Eriksson-Bique, G. Giovannardi, R. Korte, and N. Shanmugalingam; Journal of Differential Equations 306, 2022, 590-632; arXiv)

19. Function Spaces via Fractional Poisson Kernel on Carnot Groups and Applications (with A. Maaloui and A. Pinamonti; Journal d'Analyse Mathematique 149 (2023), 485–527; arXiv)

18. A C^m Lusin Approximation Theorem for Horizontal Curves in the Heisenberg Group (with M. Capolli and A. Pinamonti; Calculus of Variations and Partial Differential Equations 60(49) (2021); arXiv)

17. Universal Differentiability Sets in Carnot Groups of Arbitrarily High Step (With A. Pinamonti; Israel Journal of Mathematics 240 (2020), 445–502; arXiv)

16. A C^m Whitney Extension Theorem for Horizontal Curves in the Heisenberg Group (with A. Pinamonti and S. Zimmerman; Transactions of the American Mathematical Society 371(12) (2019), 8971-8992; arXiv)

15. Domains in Metric Measure Spaces with Boundary of Positive Mean Curvature, and the Dirichlet Problem for Functions of Least Gradient (with P. Lahti, L. Maly and N. Shanmugalingam; Journal of Geometric Analysis 29(4) (2019), 3176–3220; arXiv)

14. Porosity and Differentiability of Lipschitz Maps from Stratified Groups to Banach Homogeneous Groups (with V. Magnani and A. Pinamonti; Annali di Matematica Pura ed Applicata 199 (2020), 1197–1220; arXiv)

13. Universal Differentiability Sets and Maximal Directional Derivatives in Carnot Groups (with E. Le Donne and A. Pinamonti; Journal de Mathématiques Pures et Appliquées 121 (2019), 83-112; arXiv)

12. Structure of Porous Sets in Carnot Groups (with A. Pinamonti; Illinois Journal of Mathematics 61(1-2) (2017), 127-150; arXiv)

11. Porosity, Differentiability and Pansu's Theorem (with A. Pinamonti; Journal of Geometric Analysis, 27(3) (2017), 2055–2080; arXiv)

10. Lusin Approximation for Horizontal Curves in Step 2 Carnot Groups (with E. Le Donne; Calculus of Variations and Partial Differential Equations, 55(5) (2016), 1-22; arXiv)

9. A Measure Zero Universal Differentiability Set in the Heisenberg Group (with A. Pinamonti; Mathematische Annalen 368 (1) (2017), 233–278; arXiv)

8. Lusin Approximation and Horizontal Curves in Carnot Groups (Revista Matematica Iberoamericana 32 (4) (2016), 1425-1446; arXiv)

7. Tensorization of Cheeger Energies, the Space H^{1,1} and the Area Formula for Graphs (with L. Ambrosio and A. Pinamonti; Advances in Mathematics 281 (2015), 1145-1177; arXiv)

6. Weighted Sobolev Spaces on Metric Measure Spaces (with L. Ambrosio and A. Pinamonti; Journal fur die Reine und Angewandte Mathematik (Crelle's Journal) 746 (2019), 39-65; arXiv)

5. The p-Weak Gradient Depends on p (with S. Di Marino; Proceedings of the American Mathematical Society 143 (2015), 5239-5252; arXiv)

4. Differentiability of Lipschitz Functions in Lebesgue Null Sets (with D. Preiss; Inventiones Mathematicae 199 (2) (2015), 517-559; arXiv)

3. Directional Lower Porosity (Real Analysis Exchange 39 (1) (2013), 45-56; arXiv)

2. Surfaces Meeting Porous Sets in Positive Measure (Israel Journal of Mathematics 196 (1) (2013), 435-460; arXiv)

1. Differentiability, Porosity and Doubling in Metric Measure Spaces (with D. Bate; Proceedings of the American Mathematical Society 141 (2013), 971-985; arXiv)

### Conferences and Travel:

Geometry of Measures and Free Boundaries 2024, University of Washington in Seattle, July 22-26, 2024.

Mini-Symposium on Interactions among analysis, optimization and network science at the 9th Annual Meeting of the SIAM Central States Section, University of Missouri-Kansas City, Kansas City MO, October 5-6, 2024 (Tentative).

Special Session on Nonsmooth Analysis and Geometry at the Fall 2024 AMS Eastern Sectional Meeting, University of Albany in Albany NY, October 19-20, 2024.

Workshop on Functional and Metric Analysis and their Interactions hosted by BIRS and BIRS-IMAG, online in May 25 to May 30, 2025.

### Other Information

My CV (updated January 2024) is available here.

Previous PhD students: Marco Capolli (co-supervised with Andrea Pinamonti), PhD 2020 at the University of Trento. Hyogo Shibahara, PhD 2024 at the University of Cincinnati.

I obtained my PhD in June 2013 from the Mathematics Institute at the University of Warwick in the United Kingdom. My supervisor was David Preiss and the thesis title was Porosity and Differentiability.

Between September 2013 and May 2015 I was a postdoctoral researcher in the ERC project Geometric Measure Theory in non-Euclidean Spaces at the Scuola Normale Superiore di Pisa in Italy. My advisor was Luigi Ambrosio.

My MathSciNet mathematical reviews are available here.