Partial difference sets, disjoint difference families and external difference families are well-studied combinatorial objects, with applications to information security. We introduce two new structures which generalize these: disjoint partial difference families (DPDFs) and external partial difference families (EPDFs). This talk will demonstrate their properties and natural links to other combinatorial objects, and exhibit some construction methods. DPDFs and EPDFs may be formed from suitable collections of PDSs, while cyclotomic methods can be used to obtain DPDFs and EPDFs whose component sets are not in general PDSs. In the process, various new results on DDFs and EDFs are obtained. This is joint work with Laura Johnson (St Andrews).

Bio: Sophie Huczynska's research interests are in the area of combinatorics and finite fields. She enjoys studying combinatorial structures motivated by problems from cryptography and coding theory. She is also interested in how combinatorial objects such as graphs and permutations may be viewed as relational structures. She obtained her Ph.D. in 2003 at the University of Glasgow, on structural properties of finite fields. She is currently at the University of St Andrews, where she has been a Royal Society Dorothy Hodgkin Research Fellow, Lecturer and is now Senior Lecturer. To balance work and family commitments, she has worked part-time since 2008.