The artist M.C. Escher’s work often used ingenious tilings of the plane with interlocking figures such as fish and birds. Although these tilings could in principle extend forever, Escher could not show this on a finite picture. But a diagram from a paper by the mathematician Donald Coxeter presented one solution to this conundrum. We will look at the mathematics of this diagram and how Escher used it. We will also see how Coxeter produced mathematical research based on aspects of Escher's work.

Sarah Hart is the first woman Professor of Geometry at Gresham College, and was appointed in 2020. She is Professor of Mathematics and until recently was Head of Mathematics and Statistics at Birkbeck, University of London.

She studied at Oxford and Manchester, gaining her PhD in 2000. Postdoctoral research and teaching followed, including a prestigious Engineering and Physical Sciences Research Council Fellowship, before she was appointed to a lectureship at Birkbeck in 2004. She has been Professor of Mathematics there since 2013. In 2021 she began a three-year term as President of the British Society for the History of Mathematics.

Sarah is an active researcher, publishing mainly in the area of pure mathematics known as group theory, which has many applications both inside and outside of mathematics, for example in coding theory and cryptography. She is passionate about communicating mathematics and is a sought-after public speaker. She is particularly interested in the links between mathematics, culture and creativity: many of her public lectures and talks in schools are on this topic, especially on mathematics and art.

In 2020-21, Professor Hart will be lecturing on *Mathematics in Music and Writing*, part of a three-year exploration of *Mathematics, Culture and Creativity*.

Professor Hart's lecture series is as follows:

2021/22 Geometry: The Mathematics of Art

2020/21 Mathematics in Music and Writing

All lectures by the Gresham Professors of Geometry can be found here.