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

Mathematical Publications

1. Two Remarks on Sums of Squares (with: C. Scheiderer). Algebra, Logic and Number Theory. Banach Center Publications 2020, Vol. 121, pp.25-36.
2. 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, pp. 62-69
3. 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, pp. 78-90
4. Factorization of Integer Valued Polynomials.Python code, (cypari) , 03.2018
5. Generalizing some Results in Field Theory for Rings, 01.2017, RISC Technical Report
6. 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
7. Odd Collatz Sequence and Binary Representations, 09.2015, RISC Technical Report
8. 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
9. Real Closed * Rings, Doctoral Thesis, 10.2010
10. Generalized Artin Schreier Theorem I, 28.10.2012
11. Real Sheaf Structures, in preparation
12. Real closed * partially ordered Rings, arXiv and RAAG preprint 0.1.06.2009
13. Uniqueness of real closure * of regular rings, arXiv Preprint 01.2008
14. Uniqueness of real closure * of Baer regular rings, arXiv Preprint 08.2007, Accessed 12.12.2007.
15. Real Closed Rings and Real Closed * Rings, arXiv Preprint 06.2007, Accessed 12.12.2007.
16. Master's Thesis: Weil Pairings of Elliptic Curves, (2004) Mathematisches Institut, Ludwig Maximillian Universität, Munich, Germany.

Non-mathematical Publications

1. RRT-Binpicking for Industrial Application, IEEE International Symposium on Assembly and Manufacturing (ISAM) 2013, Xi'an, China. Accessed: 05.2013
2. RRT Planner for the Binpicking Problem, International Workshop on Robot Motion and Control (RoMoCo) 2013, Wasowo Palace, Poland. Accessed: 05.2013
3. 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
4. A few 1.e4 e6, 1.e4 d6 unorthodox variations including the Czech-Benoni (in preparation)
5. How to play like Alekhine (in preparation)
6. Hair Simulation in Makehuman alpha releases (see here)

Projects

• Algebraic path-planning of 6R/P Manipulators
• Efficient certified algorithms for robot motion planning - ECARP