Tags » Hyperbolic Geometry

Counting Matrices of Small Trace


To refresh on a bit of graph theory, we define a k-regular graph to be a graph in which every vertex has… 1,495 more words

Number Theory

Understanding Geometry - 1

When we think about mathematics, what comes to our mind are the numbers and figures. The  study of numbers is called arithmetic and the study of figures is called geometry (in very crude sense!). 494 more words

My Research

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