Geometric Analysis and Topology Seminar

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4-Dimensional Arithmetic Hyperbolic Manifolds and Quantum Error Correcting Codes

Speaker: Alex Lubotzky, Hebrew University/NYU

Location: Warren Weaver Hall 517

Date: Friday, October 31, 2014, 11 a.m.

Synopsis:

A family of quantum error correcting codes (QECC) is constructed out of congruence quotients of the 4- dimensional hyperbolic space. Using methods of systolic geometry over Z/2Z, we evaluate the parameters of these codes and disprove a conjecture of Zémor who predicted that such homological QECC do not exist. All notions will be defined and explained. A joint work with Larry Guth.