## About:

Professor Claire Voisin is Chair of Algebraic Geometry at the Collège de France. She received her PhD in 1986 from the Université Paris-Sud. She has answered fundamental questions about the geometry of complex algebraic varieties, thanks in part to her pioneering work on the study of Hodge theory and algebraic cycles.

Among many honours, she was awarded the EMS prize in 1992, the Clay research award in 2008, the CNRS Gold Medal in 2016 and the Shaw Prize in 2017. In 2016 she became the first female mathematician member of the Collège de France. She is a member of the Académie des sciences (Paris), of the Academia Europaea, and Honorary member of the London Mathematical Society.

The Terry Wall Lecture at the University of Liverpool is an annual lecture on a topic in Pure Mathematics (broadly construed) by an internationally distinguished speaker. The lecture is named in honour of Professor Terry Wall FRS, Professor of Pure Mathematics at the University of Liverpool from 1965 until his retirement in 1999. During this time he served terms as Head of the Department of Pure Mathematics and as President of the London Mathematical Society. His research has been recognised by a number of prestigious awards and honours, including the Senior Whitehead Prize and the Pólya Prize of the LMS, the Sylvester Medal of the Royal Society, and election as a Fellow of the Royal Society. Past speakers of the Terry Wall lecture include the Fields medalists Professor Martin Hairer, Professor Caucher Birkar, and Professor Stanislav Smirnov.

**Professor Claire Voisin**, Collège de France

### Quadratic extensions: Algebra and Geometry

I will present some important problems and methods of algebraic geometry and discuss them in the context of degree 2 polynomials.