
Recent Posts
 Roots, Schottky semigroups, and Bandt’s Conjecture
 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)
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 (10)
 Convex geometry (2)
 Diophantine approximation (1)
 Dynamics (13)
 Ergodic Theory (8)
 Euclidean Geometry (8)
 Foliations (2)
 Geometric structures (5)
 Groups (31)
 Hyperbolic geometry (23)
 Knot theory (1)
 Lie groups (8)
 Number theory (2)
 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
Category Archives: Dynamics
Rotation numbers and the JankinsNeumann ziggurat
I’m in Melbourne right now, where I recently attended the Hyamfest and the preceding workshop. There were many excellent talks at both the workshop and the conference (more on that in another post), but one thing that I found very interesting … Continue reading
Harmonic measure
An amenable group acting by homeomorphisms on a compact topological space preserves a probability measure on ; in fact, one can given a definition of amenability in such terms. For example, if is finite, it preserves an atomic measure supported … Continue reading
Faces of the scl norm ball
I am in Melbourne at the moment, in the middle of giving a lecture series, as part of the 2009 ClayMahler lectures (also see here). Yesterday I gave a lecture with the title “faces of the scl norm ball”, and … Continue reading
Posted in Dynamics, Groups, Surfaces
Tagged Bavard duality, free groups, immersions, maximal representation, quasimorphisms, Rigidity, rotation number, scl, Surfaces, Symplectic geometry
1 Comment
van Kampen soup and thermodynamics of DNA
The development and scope of modern biology is often held out as a fantastic opportunity for mathematicians. The accumulation of vast amounts of biological data, and the development of new tools for the manipulation of biological organisms at microscopic levels … Continue reading
Posted in Biology, Dynamics, Groups
Tagged biological computation, DNA, fatgraphs, free groups, Holliday junction, scl, thermodynamics, van Kampen diagrams
4 Comments
Orderability, and groups of homeomorphisms of the disk
I have struggled for a long time (and I continue to struggle) with the following question: Question: Is the group of selfhomeomorphisms of the unit disk (in the plane) that fix the boundary pointwise a leftorderable group? Recall that a … Continue reading
Posted in Dynamics, Groups
Tagged BurnsHale, distortion, Dynamics, orderable groups, quasimorphisms, Thurston stability theorem
4 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