Manifolds in Maths: A Beginner's Lecture in Topology

This is the 2nd event in a two-day programming series of short, interdisciplinary research talks and participatory workshops at Exposed Arts Projects, entitled 'ONE FOLD, TWO FOLD, TEN FOLD, MANIFOLD.'

In this talk, topologist Mehdi Yazdi will display mesmerising visualisations whilst providing a beginner’s introduction to mathematical concepts in topology. We will learn qualitative properties described in terms of manifolds and foliations that have long fascinated topologists, who have undertaken visual inspiration from marbleised paper, as used in handmade books, as well as in the expanding rings of trees found in nature. Free and open to all!

About the speaker:

Dr Mehdi Yazdi is an Iranian mathematician specialised in topology and geometry; his research interests include surfaces and three-dimensional manifolds, foliations, and knot theory. He is a Glasstone Research Fellow in Science at the University of Oxford's Mathematical Institute and a Junior Research Fellow at St Peter's College. He received his PhD in mathematics from Princeton University in 2017 and has given talks widely, including at University of Cambridge, Yale University, University of California at Berkley, and Columbia University, among other institutions. He draws inspiration from geometric forms found in nature and in historical and contemporary models of art and architecture.

About the programming series:

'ONE FOLD, TWO FOLD, TEN FOLD, MANIFOLD' is a series of interdisciplinary research talks and participatory workshops instigated by American artist Gina DeCagna.

To paraphrase the late-nineteenth-century British writer John Huntley Skrine, one way to define a ‘manifold’ is as a chosen abstraction that gathers into focus qualities of human duty, experience, and hope. However, the term has varied meanings across context and research discipline. An artist convenes with a mathematician, a poet, and the public to consider varied meanings of the ‘manifold’ and to understand how our internal values and external objectivities intertwine.

Through her interventionist installations of discarded cardboard, American artist Gina DeCagna employs a material and symbolic sensibility of ‘manifolds’ in building improvised organic architectures that resemble geographical strata, tree rings, and plant foliage from discarded cardboard to speculate on the forms and structures of globalised society. While in Baroque times, fabric folds were depicted to speak to a spiritual understanding of the soul, DeCagna seeks to represent the folding collapse of late capitalism, mixing indeterminacy with strength.

She brings into her orbit the topologist Dr Mehdi Yazdi, who finds similar visual inspiration to propel his mathematical intuition around questions of manifolds and foliations — research questions that ultimately could lead us to mathematically understand more structures and systems that underpin the world, including, potentially, that of the Internet and even DNA. Poet and scholar Dr Orchid Tierney brings the metaphorical world of language into researching the representations of waste and its management, most recently completing a poetic work on ocean plastic. Finally, we will critically convene these different disciplinary approaches through philosophy, starting with Kant’s ‘manifold of sense’, that of bringing particularities together through a synthetic process of understanding.

To learn more, visit www.exposedartsprojects.com.