Dr. Jose Capco
Telefon: +43 512 507-61211
E-mail: jose.capco (at) uibk.ac.at
Büro: R410
Adresse: Universität Innsbruck, Arbeitsbereich für Geometrie und Vermessung
Technikerstrasse 13, 6020 Innsbruck
Sprechstunden: n. Vereinbarung
Research Interests
- algebraic geometry (set Theoretic complete intersections) and algebraic curves (esp. elliptic curves)
- algorithmic / algebraic / analytic number theories (Artin's conjecture, Inverse Galois Problem, prime-generating functions)
- computational geometry and finite projective geometry
- cryptography (elliptic curve cryptography)
- fractal sets
- kinematics and robotics
- mathematical chess problems (see Noam Elkies on enumerative chess problems) and various unorthodox mathematical problems
- real algebraic geometry (PhD thesis, sums of squares)
- ring theory (integer valued functions, Galois theory for commutative rings)
Projects
Contributions and Presentations
ZbMath Reviews
Mathematical Presentations
- Kneser's Algorithm, 13.12.2021, Linz Algebra Research Day
- 3R Positional Robots, 14.06.2021, Online Scientific Meeting
- Implementing HuPf with 6R/P Manipulators. Conference on Geometry Theory and Applications, Innsbruck, Austria, 07.06.2019.
- Sum of Squares over Rational. Computer Algebra Seminar, Research Institute for Symbolic Computation, Hagenberg, Austria, 08.11.2018.
- An Overview of (some) Mathematical Problems in Robotics. Oberseminar Reelle Geometrie, University of Konstanz, Konstanz, Germany, 08.06.2018.
- Generalizing concepts in field theory to rings. Computer Algebra Seminar, Research Institute for Symbolic Computation, Hagenberg, Austria, 03. + 10.11.2016.
- Generalizing Some Results in Field Theory for Rings. Second International Workshop and Conference in Commutative Algebra, Tribhuvan University, Kathmandu, Nepal, 19.10.2016.
- Sufficiency sets for the Collatz conjecture. LARD Seminar, Research Institute for Symbolic Computation, Hagenberg, Austria, 09.06.2016.
- A short result on the Collatz conjecture. University of the Philippines, Diliman, Quezon City, Philippines, 20.01.2016.
- A mathematical motivation for industrial robotic motion planning. Computational Mathematics - Numerical Analysis and Symbolic Computation, Johannes Kepler University, Linz, Austria, 23.05.2014. (Slides, Paper).
- A motivational talk in real algebraic geometry. University of the Philippines, Diliman, Quezon City, Philippines, 07.12.2009.
- Real closed rings and real closed * rings. DFG Seminar, University of Regensburg, Regensburg, Germany, 06.2006.
- Crash Course in Category Theory. DFG Seminar, University of Regensburg, Regensburg, Germany, 06.2006.
- Real closed * rings. DFG Seminar, University of Passau, Passau, Germany, 05.2006.
- Reals Sheaf Structures of Partially Ordered Rings. DFG-Seminar Reelle Algebraische Geometrie, University of Passau, Passau, Germany, 12.04.2006.
- Weil Pairings of Elliptic Curves. DFG-Seminar Reelle Algebraische Geometrie, University of Passau, Passau, Germany, 09.12.2004.
- Weil Pairings of Elliptic Curves. Oberseminar Komplex Analysis, Ludwig Maximilians University, Munich, Germany, 2004.
Non-mathematical Presentations
- RRT Planner for the Binpicking Problem. International Workshop on Robot Motion and Control (RoMoCo) 2013, Wasowo Palace, Poland, 04.07.2013. (pdf, ppt)
- The Determination of Optimum CeO2 Loading on Al2O3 for CO Oxidation and the Reactivity of C3H6 to the Optimum Loading. Chemical Engineering Presentations, De La Salle University, Manila, Philippines, 03.1998.
Lehre
Wintersemester
- Vorkurs Darstellende Geometrie (844802)
- Konstruktion / CAD in der Elektrotechnik (844870)
Sommersemester
- Geometrische Modellierung, Visualisierung und CAD - Übung (844855)
- Kinematik und Robotik (844866)
Publikationen (Auswahl)
Mathematical
- 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). Computer Algebra in Scientific Computing 2019, Lecture Notes in Computer Sciences, pp.78-90, Springer 2019.
- Factorization of Integer Valued Polynomials. Python code, cypari, 2018.
- Generalizing some Results in Field Theory for Rings. RISC Technical Report, 01.2017.
- The Number of Realization 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, pp. 94-125.
- Odd Collatz Sequence and Binary Representations. RISC Technical Report, 09.2015.
- Real Closed Rings and Real Closed * Rings. Journal of Pure and Applied Algebra, Vol. 218, No. 1, pp. 101-111, 2014.
- 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 01.06.2009.
- 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.
- Weil Pairings of Elliptic Curves. Master's Thesis, Mathematics Institute, Ludwig Maximilians Universität, Munich, Germany, 2004.
Non-mathematical
- RRT-Binpicking for Industrial Application. IEEE International Symposium on Assembly and Maufacturing (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. De La Salle Univerity, Manila Philippines, 1998.
- 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 (Link)