Publications

Preprints

• A survey of recent generalisations and extensions of the Mass Transference Principle (with E. Daviaud), preprint 2023, 29 pages, arXiv:2306.15535 .

• Inhomogeneous approximation for systems of linear forms with primitivity constraints (with F. A. Ramírez), preprint 2023, 25 pages, arXiv:2305.16098 .

• Recurrence rates for shifts of finite type (with S. Baker and B. Bárány), preprint 2022, 28 pages, arXiv:2209.01919 .

• Distribution of Sequences Generated by Certain Simply-Constructed Normal Numbers (with S. Brewer), preprint (under revision), 7 pages, old arXiv version .

Accepted/In Press

1. A note on weighted simultaneous Diophantine approximation on manifolds (with B. Wang), preprint 2021, 18 pages, https://arxiv.org/abs/2103.06822 (to appear in Journal de Théorie des Nombres de Bordeaux).

In peer-reviewed journals

1. Dyadic Approximation in the Middle-Third Cantor Set (with S. Chow and H. Yu),

Selecta Math. (N.S.) 29 (2023), no. 1, Paper No. 11, 49 pp. 

2. A note on dyadic approximation in Cantor's set (with S. Baker, S. Chow and H. Yu), 

Indag. Math.(N.S.) 34 (2023), no. 1, 190-197.

3. Independence inheritance and Diophantine approximation for systems of linear forms (with F. A. Ramírez),

Int. Math. Res. Not. IMRN 2023, no. 2, 1760-1794.

4. On the Hausdorff measure of shrinking target sets on self-conformal sets (with B. Bárány), 

Mathematika 67 (2021), no. 4, 807-839.

5. A General Mass Transference Principle (with S. Baker)                                                                                                                                                                                                                                        

Selecta Math. (N.S.) 25 (2019), no. 3, Art. 39, 38 pp. 

6. The Mass Transference Principle: Ten Years On (with S. Troscheit) arXiv version                                                                                                                                                                                

Horizons of fractal geometry and complex dimensions, pp.1-33, Contemp. Math., 731, Amer. Math. Soc., Providence, RI, 2019. 

7. A mass transference principle for systems of linear forms and its applications (with V. Beresnevich)                                                                                                                                           

Compos. Math. 154 (2018), no. 5, 1014-1047.

8. Average distances on self-similar sets and higher order average distances of self-similar measures (with H. Edwards, S. Harper and L. Olsen)                                                  

Math. Z. 287 (2017), no. 1-2, 287-324.

9. No-where averagely differentiable functions: Baire category and the Takagi function (with C. Arthur, R. Dougall, H. Edwards, L. Olsen and M. Véges)                               

Monatsh. Math. 172 (2013), no. 1, 1-27. 

Other

1.  Guiding Principles for Unlocking the Workforce — What Can Mathematics Tell Us? (with D. Abrahams et al.), working paper from ICMS/VKEMS Virtual Study Group — Mathematical Principles for Unlocking the Workforce, May 2020.

2. Trends in Diophantine Approximation                                                                                                                                                                                                                                                                                                          LMS Newsletter Article (invited article), July 2018, 11--15.

3. Orponen's Distance Set Theorem, Extended abstract from the "Arbeitsgemeinschaft: Additive Combinatorics, Entropy, and Fractal Geometry" in Oberwolfach Report no. 47, 2017.

4. Jarnik, Besicovitch and Mass Transference, Extended abstract from the "Arbeitsgemeinschaft: Diophantine Approximation, Fractal Geometry and Dynamics" in Oberwolfach Report no. 48, 2016.