**
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:
*

*
*-
(fractional) quantum Hall effect 1985 & 1998 Nobel Prizes in Physics
- topological insulators, 2016 Nobel Prize in Physics
- topological semimetals, 2016 Nobel Prize in Physics

*
**
Mathematics of string theory & duality in a background flux.*

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