
Recent Posts
 Taut foliations and positive forms
 Explosions – now in glorious 2D!
 Dipoles and Pixie Dust
 Mapping class groups: the next generation
 Groups quasiisometric to planes
 Div, grad, curl and all this
 A tale of two arithmetic lattices
 3manifolds everywhere
 kleinian, a tool for visualizing Kleinian groups
 Kähler manifolds and groups, part 2
 Kähler manifolds and groups, part 1
 Liouville illiouminated
 Scharlemann on Schoenflies
 You can solve the cube – with commutators!
 Chiral subsurface projection, asymmetric metrics and quasimorphisms
 Random groups contain surface subgroups
 wireframe, a tool for drawing surfaces
 Cube complexes, Reidemeister 3, zonohedra and the missing 8th region
 Orthocentricity
 Kenyon’s squarespirals
 Thurston talks on geometrization at Harvard
 Random turtles in the hyperbolic plane
 Surface subgroups of Sapir’s group
 Upper curvature bounds and CAT(K)
 Bill Thurston 19462012
Blogroll
 0xDE
 Area 777
 Combinatorics and more
 Deep street soul
 Evaluating EDiscovery
 floerhomology
 Gaddeswarup
 Geometric Group Theory
 Godel's lost letter and P=NP
 Images des mathematiques
 Jim Woodring
 Language Log
 Letters of note
 Low dimensional topology
 Math Overflow
 Mathematics under the microscope
 nCategory Cafe
 Noncommutative geometry
 Paul Krugman
 Persiflage
 Preposterous Universe
 Questionable content
 Quomodocumque
 Real Climate
 Scott McCloud
 Secret blogging seminar
 Sketches of topology
 T Calegari
 Tanya Khovanova
 Terry Tao
 Tim Gowers
 Tony Phillips
Books
Software
Recent Comments
Danny Calegari on Explosions – now in glor… rpotrie on Explosions – now in glor… Ferran on Mapping class groups: the next… Danny Calegari on Dipoles and Pixie Dust Laura DeMarco on Dipoles and Pixie Dust Categories
 3manifolds (18)
 4manifolds (2)
 Algebraic Geometry (2)
 Biology (2)
 Commentary (4)
 Complex analysis (9)
 Convex geometry (2)
 Diophantine approximation (1)
 Dynamics (12)
 Ergodic Theory (8)
 Euclidean Geometry (8)
 Foliations (2)
 Geometric structures (5)
 Groups (31)
 Hyperbolic geometry (22)
 Knot theory (1)
 Lie groups (8)
 Number theory (1)
 Overview (2)
 Polyhedra (2)
 Probability (1)
 Projective geometry (1)
 Psychology (3)
 Riemannian geometry (1)
 Rigidity (2)
 Special functions (1)
 Surfaces (19)
 Symplectic geometry (3)
 TQFT (1)
 Uncategorized (5)
 Visualization (10)
Meta
Monthly Archives: June 2009
The topological CauchySchwarz inequality
I recently made the final edits to my paper “Positivity of the universal pairing in 3 dimensions”, written jointly with Mike Freedman and Kevin Walker, to appear in Jour. AMS. This paper is inspired by questions that arise in the … Continue reading
Posted in 3manifolds, TQFT
Tagged 3manifolds, BessonCourtoisGallot, compression body, DijkgraafWitten, Hamilton, hyperbolic manifolds, JSJ decomposition, Miles Simon, minimal surface, Perelman, Ricci flow, scalar curvature, TQFT, unitary, universal pairing, volume entropy, volume inequality
3 Comments
Big mapping class groups and dynamics
Mapping class groups (also called modular groups) are of central importance in many fields of geometry. If is an oriented surface (i.e. a manifold), the group of orientationpreserving selfhomeomorphisms of is a topological group with the compactopen topology. The mapping … Continue reading
Measure theory, topology, and the role of examples
Bill Thurston once observed that topology and measure theory are very immiscible (i.e. they don’t mix easily); this statement has always resonated with me, and I thought I would try to explain some of the (personal, psychological, and mathematical) reasons … Continue reading
Round slices of pointy objects
A regular tetrahedron (in ) can be thought of as the convex hull of four pairwise nonadjacent vertices of a regular cube. A bisecting plane parallel to a face of the cube intersects the tetrahedron in a square (one can … Continue reading
Posted in Convex geometry
Tagged Banach space, Convex geometry, Dvoretzky's theorem, L_2
Leave a comment
Ellipsoids and KAK
As many readers are no doubt aware, the title of this blog comes from the famous book Geometry and the Imagination by Hilbert and CohnVossen (based on lectures given by Hilbert). One of the first things discussed in that book … Continue reading
Posted in Visualization
Tagged classical geometry, ellipsoids, KAK decomposition, Lie groups
Leave a comment
Combable functions
The purpose of this post is to discuss my recent paper with Koji Fujiwara, which will shortly appear in Ergodic Theory and Dynamical Systems, both for its own sake, and in order to motivate some open questions that I find … Continue reading
Quasimorphisms and laws
A basic reference for the background to this post is my monograph. Let be a group, and let denote the commutator subgroup. Every element of can be expressed as a product of commutators; the commutator length of an element is the … Continue reading