Search for dissertations about: "Algebra and geometry"
Showing result 1 - 5 of 86 swedish dissertations containing the words Algebra and geometry.
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1. Waring-type problems for polynomials : Algebra meets Geometry
Abstract : In the present thesis we analyze different types of additive decompositions of homogeneous polynomials. These problems are usually called Waring-type problems and their story go back to the mid-19th century and, recently, they received the attention of a large community of mathematicians and engineers due to several applications. READ MORE
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2. Real and complex Monge-Ampère equations, statistical mechanics and canonical metrics
Abstract : Recent decades has seen a strong trend in complex geometry to study canonical metrics and the way they relate to geometric analysis, algebraic geometry and probability theory. This thesis consists of four papers each contributing to this field. The first paper sets up a probabilistic framework for real Monge-Ampère equations on tori. READ MORE
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3. Morphisms of real calculi from a geometric and algebraic perspective
Abstract : Noncommutative geometry has over the past four of decades grown into a rich field of study. Novel ideas and concepts are rapidly being developed, and a notable application of the theory outside of pure mathematics is quantum theory. READ MORE
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4. On the Clebsch-Gordan problem for quiver representations
Abstract : On the category of representations of a given quiver we define a tensor product point-wise and arrow-wise. The corresponding Clebsch-Gordan problem of how the tensor product of indecomposable representations decomposes into a direct sum of indecomposable representations is the topic of this thesis. READ MORE
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5. Hilbert schemes and Rees algebras
Abstract : The topic of this thesis is algebraic geometry, which is the mathematical subject that connects polynomial equations with geometric objects. Modern algebraic geometry has extended this framework by replacing polynomials with elements from a general commutative ring, and studies the geometry of abstract algebra. READ MORE