Symmetry and geometry

figWe use symmetry for the analytical and numerical solution to differential equations or for the construction of models in string theory. We also investigate related fields of   differential geometry and algebra, i.e., the structure and application of Lie groups and their algebras.

We qualify various classes of Lie algebras, study them and use them in applications, e.g.,in the construction of special functions or for the study of string theory models.

We look for symmetry groups of interesting differential equations and use them for solutions. And vice versa, we assemble equations with chosen symmetries and study their common properties.

Using the symmetry of simple Lie algebras we investigate symmetric function properties of more variables and appropriate orthogonal polynomials. We formulate their discrete Fourier analysis and test applications during digital data processing. 

Group Members

Faculty

prof. Ing. Goce Chadzitaskos, CSc.
e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it., room: 219, Břehová 7, Praha, phone: 420224358263
Field of interest:

prof. RNDr. Ladislav Hlavatý, DrSc.
e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it., room: 120, Břehová 7, Praha, phone: 420224358294
Field of interest:
* Dualita v teorii strun
* Yang-Baxterovy rovnice
* Integrabilita a symetrie diferenciálních rovnic

prof. Ing. Jiří Tolar, DrSc.
e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it., room: 219, Břehová 7, Praha, phone: 420224358264
Field of interest:

doc. Ing. Jiří Hrivnák, Ph.D.
e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it., room: 219, Břehová 7, Praha, phone: 420224358264
Field of interest:
* Lieovy algebry a grupy
* Coxeterovy grupy
* Fourierova analýza
* speciální funkce a ortogonální polynomy
* aplikace Lieovy teorie v CFT

doc. Ing. Libor Šnobl, Ph.D.
e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it., room: 216, Břehová 7, Praha, phone: 420224358260
Field of interest:
* Lieovy grupy a algebry
* Symetrie diferenciálních rovnic
* Diferenciální geometrie
* Duality v teorii strun

Ing. Petr Novotný, Ph.D.
e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it., room: 219, Břehová 7, Praha, phone: 420224358360
Field of interest:
* Gradace a gradované kontrakce * Lieových algeber
* Klasifikace Lieových algeber

Ing. Filip Petrásek, Ph.D.
e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
Field of interest:

Ing. Jan Vysoký, Ph.D.
e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it., room: 14b, Břehová 7, Praha, phone: 420224358351
Field of interest:
* Diferenciální geometrie
* Aplikace geometrie v matematické fyzice
* Teorie strun, M-teorie

Students

Ing. Adam Brus
e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
Supervisor: Ing. Jiří Hrivnák, PhD.
Topic: Speciálních funkce a polynomy afinních Weylových grup

Ing. Ivo Petr, Ph.D.
e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it., room: A-1426, Thákurova 7, Praha 6, phone: 224359875
Supervisor: prof. RNDr. Ladislav Hlavatý, DrSc.
Topic: Geometrické aspekty strunové teorie