Noncommutative Geometry Seminar

Geometry, Topology, and Modern Classifications of Quantum Matter

Wentao (Winston) Fan, Undergraduate, Caltech,

The topological and SPT orders recently found in certain

condensed-matter systems characterize new phases of matter with no broken

symmetries. This talk will be an introduction to the topic for

mathematicians. I will first introduce quantum Hall liquids as well as

TI's; emphasis will be put on FQH liquids and the corresponding anyonic

statistics, topologydependent ground-state degeneracy, as well as parton

and composite fermion constructions with emergent Chern-Simons gauge

theories. The second half of the talk will focus on the mathematical

aspects of some recent theories, explaining the emergent geometry in FQH

liquids, Berry curvature, quantum metric, and NCG approach to quantum Hall

states with disorder. Kitaev's K-theoretical classification of TI will

also be introduced briefly.

Event Sponsors:

For more information, please contact Farzad Fathizadeh by email at [email protected] or visit http://www.math.caltech.edu/~ncg/.