Research Interests of Mathai Varghese

My recent research interests include:

index theory of elliptic operators;

secondary invariants of elliptic operators;

geometric quantization: noncompact context;

and noncommutative geometry.

Several mathematical problems that I currently work on originate
from physics, for example:

topological field theories,

Mathematics of Condensed matter physics:

  1. (fractional) quantum Hall effect 1985 & 1998 Nobel Prizes in Physics
  2. topological insulators, 2016 Nobel Prize in Physics
  3. topological semimetals, 2016 Nobel Prize in Physics

Mathematics of string theory & duality in a background flux.

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