Exhibits

Negatively Curved Crystals

(Harvard 2019)

Koebe 1/4

(Channel)

Video

TEDx Interview 2024

(Context)

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)

Renormalization

(Stockholm, 2003)

Brevities

Antonyms (Jeopardy, 13 Oct 2015)

Mosaique spherique

Renormalization

Backgammon Ends

Interviews, 1999 and 2015

Rope Trick

The Math Moth: 1,099

Graphics

those that from a long way off
look like flies

Quotes

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

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