Research: I am a third year PhD student supervised by András MáthéLink opens in a new window. My research area is fractal geometry, particularly from the perspective of geometric measure theory & additive combinatorics.

Education: I completed a MSci in Mathematics at the University of Bristol. My fourth year project was supervised by Thomas JordanLink opens in a new window and was entitled 'Large deviations on self-affine sets'.

Preprints: Discretised sum-product problems by Shannon-type inequalities, (joint with András MáthéLink opens in a new window), 2023 [arxiv].

Administrative duties: I help to organise the DAGGER seminar, an informal seminar for young researchers (Masters, PhD, Postdoc), predominantly in Dynamics. Please email me if you would like to give a talk.

Talks:

• Efficiently covering the Sierpiński carpet with tubes, Warwick postgraduate seminar (Coventry, England), 20/10/21.
• Dimension drop for projected self-similar measures, Warwick DAGGER seminar (Coventry, England), 6/3/22.
• Efficiently covering sets with tubes, Workshop on affine and overlapping iterated function systems (Bristol, England), 11/5/22.
• Efficiently covering carpets with tubes, Geometry of deterministic and random fractals (Budapest, Hungary), 27/7/22.
• Efficiently covering carpets with tubes/ Large deviations on self affine sets, Fractals and related fields IV (Porquerolles, France), 8/9/22.
• Sum-product phenomena. Junior number theory seminar, (Coventry, England), 7/11/22.
• Introduction to fractal geometry. Warwick postgraduate seminar, (Coventry, England), 1/2/23.
• A selected survey of projection theorems. Junior analysis and probability seminar, (Coventry, England), 9/2/23.
• A new proof of the discretised sum-product problem. Incidence problems in harmonic analysis, geometric measure theory, and ergodic theory, (Oberwolfach, Germany), 5/6/23.

Conferences/ workshops/ meetings attended:

• Junior ergodic theory meeting (Edinburgh, Scotland)
• Workshop on affine and overlapping iterated function systems (Bristol, England)
• Geometry of deterministic and random fractals (Budapest, Hungary)
• Fractals and related fields IV (Porquerolles, France)
• Ergodic theory & fractal geometry (Birmingham, England)
• Ergodic theory meeting (Manchester, England)
• Ergodic theory meeting (London, England)
• Ergodic theory meeting (Coventry, England)
• Incidence problems in harmonic analysis, geometric measure theory, and ergodic theory (Oberwolfach, Germany)

Upcoming conferences/ workshops/ meetings:

• Harmonic analysis, partial differential equations, and geometric measure theory (Bilbao, Basque Country (Spain))
• Fractal Geometry (Edinburgh, Scotland)

Teaching 2020/21:

Term 1	Term 2
Undergraduate Supervision Group x2	Fractal Geometry Teaching Assistant
	Undergraduate Supervision Group x2

Teaching 2021/22:

Term 1	Term 2
Analysis III Teaching Assistant	Fractal Geometry Teaching Assistant
Undergraduate Supervision Group x1

Teaching 2022/23:

Term 1	Term 2
Dynamical Systems Teaching Assistant	Fractal Geometry Teaching Assistant
Fourier Analysis Teaching Assistant

Contact: william.o-regan at warwick dot ac dot uk