Sökning: "Sergei A. Merkulov"

Visar resultat 1 - 5 av 6 avhandlingar innehållade orden Sergei A. Merkulov.

1. 1. Configuration spaces, props and wheel-free deformation quantization

   Författare :Theo Backman; Sergei Merkulov; Sergei Shadrin; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; operad; properad; prop; deformation quantization; configuration space; Lie bialgebra; Poisson manifold; Mathematics; matematik;

   Sammanfattning : The main theme of this thesis is higher algebraic structures that come from operads and props.The first chapter is an introduction to the mathematical framework needed for the content of this thesis. The chapter does not contain any new results. LÄS MER

3. 2. Wheeled Operads in Algebra, Geometry, and Quantization

   Författare :Johan Granåker; Sergei A. Merkulov; Andrey Lazarev; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; operads; deformation theory; homotopy algebra; deformation quantization; MATHEMATICS; MATEMATIK; Mathematics; matematik;

   Sammanfattning : The theory of generalized operads, the foundational conceptual framework of this thesis, has become a universal language, relating various areas such as algebraic topology, derived categories of algebras, deformation theory, differential geometry and the mathematical theory of quantization.The thesis consists of a preliminary chapter followed by four main chapters. LÄS MER

4. 3. Compactified Configuration Space of Points on a Line and Homotopies of A_ infty Morphisms

   Författare :Theo Backman; Sergei Merkulov; Alexander Berglund; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematics; matematik;

   Sammanfattning : In this thesis we construct a configuration space model for a particular 2-colored dg operad encoding the structure of two A_infty algebras with two A_infty morphism and a homotopy between the morphisms. We determine the cohomology of this operad to be the well-known 2-colored operad encoding the structure of a two associative algebras and an associative algebra morphism between them. LÄS MER

5. 4. Prop profiles of compatible Poisson and Nijenhuis structures

   Författare :Henrik Strohmayer; Sergei Merkulov; Gilles Halbout; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Koszul duality; resolutions; props; operads; compatible structures; MATHEMATICS; MATEMATIK; Mathematics; matematik;

   Sammanfattning : A prop profile of a differential geometric structure is a minimal resolution of an algebraic prop such that representations of this resolution are in one-to-one correspondence with structures of the given type. We begin this thesis with a detailed account of the algebraic tools necessary to construct prop profiles; we treat operads and props, and resolutions of these through Koszul duality. LÄS MER

7. 5. Universal algebraic structures on polyvector fields

   Författare :Johan Alm; Sergei Merkulov; Anton Alekseev; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematics; matematik;

   Sammanfattning : The theory of operads is a conceptual framework that has become a kind of universal language, relating branches of topology and algebra. This thesis uses the operadic framework to study the derived algebraic properties of polyvector fields on manifolds.The thesis is divided into eight chapters. LÄS MER