ÌÇÐÄTV

About

During my time at ÌÇÐÄTV, I worked on analytic and probabilistic number theory under the supervision of Professor Adam Harper. Before that, I completed my MSci in Mathematics at University College London; my master's project was titled 'Exploring recent developments in gaps between prime numbers' and was supervised by .

I have now . Feel free to contact me at hardy@maths.ox.ac.uk.

Research

• Character sums over smooth numbers, with (2026). []
• Helson's conjecture for smooth numbers, with (2025). []
• The distribution of partial sums of random multiplicative functions with a large prime factor (2025). []
• Bounds for exponential sums with random multiplicative coefficients (2024). International Mathematics Research Notices, rnae234. doi:. []
• Almost sure bounds for a weighted Steinhaus random multiplicative function (2023). J. London Math. Soc., 110: e12979. doi:. [].

Talks

• May 2026: Character sums over smooth numbers, Probability in Number Theory Seminar, CRM, Université de Montréal
• March 2026: Character sums over smooth numbers, Heilbronn Number Theory , University of Bristol.
• June 2025: Random multiplicative functions and their distribution, Oxford Random Matrix Theory .
• March 2025: The distribution of random multiplicative functions with a large prime factor, Multiplicative Chaos in Number Theory Workshop, University of ÌÇÐÄTV.
• March 2025: Random multiplicative functions and their distribution, , Institut Henri Poincaré.
• March 2025: Exponential sums with random multiplicative coefficients, de Théorie des Nombres de Nancy-Metz, Institut Élie Cartan de Lorraine.
• January 2025: Exponential sums with random multiplicative coefficients, .
• June 2024: Almost sure bounds for partial sums of a weighted Steinhaus random multiplicative function, London number theory study group.
• May 2024: Exponential sums with random multiplicative coefficients, Bristol Linfoot Number Theory .
• April 2024: Exponential sums with random multiplicative coefficients, London Junior Number Theory .
• March 2024: Bounds for exponential sums with random multiplicative coefficients, Stanford Student Analytic Number Theory .
• March 2024: Bounds for exponential sums with random multiplicative coefficients, FRG Grad .

Writing

Large values of Dirichlet polynomials - study group notes about a mean value of Heath-Brown. [pdf].
The Dickman function in probability (for MA946) [pdf].
My MSci Thesis: Gaps between prime numbers [pdf].

Teaching

Autumn Term 2025- Teaching Assistant for MA3B8 Complex Analysis.
Spring Term 2025 - Teaching Assistant for MA257 Introduction to Number Theory.
Autumn Term 2024- Teaching Assistant for MA4L6 Analytic Number Theory.
Spring Term 2024 - Supervisor for first year students.
Autumn Term 2023- Supervisor for first year students.
Spring Term 2023 - Teaching Assistant for MA257 Introduction to Number Theory.