I am a Senior Lecturer in Pure Mathematics at the School of Mathematics and Statistics at the University of St Andrews. Until October 2010, I was a Royal Society Dorothy Hodgkin Research Fellow . My research is mainly in the areas of combinatorics and finite fields; I also have interests in algebra and theoretical computer science. I am a member of the Centre for Interdiscipinary Research in Computational Algebra (CIRCA).

Please note: I work on a- Session 2018-9: I am teaching MT4514 Graph Theory in Semester 1, and MT3505 Rings and Fields in Semester 2.
- I am Advising Coordinator for the School of Mathematics and Statistics, and a Subhonours Advisor.

I am interested in a range of areas in, and related to, combinatorics. My original background is in the structural theory of finite fields, and I have worked on various questions related to the existence of primitive normal bases for finite fields. I am also interested in applications of finite fields to combinatorial designs, and to coding theory and cryptography.

Recently I have been investigating connections between combinatorics and cryptography, via the concept of external difference families and their generalizations. These have a natural connection to optimal AMD codes. Many of the constructions in this area use cyclotomic methods from finite fields, but there are rich connections with other areas of combinatorics, finite geometry and group theory. I was recently funded by a Carnegie Research Incentive Grant to work on this with my collaborators.

Another strand of my research is viewing combinatorial objects as relational structures, and asking questions about partial orders on these structures. In particular, I have been investigating the homomorphic image order, a natural analogue of the substructure order, with a focus on the setting of graphs and digraphs.

- Member of the EMS Education Committee, having been a committee member for several years and Chair 2018-19.
- For several years I was a member of the British Combinatorial Committee.

- To read a non-specialist account of my work and its possible applications, see the article "Euler's Revolution" by Ian Stewart, which appeared in the New Scientist magazine (issue 24-30 March 2007).

**Books**

**Book chapters**

**Journal papers**

**Conference papers**

Sophie Huczynska

School of Mathematics and Statistics

University of St Andrews

Mathematical Institute (Room 312)

North Haugh

St Andrews, Fife, KY16 9SS

SCOTLAND

**Tel:** +44 (0)1334 463711

**E-mail:** My departmental email address is: sh70 'at'st-andrews.ac.uk