Research Expositions


Negatively Curved Crystals
(Harvard 2019)
Koebe 1/4


Billiards and number theory
(Luminy, 2023); Slides
Low-dimensional mathematics
(MSRI, 2023)
Work of Sullivan in Topology and Dynamics
(MSRI 2022)
Negatively curved crystals
(Frontiers of Science, Utah, 2021)
Art and Math Panel
(ICERM 2019)
A Skeptical History of Numbers
(Harvard 2019); Slides
Mathematics as Metaphor
(Stanford 2018)
Billiards, quadrilaterals and moduli spaces
(Grenoble 2018)
Entropy, algebraic integers and moduli of surfaces
(IAS 2016)
Coupled rotations and snow falling on cedars
(Luminy 2015)
Laudation for Mirzakhani
(ICM Seoul 2014)
Perspectives on Thurston's last theorem
(Cornell 2014)
Abel Lecture on Milnor's work
(Oslo 2011)
The evolution of geometric structures on 3-manifolds
(Paris 2010); Slides
Billiards and Teichmueller theory
(Harvard, 2009)
Algebraic dynamics
(Harvard, 2007)
The Geometry of 3-Manifolds
(Harvard, 2006)
(Stockholm, 2003)


Antonyms (Jeopardy, 13 Oct 2015)
Mosaique spherique
Backgammon Ends
Interviews, 1999 and 2015
Rope Trick
The Math Moth: 1,099


those that from a long way off
look like flies


[His] curiosity was desultory; it drew him towards
isolated marvels rather than general laws.

Not having achieved what they desired, they
pretended to desire what they had achieved.
--M. Montel

Selected Lectures

2023 MSRI 40th Anniversary
Low-dimensional mathematics

2022 Schloss Elmau
Algebraic curves and complex dynamics

2020 BiSTRO
Billiards, heights and modular symbols

2019 Mathematical Illustration, ICERM
Illustrating Infinity

2018 Coxeter Lectures III, Toronto
Billiards and the arithmetic of non-arithmetic groups

2018 Dynamical numbers, Bonn
Rigidity of planes in hyperbolic 3-manifolds

2017 No Boundaries, Chicago
Solving polynomials: Braids, rigidity and dynamics

2017 Yoccoz Memorial Conference, Paris
Billiards, quadrilaterals and moduli spaces

2016 Holomorphic Dynamics, Cancun
Surfaces in the space of surfaces

2015 Fefferman Lecture, Chicago
A Skeptical History of Numbers

2014 ICM Seoul
The Mathematical Work of Maryam Mirzakhani

2014 Thurston Legacy
Dynamics and algebraic integers: Perspectives on Thurston's last theorem

2014 Stonybrook
Billiards and curves in moduli space

2013 Heidelberg
Billiards and Moduli Spaces (review)

2013 ICERM
The Gauss-Bonnet theorem for cone manifolds and volumes of moduli spaces

2013 Pecha Kucha, Harvard
A Handful of Metaphors

2012 Thin Groups, MSRI
Dynamics of Units and Packing Constants of Ideals

2011 Sullivan conference, SUNY
Algebraic patterns for dynamical systems

2011 Abel Lecture, Oslo
The work of John Milnor: Manifolds, topology and dynamics

2011 JDG Lecture
Dynamics on Riemann Surfaces and Geometry of Moduli Space

2010 IAS Lecture
Entropy, algebraic integers and moduli of surfaces

2009 MPI - Reimar Lüst Lecture
From Platonic Solids to Quantum Topology

2008 IHP - Douady Memorial
1/7, 2/7, 4/7

2008 AAAS Boston
The Geometry of 3-Manifolds

2008 Ziwet Lectures, Ann Arbor, MI.
Dynamics and moduli spaces

2005 Hopf Vorlesung, Zürich
Algebraic Dynamics / Topology of numbers

2003 Namboodiri Lectures, Chicago
Dynamics and algebraic surfaces

2002 AMS Ross Lecture, Boston
From triangles to infinity

2000 AMS Colloquium Lectures, Washington, DC.
Riemann surfaces in dynamics, topology and arithmetic

Curtis T McMullen