Pascal Lecture 2016
Professor Caroline Series (Warwick)
"Mirzakhani’s starting point"
Abstract: In 2014, Maryam Mirzakhani of Stanford University became the first women to be awarded the Fields medal. The starting point of her work was a remarkable relationship called McShane’s identity, about the lengths of simple closed curves on certain hyperbolic surfaces. The proof of this identity, including the Birman-Series theorem about simple curves on surfaces, uses only quite basic ideas in hyperbolic geometry which I will try to explain. We will then look briefly at Mirzakhani’s ingenious way of exploiting the identity and where it led.
Caroline Series is Emeritus Professor of Mathematics at the University of Warwick, where she has been since 1978. Following her first degree at Somerville College, Oxford, she won a Kennedy Scholarship to Harvard where she did a Ph.D. under George Mackey. Her early research was in dynamical systems and chaos, for which she won an LMS Junior Whitehead prize in 1987. She held an EPSRC Senior Research Fellowship in 1999 -- 2004. A flavour of her recent work, about the geometry of three dimensional hyperbolic manifolds and the fractal sets associated to their symmetry groups, can be gained from her widely praised book Indra's Pearls, coauthored by D. Mumford and D. Wright, recently republished in paperback (CUP 2015).
Professor Series has served the mathematical community on many committees both national and international, and was a member of both the RAE and REF maths panels. She has given many distinguished public lectures. Throughout her career she has taken a leading role in encouraging women mathematicians. In 2014, she was awarded the first Senior Anne Bennett prize of the London Mathematical Society and she is vice-chair of the newly formed IMU Committee for Women in Mathematics.