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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Combinatorial Gap Label Cover
 Bialas, Filip ; Barto, Libor (advisor) ; Kompatscher, Michael (referee)
Theorems about probabilistically checkable proofs (PCP) are famous hard-to-prove results from the theoretical computer science. They provide constructions of PCP sys- tems with interesting surprising properties and serve as a starting point for proofs of NP-hardness of many approximation problems. Recently, a weaker combinatorial version of one of these theorems (Gap Label Cover) was proved using only combinatorial tools. After summarizing the main results in the classical PCP theory, I explore the combina- torial version thoroughly. Original results of this thesis consist of counterexamples to the expected behavior of two concepts from the classical theory in the combinatorial setting - probabilistic version and parallel repetition. 1
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AKSZ formalism and applications
 Bialas, Filip ; Jurčo, Branislav (advisor) ; Vysoký, Jan (referee)
Generalization of manifolds to the case of both commuting and anticommut- ing variables - Z-graded manifolds are described in this thesis. The language of categories and algebraic geometry is used for defining them and generalizing a few geometrical concepts such as vector fields, differential forms, and symplectic geometry. In the rest of the text, AKSZ construction is described. This construc- tion unifies a few topological field theories by constructing an action functional which is a solution to the classical BV master equation. We will describe one such theory (Poisson sigma model) using AKSZ formalism in greater detail. 1
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