Research Interests:
- algebraic geometry (set theoretic complete intersections) and algebraic curves (esp. elliptic curves)
- kinematics and robotics
- algorithmic/algebraic/analytic number theories (Artin's conjecture, Inverse Galois Problem, prime-generating functions)
- cryptography (elliptic curve cryptography)
- real algebraic geometry (my PhD thesis, sums of squares)
- ring theory (integer valued functions, Galois theory for commutative rings)
- computational geometry and finite projective geometry
- fractal sets
- mathematical chess problems (see Noam Elkies on enumerative chess problems) and various unorthodox mathematical problems
The reviews I have written for journals are confidential, but, to have an idea how I review, one could access my zbMath reviews.
Mathematical Publications
- Topology of the Singularities of 3-RPR Planar Parallel
Robots (with: C. Spartalis), Computer Aided Geometric Design 2022, Vol. 99, in Press.
- Geometry Based Analysis of 3R Serial Robots (with:
P. Wenger, et al.).
In: Advances in Robot and Kinematics, Springer 2022, Vol.24, p.65-72.
- Positive dimensional parametric polynomial systems,
connectivity queries and
applications in robotics (with: M. Safey El Din and J. Schicho). Journal of Symbolic Computation 2022, Vol. 115,
p. 320-345.
- Necessary and Sufficient condition for a
generic 3R serial manipulator to be cuspidal (with: D. Salunkhe et al.). Mechanism and Machine Theory 2022, Vol. 171
- Two Remarks on Sums of Squares (with: C. Scheiderer). Algebra,
Logic and Number Theory. Banach Center Publications 2020, Vol. 121, p.25-36.
-
Robots, Computer Algebra and Eight Connected Components (with: M. Safey El Din and J. Schicho). Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation,
ACM 2020, p. 62-69
- Implementing HuPf algorithm for the inverse kinematics of general 6R/P manipulators (with: S.M. Manongsong), In: Computer Algebra in Scientific Computing 2019, Lecture Notes in Computer
Science, Springer 2019, p. 78-90
- Factorization of Integer Valued Polynomials.Python code, (cypari)
, 03.2018
- Generalizing some Results
in Field Theory for Rings, 01.2017, RISC Technical Report
- The Number of Realizations of a Laman Graph, (with: M. Gallet, C. Koutschan, G. Grasseger, N. Lubbes
and J.Schicho), SIAM Journal on Applied Algebra and Geometry (SIAGA) 2017, Vol. 2, No. 1, p.94-125
- Odd Collatz Sequence and Binary Representations,
09.2015, RISC Technical Report
- Real Closed Rings and Real Closed * Rings,
Journal of Pure and Applied Algebra, Journal of Pure and Applied Algebra, 2014, Vol. 218, No. 1, p.101-111
- Real Closed * Rings, Doctoral Thesis,
10.2010
- Generalized Artin Schreier Theorem I, 28.10.2012
- Real Sheaf Structures, in preparation
- Real closed * partially ordered Rings, arXiv and
RAAG preprint 0.1.06.2009
- Uniqueness of real closure * of regular rings,
arXiv Preprint 01.2008
- Uniqueness of real closure * of Baer regular rings,
arXiv Preprint 08.2007, Accessed 12.12.2007.
- Real Closed Rings and Real Closed * Rings,
arXiv Preprint 06.2007, Accessed 12.12.2007.
- Master's Thesis: Weil Pairings of Elliptic Curves,
(2004) Mathematisches Institut, Ludwig Maximillian Universität, Munich, Germany.
Non-mathematical Publications
- RRT-Binpicking for Industrial Application, IEEE International Symposium on Assembly and Manufacturing (ISAM) 2013, Xi'an, China. Accessed: 05.2013
- RRT Planner for the Binpicking Problem, International Workshop on Robot Motion and Control (RoMoCo) 2013, Wasowo Palace, Poland. Accessed: 05.2013
- The Determination of Optimum CeO2 Loading on Al2O3
for CO Oxidation and the Reactivity of C3H6 to the Optimum Loading (1998),
De La Salle University, Manila, Philippines
- A few 1.e4 e6, 1.e4 d6 unorthodox variations including the Czech-Benoni (in preparation)
- How to play like Alekhine (in preparation)
- Hair Simulation in Makehuman alpha releases (see here)
Projects