Theses

• Diploma thesis (Mgr.): Substitutional disorder in systems with correlated f-electrons, KFES MFF UK, Prague, 2003
• Dissertation thesis (Ph.D.): Several Dirac operators in parabolic geometry, MU UK, Prague, 2006

Journal publications

• Turek, I., Kudrnovsky J., Divis M., Franek P., Bihlmayer G., Blugel S.: First-principles Study of the Electronic Structure and Exchange Interactions in BCC Europium, Phys. Rev. B 68, 2003
• Franek, P.: Generalized Verma Module Homomorphisms in Singular Character, Archivum Mathematicum, Proceedings of the 26th Winter school Geomtry and Physics 2006
• Franek, P.: Dirac Operator in Two Variables from the Viewpoint of Parabolic Geometry, Advances in Applied Clifford Algebras, Birkhauser Basel, vol. 17, 2007
• Franek, P.: Generalized Dolbeault Sequences in Parabolic Geometry, Journal of Lie Theory 18 (2008) No. 4, 757--774, preprint
• Franek, P.: Description of a Complex of Operators Acting Between Higher Spinor Modules, Trends in mathematics, Hypercomplex analysys, Springer 2009, 151--164
• Franek, P.: Invariant Operators of First Order Generalizing the Dirac Operator in 2 Variables, Trends in mathematics, Hypercomplex analysys, Springer 2010, 81--93
• Pazourek, K., Tuček V., Franek P.: Hyperplane Section of the Complex Cayley Plane as the Homogenous Space F4/P4, Comment.Math.Univ.Carolin. 52,4 (2011) 535-549, preprint
• Franek P., Ratschan S., Zgliczynski P.: Satisfiability of Systems of Equations of Real Analytic Functions is Quasi-decidable, Mathematical Foundations of Computer Science 2011, Lecture Notes in Computer Science Volume 6907, 2011, pp 315-326,
• Franek P., Ratschan S.: Effective Topological Degree Computation Based on Interval Arithmetic, AMS Math. of Computation, published electronically: September 17, 2014 (preprint)
• Kuběna A., Franek P.: Symmetries of Quasi-values, Algorithmic Game Theory, Lecture Notes in Computer Science, Volume 8146, 2013, pp 159-170 (preprint)
• Franek P., Krčál M.: Robust satisfiability of systems of equations, Proceedings of ACM-SIAM Symposium of Discrete algorithms, Portland 2014, pp 193--203.
  • Extended version Robust satisfiability of systems of equations, Journal of the ACM, 62 (4), August 2015 (preprint)
• Franek P., Krcal M: On Computability and Triviality of Well Groups, Symposium on Computational Geometry 2015, LIPIcs 34, 2015, pp 842--856. Extended version published in Discrete & Computational Geometry, 2016, pp 126--164.
• Franek P., Ratschan S., Zgliczynski P: Quasi-decidability of a Fragment of the First-order Theory of Real Numbers, Journal of Automatic Reasoning (2015). Preprint arXiv:1309.6280
• Franek P., Krčál M, Persistence of zero set. Homology, Homotopy and Applications, 19 (2), 2017, pp 313--342. Preprint arXiv:1507.04310.
• Franek P., Krčál M., Wagner H.Solving equations and optimisation problems with uncertainty. Journal of Applied and Computational Topology. Preprint arXiv:1607.06344.
• Filakovsky M., Franek, P., Wagner, U., Zhechev, S. Computing simplicial representatives of homotopy group elements. (Accepted to SODA 2018.) Preprint

Recently submitted

Rohou S, Franek P, Aubry C, Jaulin L. Proving the existence of loops in robot trajectories. Preprint arXiv:1712.01341