Program v akademickém roce 2018/2019

27. 6. 2019

dr hab. Andrzej Frydryszak, prof. UWr (Uniwersytet Wrocławski, Polsko) Functions of Nilpotent Variables and Entanglement

Abstrakt:

I will give an introduction to the description of a new quantum mechanical resource called entanglement. In its basic version it is related to the question whether a tensor which is used to represent a physical state of a compound system is a simple tensor or not. Then, a natural desire arises to define a 'measure' of its departure from being simple. This yields to the study of sets of invariants of products of the SU(2) groups. I will present elements of the formalism of functions of nilpotent variables and I will explain how entanglement questions concerning the pure states find natural solutions in this approach, producing relevant invariants.

20. 6. 2019

RNDr. Petr Vojčák, Ph.D. Nelokální symetrie čtyřdimenzionální Martínez Alonsovy - Shabatovy rovnice

Abstrakt:

V přednášce budou prezentovány průběžné výsledky výzkumu nakrytí a hierarchií nelokálních symetrií čtyřdimenzionální Martínez Alonsovy - Shabatovy rovnice.

25. 4. 2019

RNDr. Petr Vojčák, Ph.D., Nonlocal symmetries, conservation laws, and recursion operators of the Veronese web equation

18. 4. 2019

doc. RNDr. Artur Sergyeyev, Ph.D., The Gardner method for symmetries (after the paper by A. Rasin and J. Schiff)

15. 2. 2019

Roman Popovych, D.Sc. (University of Vienna, Rakousko), Extended symmetry analysis of isothermal no-slip drift flux model II

Jedná se o volné pokračování předchozí přednášky.

Seminář proběhne v mimořádném termínu v pátek 15. 2. od 14.00.

7. 2. 2019

Roman Popovych, D.Sc. (University of Vienna, Rakousko), Extended symmetry analysis of isothermal no-slip drift flux model

Abstrakt:

We perform extended group analysis for a system of differential equations modeling an isothermal no-slip drift flux. The maximal Lie invariance algebra of this system is proved to be infinite-dimensional. We also find the complete point symmetry group of this system, including discrete symmetries, using the megaideal-based version of the algebraic method. Optimal lists of one- and two-dimensional subalgebras of the maximal Lie invariance algebra in question are constructed and employed for obtaining reductions of the system under study. Since this system contains a subsystem of two equations that involves only two of three dependent variables, we also perform group analysis of this subsystem. The latter can be linearized by a composition of a fiber-preserving point transformation with a two-dimensional hodograph transformation to the Klein-Gordon equation. We also employ both the linearization and the generalized hodograph method for constructing the general solution of the entire system under study. We find inter alia genuinely generalized symmetries for this system and present the connection between them and the Lie symmetries of the subsystem we mentioned earlier. Hydrodynamic conservation laws and their generalizations are also constructed.

This is joint work with S. Opanasenko, A. Bihlo and A. Sergyeyev.

6. 12. 2018

doc. RNDr. Artur Sergyeyev, Ph.D. The Gardner method for symmetries (after Rasin and Schiff)

Přednáška začne v 14.50.

22. 11. 2018

Priscila Leal da Silva, Ph.D. (Universidade Federal de São Carlos, Brazílie), Classification of bounded travelling wave solutions of Dullin-Gotwald-Holm equations

Abstrakt:

In this talk we will discuss the problem of existence of bounded traveling wave solutions of Dullin-Gottwald-Holm equations. The classification presents both smooth and weak solutions of the equations under consideration.

15. 11. 2018

Roman Popovych, D.Sc. (University of Vienna, Rakousko), Effective generalized equivalence groups for classes of differential equations

Seminář prof. Popovyche začne ve 14:30.

1. 11. 2018

Igor Leite Freire, D.Sc. (UFABC, Brazílie), Some results on the rotation Camassa-Holm equation

Abstrakt:

Recently, a mathematical model of the equatorial water waves with Coriollis effect was derived. This model is a generalization of the Dullin-Gottwald-Holm equation, which itself is a generalization of the Camassa-Holm equation. In this talk we shall discuss some results on the model in question, known as the rotation Camassa-Holm equation.

18. 10. 2018

Roman Popovych, D.Sc. (University of Vienna, Rakousko), Generalized symmetries and conservation laws of (1+1)-dimensional Klein--Gordon equation

Abstrakt:

We explicitly find the algebra of generalized symmetries of the (1+1)-dimensional Klein--Gordon equation, which allows us to describe this algebra in terms of the universal enveloping algebra of the essential Lie invariance algebra of the Klein--Gordon equation. Then we single out variational symmetries of this equation and compute the space of its local conservation laws.

11. 10. 2018

doc. RNDr. Artur Sergyeyev, Ph.D., Integrable systems in 4D from contact geometry

Abstrakt:

In this talk we present a survey of results from the paper A. Sergyeyev, New integrable (3+1)-dimensional systems and contact geometry, Lett. Math. Phys. 108 (2018), no. 2, 359-376.

4. 10. 2018

Igor Leite Freire, D.Sc. (UFABC, Brazílie), A look on some results about Camassa-Holm type equations

Abstrakt:

We discuss some results on families of equations including the Camassa-Holm and Novikov equations, and the generalizations thereof. The talk is based on joint works with S.C. Anco, P. L. da Silva, and D.C. Ferraioli.

26. 9. 2018

Seminář je spojen se slavnostním seminářem prof. Smítala a doc. Štefánkové - zahájení mimořádně od 12:00 v aule:

Martin Černohorský, Úspěch historie a lingvistiky při rehabilitaci Newtona a jeho prvního axiomu pohybu vykládaného po tři staletí neoprávněně jako jen pouhý zvláštní případ druhého axiomu (kolokviální přednáška).

 

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.