Dr Sara Herke

Research Field: Mathematics

Dr Herke’s research investigates the properties of networks, or ‘graphs’, that can be
used to describe the notion of connections between people, cities, computers or
even cells in our bodies. A friendship network is a good example of a graph, which
is used to study our social dynamics, to improve our transportation networks and to
make better decision-making algorithms.

Graphs are structures in which two nodes may be joined by an edge, while a
hypergraph is a generalization of a graph in that a hyperedge may contain any
number of nodes. She has worked on a famous problem on hypergraphs, known
as Ryser’s conjecture, and with a team of collaborators she proved the conjecture
holds under certain circumstances.

The full problem remains open and is an active
area of research for many mathematicians. The structures under consideration in
Ryser’s conjecture are often used in studying knowledge databases for artificial
intelligence design as well as in computational biology.

Sarah engages with audiences at all levels through professional development
workshops for teachers, general interest talks and via Laborastory, a public science
story-telling event in Melbourne.