Program v akademickém roce 2022/2023
23. 3. 2023
doc. RNDr. Hynek Baran, Ph.D., Classification of PDEs by their integrability properties using the package Jets
15. 12. 2022
Univ.-Prof. Dr. Eva Kopecká (University of Innsbruck, Rakousko), Approximating convex sets by cylinders
Abstrakt: Let K be a compact convex set in Rd which is an intersection of halfspaces defined by at most two coordinates.
Let Q be the smallest axes-parallel box containing K. We show that when the dimension d grows, the ratio of the diameters diam Q/diam K of the two sets can be arbitrarily large. How large exactly is open.
24. 11. 2022
RNDr. Jaroslav Bradík, Quantization
10. 11. 2022
Maryna Nesterenko, D.Sc. (Institute of Mathematics, NAS of Ukraine, Ukrajina), Quasicrystal models, root systems and almost periodic functions
3. 11. 2022
prof. Francisco J. Herranz (Universidad de Burgos, Španělsko), Lie-Hamilton systems and their Poisson-Hopf deformations: Constants of the motion, superposition rules and applications
Abstrakt: A Lie-Hamilton (LH) system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a t-dependent vector field taking values in a finite-dimensional real Lie algebra of Hamiltonian vector fields with respect to a Poisson structure. Thus LH systems form a subclass of Lie systems so that their general solution can be written as a superposition rule of a family of particular solutions and some constants. We show that LH systems can always be endowed with a (nondeformed) Poisson-Hopf algebra structure which, in turn, allows us to obtain t-independent constants of the motion from the Casimir functions of the corresponding LH algebra straightforwardly and, from these, superposition rules in an algebraic way. In addition, we also present the recent formalism of Poisson-Hopf deformations of LH systems which combines the classical theory of Lie systems with methods from quantum algebras and integrable systems. The dynamics of a deformed LH system is now described by a t-dependent vector field taking values in a linear space of vector fields spanning a smooth distribution in the sense of Stefan-Sussmann, and no longer a (Vessiot–Guldberg) Lie algebra. These results are illustrated by considering Riccati, Milne-Pinney and Kummer-Schwarz equations along with the Ermakov system and the oscillator one.
26. 10. 2022
Mgr. Jakub Vašíček, Hamiltonovské struktury pro WDVV rovnice
Seminář se mimořádně koná 26.10.2022 od 16:25 v posluchárně R1
20. 10. 2022
Igor Leite Freire, D.Sc. (UFABC, Brazílie), A new Novikov equation II: analytic and geometric aspects
Abstrakt: In this talk we continue our discussions about the equation studied in the previous seminar. Our focus will be on certain analytic aspects of its solutions and geometric implications.
13. 10. 2022
Igor Leite Freire, D.Sc. (UFABC, Brazílie), A new Novikov equation I: solutions and conservation laws
Abstrakt: In this talk we explore some structural properties of a Novikov equation, namely, we discuss its Lie point symmetries, exact solutions, conservation laws, and certain non-negative solutions.
6. 10. 2022
Igor Leite Freire, D.Sc. (UFABC, Brazílie), Conserved quantities and the problem of continuation of solutions for the Camassa-Holm equation
Abstrakt: We use conserved quantities to answer the following question: given a solution of the Camassa-Holm equation, if there exists an open set for which it vanishes, what can we say about its behavior outside this given subset?
Program v akademickém roce 2021/2022
19. 5. 2022
prof. dr hab. Maciej Błaszak (Adam Mickiewicz University, Poznań, Polsko), Interacting solitons
doc. Krzysztof Marciniak, Ph.D. (Linköping University, Švédsko), King Oscar II and the origins of the qualitative theory of dynamical systems
12. 5. 2022
doc. Krzysztof Marciniak, Ph.D. (Linköping University, Švédsko), Inifinite dimensional Hamiltonian systems and their integrability
5. 5. 2022
prof. dr hab. Maciej Błaszak (Adam Mickiewicz University, Poznań, Polsko), Hamiltonian integrable nonlinear ODEs
21. 4. 2022
dr hab. Javier de Lucas Araujo (University of Warsaw, Polsko), A historical survey on Lie systems from their origins to modern generalisations
17. 2. 2022
doc. Roman O. Popovych, D.Sc. (University of Vienna, Rakousko), Group classification problems revisited
9. 12. 2021
doc. Roman O. Popovych, D.Sc. (University of Vienna, Rakousko), Equivalence Groups and Their Applications II: Rigorous Definition and Generalizations
30. 11. 2021
RNDr. Jaroslav Bradík, Calculating weighted harmonic Bergman kernel and asymptotic expansion of the harmonic Berezin transform on half-space
Seminář se koná mimořádně v úterý ve 14.00 v místnosti R2.
25. 11. 2021
doc. Roman O. Popovych, D.Sc. (University of Vienna, Rakousko), Equivalence Groups and Their Applications I: Classes of Differential Equations
Mgr. Pavel Holba, Zákony zachování pro zobecněnou Kuramotovu-Sivashinskeho rovnici
11. 11. 2021
doc. RNDr. Artur Sergyeyev, DSc., Symetrie, zákony zachování a řešení pro model z mechaniky tekutin
Jde o společnou práci s A. Bihlem, S. Opanasenkem a R.O. Popovychem, podrobnosti viz S. Opanasenko, A. Bihlo, R.O. Popovych, A. Sergyeyev, Physica D 402 (2020), art. 132188 a Physica D 411 (2020), art. 132546
5. 10. 2021
RNDr. Hynek Baran, Ph.D., Symetrie integrabilních parciálních diferenciálních rovnic (habilitační přednáška)
Seminář se koná mimořádně v úterý ve 14.45 v místnosti R1.
Semináře se obvykle konají ve čtvrtek od 14.00 hod. v budově Matematického ústavu, Na Rybníčku 1 v Opavě, v místnosti R1. Všichni zájemci jsou srdečně zváni.
