During my Ph.D. for which I have submitted my thesis in July 2009, I worked with Prof. A. D. Gangal as my advisor towards developing a Calculus suitable on Fractal domains. Here is my list of publications and preprints:
- Calculus on Fractal Subsets of Real Line – I: Formulation, Abhay Parvate and A. D. Gangal, Fractals, 17(1), 53–81 (2009)
- Calculus on Fractal Subsets of Real Line – II: Conjugacy with Ordinary Calculus, Abhay Parvate and A. D. Gangal, Fractals, 19(3), 271–290 (2011)
- Fractal Differential Equations and Fractal-time Dynamical Systems, Abhay Parvate and A. D. Gangal, Pramana J. Phys. 64(3), 389 (2005)
- Calculus on Fractal Curves in Rn, Abhay Parvate, Seema Satin, and A. D. Gangal, arXiv:0906.0676, Fractals, 19(1), 15–27 (2011)
- Fokker-Planck Equation on Fractal Curves, Seema Satin, Abhay Parvate and A. D. Gangal, arXiv:1004.4422, Chaos, Solitons & Fractals, 52, 30–35 (2013)
During 2005–2009, I was involved in teaching, programme coordination, and curriculum revision activities at the Centre for Modeling and Simulation, University of Pune. Teaching involved programming related courses in the main, and occasionally mathematical topics. The posts held have varied according to my experience and funding available.
I developed my love for computers long back, during my B.Sc. days. Mostly self-taught, I have explored a variety of programming languages to a varying degree. They include C, Haskell, Scheme, PHP, MySQL, Python, Fortran, Eiffel, C++, to mention a few. Currently my favorite one is Haskell. I mainly use the GNU/Linux platform.
For the period from May 1998 to February 2004, I maintained almost all aspects of the server and network within the Department of Physics, University of Pune, including automation of many on-site requirements with the help of shell scripts.
Though not a degree holder in Mathematics, my approach to most of my activities is driven by a craving for mathematical clarity and elegance in understanding and dealing with the world.
I have some very elementary training in Indian classical music, which is sufficient to enrich my own popular music appreciation, although insufficient from professional point of view.