Knots, graphs, and algebra: a story of surprises

Knots are everywhere: in the strings of our DNA, in the structure of super-strong materials, and in mathematics, where knots lurk behind all three-dimensional shapes.

Graphs model social networks, transit maps, neural nets, and are one of the most basic objects in modern combinatorics. But what does the mathematics of knots have to do with the mathematics of networks? And how can we use algebra — the science of numbers, operations, and structure — to solve mysteries about both?

This public lecture is hosted by the Sydney Mathematical Research Institute as part of our program for National Science Week 2025. The talk will be tailored to a general audience and suitable for individuals from Year 10 onward. This is a free event, however registration is essential.

About the speaker: Zsuzsanna Dancso is an Associate Professor of Mathematics at the University of Sydney. In her research she uses algebra and discrete mathematics to study knots and shapes in three and four dimensions. Zsuzsanna’s research is influenced by diverse international experiences and the collaborations she built along the way: born and raised in Hungary, she completed her PhD at the University of Toronto in Canada, and worked at multiple top research institutes and universities in North America and Australia, before joining the University of Sydney in 2017.

Zsuzsanna values the fresh perspectives that students and young mathematicians bring to the field: indeed, the project which inspired this lecture included two University of Sydney students, in addition to an international collaborator. Outside of mathematics, Zsuzsanna enjoys dance, musical theatre, and feeding people.