"Finally, two days ago, I succeeded - not on account of my hard efforts, but by the grace of the Lord. Like a sudden flash of lightning, the riddle was solved. I am unable to say what was the conducting thread that connected what I previously knew with what made my success possible." Karl Friedrich Gauß (1777-1855)

## My Research

*Disclaimer*: The subject areas listed below are the ones that I am interested in studying and doing research. In NO way, I claim that I am an expert of all those mentioned subject areas below.

### Research Areas/Areas of Interests

#### Mathematics

#### Theoretical Physics

#### Theoretical Computer Science

### Current Research Interests

#### Mathematics

Geometry and Topological Defects (Instantons, Monopoles and Solitons)#### Theoretical Physics

Foundations of Quantum Mechanics#### Theoretical Computer Science

The Efficiency of Quantum Algorithms on Classical Computers

Differential Geometry, Mathematical Physics, Noncommutative Geometry, Number Theory, Quantum Algebra, Representation Theory

General Relativity, High Energy Physics, Quantum Physics

Cryptography, Information Theory, Quantum Computing, Quantum Information Science, Theory of Computation

Noncommutative Geometry and Physics

Gauge Theory

Synopsis: Can simulations of quantum algorithms on classical computers be more efficient than classical algorithms? In particular, can there be an efficient simulation of Shor's algorithm on classical computers? If the answer is affirmative, it proves that factoring is in the complexity class P for classical computers.