My main research interests are in algebra, Galois module theory, the Yang-Baxter equation, and arithmetic geometry. For my PhD I classified all Hopf-Galois structures and skew braces of order p3: An intricate and beautiful piece of work containing mainly group theoretic calculations which has vast applications in Galois module theory of p-extensions and set-theoretic solutions of the quantum Yang-Baxter equation. I also hold an interested for research in data science, machine learning, and statistical programming with R and Python.
Research group membership
Algebra, Number Theory, Arithmetic Geometry, Data Analytics
I enjoy spending most of my time thinking about problems relating to skew braces and Hopf-Galois structures. In particular, I focus on the problem of classification of skew braces, hence obtaining a classification for certain Hopf-Galois structures, on the one hand, and using these results to study rings of integers of extensions of global or local fields in Galois module theory on the other hand. See my research statement for a detailed account of my work.
Visit my personal website http://www.nejabatiz.com for more, and up to date, information.