Seth Hardy
About
I am a third-year PhD student studying analytic and probabilistic number theory under the supervision of Professor Adam Harper. My research thus far has primarily focused on the study of random multiplicative functions. I currently organise the Warwick Junior Number Theory Seminar.
I previously completed my MSci in Mathematics at University College London. During my 4th year, I completed a project titled 'Exploring recent developments in gaps between prime numbers' under the supervision of Dr Ian Petrow.
Research
• The distribution of partial sums of random multiplicative functions with a large prime factor (2025). [arXiv]
• Bounds for exponential sums with random multiplicative coefficients (2024). International Mathematics Research Notices, rnae234. doi:10.1093/imrn/rnae234. [arXiv]
• Almost sure bounds for a weighted Steinhaus random multiplicative function (2023). J. London Math. Soc., 110: e12979. doi:10.1112/jlms.12979. [arXiv].
Talks
• March 2025: Random multiplicative functions and their distribution, Rencontres de théorie analytique et élémentaire des nombres.
• March 2025: Exponential sums with random multiplicative coefficients, Séminaire de Théorie des Nombres de Nancy-Metz.
• January 2025: Exponential sums with random multiplicative coefficients, WOMBL15.
• 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 Seminar.
• April 2024: Exponential sums with random multiplicative coefficients, London Junior Number Theory Seminar.
• March 2024: Bounds for exponential sums with random multiplicative coefficients, Stanford Student Analytic Number Theory Seminar.
• March 2024: Bounds for exponential sums with random multiplicative coefficients, FRG Grad Seminar.
Writing
Large values of Dirichlet polynomials - study group notes about a mean value theorem of Heath-Brown. [pdf].
The Dickman function in probability (for MA946) [pdf].
My MSci Thesis: Gaps between prime numbers [pdf].
Teaching
Spring Term 2025 - Teaching Assistant for MA257 Introduction to Number Theory.
Autumn Term 2024/25 - Teaching Assistant for MA4L6 Analytic Number Theory.
Spring Term 2024 - Supervisor for first year students.
Autumn Term 2023/24 - Supervisor for first year students.
Spring Term 2023 - Teaching Assistant for MA257 Introduction to Number Theory.
Contact
