Program v akademickém roce 2023/2024

15. 2. 2024

Mgr. Pavel Holba, Introduction to Neural Networks

23. 11. 2023

RNDr. Petr Vojčák, Ph.D., On recursion operators for full-fledged nonlocal symmetries of the reduced quasi-classical self-dual Yang-Mills equation II

16. 11. 2023

RNDr. Jiřina Jahnová, Ph.D., On recursion operators for full-fledged nonlocal symmetries of the reduced quasi-classical self-dual Yang-Mills equation

2. 11. 2023

doc. Roman Popovych, D.Sc., Extended symmetry analysis of dispersionless Nizhnik equation

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.

Program v akademickém roce 2022/2023

20. 7. 2023

M.Sc. Antonio Pan-Collantes (Universidad de Cádiz, Španělsko), Solvable structures and C∞-structures

15. 6. 2023

dr. hab. Wojciech Kryński, prof. IM PAN (IM PAN, Varšava, Polsko), On deformations of dispersionless Lax systems

25. 5. 2023

RNDr. Jaroslav Bradík, Harmonic Bergman kernel and harmonic Berezin transform

11. 5. 2023

Dr. Tamara Garrido Letrán (Universidad de Cádiz, Španělsko), New conserved quantities and modern symmetry analysis applied to a dissipative Westervelt equation

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 R^d 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?

Semináře se obvykle konají ve čtvrtek od 14.00 hod. v budově Matematického ústavu, Na Rybníčku 1 v Opavě, v místnosti RZ. Všichni zájemci jsou srdečně zváni.