Alice Roth Lecture 2025
It is with great pleasure we announce Professor Caroline Series as the keynote speaker of the 2025 Alice Roth Lecture.
About Caroline Series
Caroline Series is an English mathematician renowned for her contributions to hyperbolic geometry, Kleinian groups, and dynamical systems. She earned a B.A. in Mathematics in 1972 and was awarded a Kennedy Scholarship to study at Harvard University, where she completed her Ph.D. in 1976. Series held academic positions at the University of California, Berkeley, and Newnham College, Cambridge. In 1978, she joined the University of Warwick, where she progressed from lecturer to professor, a position she held until becoming Emeritus Professor in 2015.
Throughout her career, Series has been recognised with several honours, including the Junior Whitehead Prize from the London Mathematical Society in 1987 and election as a Fellow of the Royal Society in 2016. In 2023, she was appointed Commander of the Order of the British Empire (CBE) for her services to mathematics.
Abstract
A hyperbolic 3-manifold is the quotient of hyperbolic 3-space by a discrete group of hyperbolic isometries, equivalently by a discrete subgroup of SL(2,C). The Mostow Rigidity theorem states that a compact hyperbolic 3-manifold is rigid, in fact uniquely determined by the abstract isomorphic class of its defining group.
Flexibility occurs when the manifold M has boundary surfaces which inherit a complex structure from the action of SL(2,C) on the Riemann sphere at infinity. Classically, deformations are studied in terms of the Teichmüller theory of these surfaces. An alternative method, originated by Linda Keen and the speaker, enables one to foliate the parameter space of a family of groups by so-called pleating rays, defined in terms of the three dimensional geometry of M.
We illustrate the general idea with a specific family of groups called the Earle Slice in which one can explicitly compute an intricate picture of the corresponding parameter space. We discuss to what extent the method applies more broadly, what questions remain open, and touch on a wider conjecture about how pleating rays may be key to locating other isolated discrete groups.