"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

  • Areas of Interests and 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 any of the subject areas mentioned below.

    • Mathematics

      • Differential Geometry, Mathematical Physics, (Analytic) Number Theory

    • Theoretical Physics

      • General Relativity, High Energy Physics, Quantum Physics

    • Theoretical Computer Science

      • Computational Complexity, Information Theory, Quantum Computing

  • A Collection of Papers and Lecture Notes

    • My collection of papers and lecture notes in mathematics and physics.

    Gauge Theory and Topological Defects (Instantons, Monopoles and Solitons)
    Noncommmutative Spaces, Finite Quantum Physics and Field Theory
    Noncommutative Geometry and Physics
    String Theory and M-Theory
    String Theory in \(\mathrm{AdS}_3\)
    AdS/CFT Correspondence and Holography

  • Current Research Interests

    • I am interested in tackling mathematical and physical problems arising from General Relativity and Quantum Physics. I am also interested in exploring peculiar connections between Number Theory and Physics.

  • Big Questions

    • Quantum Field Theory without Euclideanization?

      • It is a great deal of puzzlement that much of quantum field theory along with gauge field theory and string theory is not done in actual spacetime but in Euclidean space. One reason is that the original path integral that defines the amplitude of a particle diverges in spacetime but its Euclidean counterpart converges in Eucldean space. It is troubling that the path integral, while it makes perfect physical sense, in nature cannot be calculated in actual physical space. Even more troubling is most physicists (except notably Sir Roger Penrose) do not appear to be bothered by this. They appear to be satisfied with the resolution, analytic continuation via Wick rotation, which results in the Euclideanization of quantum field theory. I don't believe that there is actually a rigorous proof of the analytic continuation but even if there is, the analytic continuation would be problematic when spacetime is curved i.e. when gravitation is considered. I cautiously speculate that this issue is originated from quantum mechanics rather than quantum field theory, more specifically from the way quantum mechanics was originally formulated.

    • The Efficiency of Quantum Algorithms on Classical Computers

      • 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.