Tags » Hyperbolic Geometry

A Solution to High-Energy Quantum Gravity: AdS/CFT + Quantum Error Correcting Code = ???!

I went to a talk given by Daniel Harlow at Stanford last Thursday (2016 Oct) on Emergent Locality and Gravity & Quantum Error Correction. He started from summarizing the existing attempts to  solve the short distance quantum gravity problem including string theory and the attempt to quantize the metric as a local field. 147 more words


Teichmüller geometry: a primer

The genus g Teichmüller space Teich(g) is the space of all marked hyperbolic metrics on a genus g surface , modulo homotopy, or equivalently the space of all conformal structures, modulo biholomorphisms isotopic to the identity. 1,060 more words


Hyperbolic Plane Example

Few months ago I gave a lecture on Non-euclidean geometry and it was a bit difficult for me to give audience an example of hyperbolic surface from their day-to-day life. 236 more words

Problem Solving

Isomorphic groups via hyperbolic geometry

is the isometry group of hyperbolic 2-space under the hyperboloid model; is the isometry group of the upper half-plane; is the isometry group of the Poincaré unit disk. 58 more words


Mostow Rigidity: several proofs

Mostow rigidity (or, technically, the special case thereof, for ) states that if M and N are two closed (i.e. compact and boundary-less) hyperbolic 3-manifolds, and is a homotopy equivalence, then… 1,183 more words

Teichmueller Theory

Arguments using moduli spaces: some examples

This blogpost started as a response to the question “why moduli spaces?” … but then David Ben-Zvi had a good pithy answer to that in his   2,288 more words