Prof Adam Harper has been awarded a Frontiers of Science Award, which recognises the most outstanding research in the past 10 years.

Prof Harper was awarded for his paper 'Moments of random multiplicative functions, I: Low moments, better than squareroot cancellation, and critical multiplicative chaos' published in Forum of Mathematics, Pi (2020).

Prof Harper writes:

"This paper studies a probabilistic object, called random multiplicative functions, that we think might provide a useful random model to help us understand interesting functions from number theory (like the Mobius function, or the multiplicative characters introduced by Dirichlet in his work on primes in arithmetic progressions).

A basic question is to understand whether, when one adds up the values of a random multiplicative function, the behaviour is similar as in classical theorems for sums of independent random variables. For example, does one have a central limit theorem guaranteeing an approximately Gaussian distribution? This paper showed that the answer is No, because when one adds up the values of a random multiplicative function one gets a little bit more cancellation than in the classical setting ("better than squareroot cancellation"). In fact, the exact amount of cancellation that one (typically) obtains is determined. This turns out to be closely connected to a construction from mathematical physics called multiplicative chaos, a connection that is exploited in the proofs.

A major ongoing theme of my research is to now prove appropriate analogues of these random results for deterministic number theoretic functions."

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