leader doc. Hrdina
"In these days the angel of geometry and the devil of abstract algebra fight for the soul of every individual discipline of mathematics" Hermann Weyl :)
We are interested in
Linear Algebra – Geometric (Clifford) Algebras – Quaternions – Lie Groups and Algebras – Representation Theory – Mathematical (Geometric) Control Theory – Geometric Structures – Symmetry – Differential Geometry – Sub Riemannian Geometry
with applications in
Robotics – Mechanics – Nonholonomic systems – Inverse problems – Control theory – Route planning – Binocular vision – Quantum mechanics – Quantum computing – Theoretical physics
Members:
Jaroslav Hrdina, Petr Vašik, Aleš Návrat, Ivan Eryganov
PhD students: Roman Byrtus, Marek Stodola, Johanka Brdečková
If you are interested in our topics and are interested in participating in the form of thesis or a joint article, please contact us (hrdina@fme.vutbr.cz, vasik@fme.vutbr.cz, navrat.a@fme.vutbr.cz) we will be happy .
Currently realized topics
Control of a planar mechanism using symmetries
[1] J. Hrdina, A. Návrat, P. Vašík, L. Zalabová, Note on geometric algebras and control problems with SO(3) - symmetries, Mathematical Methods in the Applied Sciences (2022)
[2] J. Hrdina, A. Návrat, L. Zalabová, On symmetries of Sub--Riemannian structure with growth vector (4,7), Annali di Matematica Pura ed Applicata (2022)
[3] Hrdina, J., Návrat, A., Zalabová, L., Symmetries in geometric control theory using Maple, Mathematics and Computers in Simulation, 2021, 190, pp. 474–493
[DP 1] FROLÍK, S., Geometrická teorie řízení na nilpotentních Lieových grupách. Brno University of technology, Master's thesis.
Use of real geometric algebras in robotics
[4] Hrdina, J., Návrat, A., Vašík, P., Dorst, L., Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra, Advances in Applied Clifford Algebras, 2021, 31(2), 18
[5] Hrdina, J., Návrat, A. Binocular Computer Vision Based on Conformal Geometric Algebra. Adv. Appl. Clifford Algebras 27, 1945–1959 (2017)
[6] Hildenbrand, D., Hrdina, J., Návrat, A. et al. Local Controllability of Snake Robots Based on CRA, Theory and Practice. Adv. Appl. Clifford Algebras 30, 2 (2020).
[DP 2] STODOLA, M., Robotický manipulátor prostředky CGA Brno University of technology, 2019, Master's thesis.
Quantum computing (quantum game theory) using complex geometric algebras
[7] Hrdina J., Návrat A., Vašík P., Quantum computing based on complex Clifford algebras, Quantum Information Processing (2022)
[8] Alves, R., D. Hildenbrand, J. Hrdina, and C. Lavor, An Online Calculator for Quantum Computing Operations Based on Geometric Algebra, Advances in Applied Clifford Algebras 32 (1). 2022.
[9] Eryganov, I. Hrdina, J., Clifford algebra in repeated quantum prisoner's dilemma. Math Meth Appl Sci. 2022
[DP 3] KATABIRA, J.Groverův algoritmus v kvantovém počítání a jeho aplikace. Brno University of technology, 2021. Master's thesis.
Projects:
- OC-2021-1-25132 Cost project, Cartan geometry, Lie, Integrable Systems, quantum group Theories for Applications – funding of participation in seminars and workshops of the network. 2023-2025
- Cambridge University – Memorandum of Understanding – collaboration on topics related to geometric algebras
- University of Defense - collaboration on the development of autonomous control.
- OPVVV MSM EF16 026/0008404, Machine Tools and Precision Engineering, 2019–2022