Dr Val Gladkova

PhD thesis

Arithmetic Regularity Lemmas and Applications

My research is within additive combinatorics, a field in pure mathematics that exists in the intersection of combinatorics and number theory. It explores questions about sets of numbers with certain restrictions, like sets of a certain density or sets that do not contain solutions to a given equation, and studies what structure such restrictions impose. One major tool in additive combinatorics is the arithmetic regularity lemma, which roughly says that we can split up the space we’re working in into a relatively small number of parts in such a way that our set “looks random” on almost all parts. We can then exploit that randomness to make statements about the given set. My thesis focused on different types of arithmetic regularity lemmas and quantitative bounds they produce in applications, and obtained new results by modifying and adapting existing techniques.

After the PhD

I am currently a postdoctoral research associate at Cambridge, moving to a similar position at the University of Manchester in autumn 2025. My long-term plans are to transition towards doing research in industry, for instance in cryptography or quantum computing.