Sophie Huczynska

Publications


Teaching


Service, supervision & events
Reader in Pure Mathematics


Address:
School of Mathematics and Statistics (Room 312)
University of St Andrews
North Haugh
St Andrews
Fife
KY16 9SS
Scotland

E-mail:
sh70(at)st-andrews.ac.uk


Brief history:
    I am a Reader in Pure Mathematics at the University of St Andrews. I am Head of the Algebra and Combinatorics Research Group and Deputy Director of the research centre CIRCA. Previously, I was a Senior Lecturer (2015-2023), Lecturer (2010-2015) and Royal Society Dorothy Hodgkin Research Fellow (2004-2010). Prior to my arrival at St Andrews, I was a researcher in the School of Informatics at the University of Edinburgh, having completed my PhD in the School of Mathematics and Statistics at the University of Glasgow. I have worked part-time since 2008; typically my hours are 9:30am-3:30pm.

Proceedings of the RSE, Section A (Mathematics):
    I am an editor for the Proceedings of the Royal Society of Edinburgh, Section A (Mathematics). If you would like to submit an article, please follow the instructions here.
Research Interests:

    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 enjoy exploring applications of finite fields to combinatorial structures, coding theory and cryptography.

    Currently, a key focus of my resarch is investigating connections between combinatorics and cryptography, with an emphasis on difference families and their many generalizations. These have a natural connection to optimal AMD codes and secret-sharing schemes. In my work, information security applications motivate the development of new combinatorial objects, which often prove to be of great mathematical interest in their own right. 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 also enjoy working on fundamental existence results for difference structures, including recent work on Denniston partial difference sets.

    Recently, I have become interested in additive combinatorial questions about sumsets and additive tuples, particularly in abelian groups related to finite fields, such as Z_p and Z_2^n.

    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 investigated the homomorphic image order (with a focus on the setting of graphs and digraphs), and studied permutations under the pattern-containment relation.

    My work has a strong interdisciplinary strand, with significant links to theoretical computer science. I collaborate with computer scientists working in constraint satisfaction programming, which has led to productive cross-pollination in terms of developing new computer search techniques and benchmarks, and new examples and conjectures in mathematics.