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Geometrie symplektických gradovaných variet a jejich morfismů
Zika, Martin ; Jurčo, Branislav (advisor) ; Bugden, Mark (referee)
Graded manifolds naturally arise in the context of Batalin-Vilkovisky quantization as one introduces fields of non-trivial ghost degrees. We study the structures tied to the dy- namics and gauge symmetry of AKSZ models involving the classical master action or the antibracket on symplectic differential non-negatively graded manifolds (NQP manifolds) in the language of sheaves of graded-commutative algebras. We review the one-to-one correspondence between isomorphism classes of Courant algebroids and NQP manifolds of degree 2. Applying the construction of Lagrangian correspondences in the spirit of Weinstein's symplectic category, we extend the one-to-one correspondence on objects to an equivalence of categories. 1
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Zobecněná komplexní geometrie
Zika, Martin ; Jurčo, Branislav (advisor) ; Bugden, Mark (referee)
In an attempt to unify the underlying geometry of Hamilton's equations with the language of complex geometry, we motivate the research of generalized com- plex geometry. We construct the structure of a Courant algebroid on the di- rect sum of the tangent and cotangent bundle TM ⊕ T∗ M as we research the Courant bracket. The key notion of an involutive fibre-wise isotropic subbun- dle, a Dirac structure, is introduced and serves to specify a generalized complex structure. Generalized complex submanifolds are mentioned as well as the process of Dirac redution. Generalized complex geometry and the natural mechanisms in the Courant algebroid setting are then utilised as an interpretational tool in mathematical physics and related areas. We study a reduction of the symplectic structure of a harmonic oscillator, reflect on the nature of the Dirac bracket in string theory and relate a solution of a PDE to a generalized complex submanifold through the Monge-Amp`ere equations. 1
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Influence of the welfare state type on the pension system
Zika, Martin ; Čabanová, Bohumila (advisor) ; Potůček, Martin (referee)
Diploma thesis "Influence of the welfare state type on the pension system" deals with the way in which certain type of the welfare state influences settings of the individual parts of the social system, concretely pension system. The theoretical section deals with the classical theory of Gösta Esping-Andersen, who distinguished three basic types of welfare state: liberal, conservative and social-democratic, further reflection of his attitude and also new social risks. As representives of individual types of the welfare states were chosen Great Britain, Sweden and Germany. Author deals with analysis of pension systems of these countries and compares them on the basis of chosen criteria: demographic prospects, types of the pension systems, way of financing and public expenditures on the pension system. He tries to find out how the concrete type of the welfare state reflects in the specific settings of the pension systems in these countries. On the basic of this analysis, scholarly literature and the analysis of current situation in the Czech Republic (carried out among other things through the interviews with important actors) he tries to specify few recomendations for the Czech Republic, which prepares itself for a pension reform.
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