Program v akademickém roce 2019/2020
12. 12. 2019
doc. Igor Khavkine, PhD. (Matematický ústav AV ČR, Praha), Initial data for closed conformal Killing-Yano 2-forms
The Kerr-NUT-(A)dS family of exactly integrable higher dimensional black hole solutions of Einstein's equations is characterized by the existence of a non-degenerate closed conformal Killing-Yano (cCYK) 2-form. Using an exhaustive search, we identify a family of 2nd order propagation identities for the cCYK equation on 2-forms in n>4 dimensions. These identities allow us to project the cCYK equations onto a spacelike surface and thus characterize the initial data for Einstein's equations whose development admits a cCYK.
5. 12. 2019
RNDr. Hynek Baran, Ph.D., Infinitely Many Commuting Nonlocal Symmetries for Modified Martínez Alonso–Shabat Equation
We present a recursion operator and an infinite hierarchy of nonlocal commuting symmetries for the modified Martínez Alonso–Shabat equation uy uxz+α ux uty−(uz+α ut)uxy=0.
14. 11. 2019
Roman Popovych, D.Sc. (University of Vienna, Rakousko), Conditional symmetries of linear partial differential equations with two independent variables
We discuss reduction operators, i.e., operators of nonclassical (conditional) symmetry, of (1+1)-dimensional linear partial differential equations.
In particular, the reduction operators of (1+1)-dimensional second-order linear parabolic partial differential equations and all the possible reductions of these equations to ordinary differential ones are exhaustively described. This problem proves to be equivalent, in some sense, to solving the initial equations. This “no-go” result is extended to the investigation of point transformations (admissible transformations, equivalence transformations, Lie symmetries) and Lie reductions of the determining equations for the nonclassical symmetries. Transformations linearizing the determining equations are obtained in the general case and under different additional constraints.
The consideration of the above equations and of the (1+1)-dimensional linear rod equation is used to illustrate a new theorem on linear reduction operators of general linear partial differential equations.
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.