"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

  • Research Areas/Areas of Interests

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

    Mathematics: Differential Geometry, Mathematical Physics, Number Theory
    Physics: General Relativity, High Energy Physics, Quantum Physics
    Computer Science: Computational Complexity, Information Theory, Quantum Computing
  • Collection of Papers and Lecture Notes

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

  • Current Research Interests

  • My research interests lie in Geometry and Physics. I am also dabbling in Number Theory, particularly Analytic Number Theory and in Quantum Computing, particularly Computational Complexity problems associated with it.

    • Mathematics

    • Physics

      • Quantum Field Theory without Euclideanization?
      • Synopsis: 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.

    • Computer Science

      • The Efficiency of Quantum Algorithms on Classical Computers

        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.

"A scientist worthy of his name, about all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature." Jules Henri Poincaré (1854-1912)