Summary: Topological Phases of Matter
Modeling and Classification
Microsoft Station Q
RTG in Topology and Geometry, UCSB Oct 21, 2011
Prediction of Quantum Theory
· Quantum computing is possible
· There are non-abelian anyons
Thm: Prediction 2 implies Prediction 1.
Anyon=Localized Non-Local Properties
· Poincare-Hopf Index Thm
· Gauss-Bonnet-Chern Thm
· A pair Q=(L, H), where L is a Hilbert space
and H an Hermitian operator, physically H
should be local.
0) L = C2, H= I