Caroline Series   CBE   FRS   FIMA
Professor of Mathematics (Emeritus)
Research: Hyperbolic 3-manifolds, Kleinian groups, Dynamical systems

Publications   List   and   Curriculum   Vitae
Selected   Professional   Service
  David Crighton Medal

( Caroline Series and Hyperbolic Geometry March 2023 )

Riley Slice
LMS Presidential Lecture 2019

Research Papers
Primitive stability and the Bowditch conditions revisited,   To   Appear
Convergence of spherical averages for actions of Fuchsian groups, Comment. Math. Helv. 98 2023
An ergodic theorem for the action of a Fuchsian group (Russian), Uspekhi Math. Nauk Vol 78, 2023
A symmetric Markov coding & the ergodic theorem for actions of Fuchsian groups, 2020
The diagonal slice of Schottky space,   Algebraic & Geometric Topology, Vol.17,     2017
Limits of limit sets II:   Geometrically Infinite Groups, Geometry & Topology V. 21,   2017
Limits of limit sets I ,   Geometriae Dedicata,   Volume 167, Issue 1, pp 35 -- 67,     2013
Lines of minima in Teichmüller space. Handbook of Teichmüller Theory III, EMS     2012
A pointwise ergodic theorem for Fuchsian groups, Math. Proc. Camb. Phil. Society 2011
Top terms of polynomial traces in Kra's plumbing construction, Alg. Geo. Topology 2010
The Maskit embedding of the twice punctured torus,   Geometry and Topology 14   2010

Lectures (selected)
Atiyah Lecture, Maxwell Institute for Mathematical Sciences, Edinburgh, 2024  
Hamilton Lecture, Royal Irish Academy, Trinity College Dublin, 15 October 2021
Geometry, Topology & Dynamics in Low Dimensions, U. of Warwick 2017/ 2018
Annual Charlotte Scott Lecture in Mathematics, University of Lincoln, 2018
Mathematical Legacy of Rufus Bowen, University of British Columbia, 2017

Lecture Notes and Interviews
Interviews in   EMS NewsLetter   2022,   Bhavana   2021,   NUS   2013
Hyperbolic geometry   MA448   2010,   A crash course on Kleinian groups Trieste 2005
Continued Fractions & Hyperbolic Geometry Lecture Notes, LMS Summer School 2015

Low-dimensional Topology, Geometry & Dynamics,   ICERM Brown U.   2013
Geometry, Topology and Dynamics of Character Varieties,   Singapore   2010
EPSRC Symposium: Low Dimensional Geometry and Topology, 2006 -- 2007
SKG Programme, Isaac Newton Institute for Maths Sciences, Cambridge 2003

Indra's Pearls
MATLAB Indra's Pearls website by Chris King, Mathematical Imagery by Jos Leys.
New Paperback Edition   Indra's Pearls 2015 ,   D. Mumford, C. Series & D. Wright

Conference Proceedings
Geometry, Topology & Dynamics of Character Varieties, Editors W. Goldman, C. Series & S. Tan, World Scientific 2012
Spaces of Kleinian Groups, Editors Y. Minsky, M. Sakuma and C. Series, LMS Lecture Note Series vol. 329, CUP 2006
Kleinian Groups & Hyperbolic 3-Manifolds, Eds Y. Komori, V. Markovic & C. Series, LMS Lecture Notes 299, CUP 2003
The Epstein Birthday Schrift, Geometry & Topology Monographs Vol. 1, Eds I. Rivin, C. Rourke and C. Series, GT 1998
Ergodic Theory and Symbolic Dynamics in Hyperbolic Spaces, Eds T. Bedford, M. Keane and C. Series, OUP 1991

Last revised January 2024