Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 125 for “"algebraic geometry"”.
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Derived algebraic geometry
… the foundations for a theory of derived algebraic geometry based upon simplicial commutative rings. We define derived versions of schemes, algebraic spaces, and algebraic stacks. Our main result is a derived analogue of Artin's representability theorem, which provides a precise criteria …
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Quantum Algebraic Geometry Codes
… error correction codes derived from classical algebraic geometry (AG) codes. We present two distinct construction techniques, highlighting the flexibility and self-orthogonality of AG codes, and demonstrate their ability to produce asymptotically good quantum codes. Additionally, we explore …
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Algebraic Geometry of Bayesian Networks
We develop the necessary theory in algebraic geometry to place Bayesian networks into the realm of algebraic statistics. This allows us to create an algebraic geometry--statistics dictionary. In particular, we study the algebraic varieties defined by the conditional independence statements of …
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Derived algebraic geometry over En̳-rings
We develop a theory of less commutative algebraic geometry where the role of commutative rings is assumed by En-rings, that is, rings with multiplication parametrized by configuration spaces of points in Rn. As n increases, these theories converge to the derived algebraic geometry of Tobn-Vezzosi …
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Real Algebraic Geometry of the Sextic Curves
… part of this thesis revolves around the real algebraic geometry of curves, especially curves of degree six. We use the topological and rigid isotopy classifications of plane sextics to explore the reality of several features associated to each class, such as the bitangents, inflection points, …
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Applications of algebraic geometry to coding & cryptography
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.
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Computational Algebraic Geometry Applied to Invariant Theory
Commutative algebra finds its roots in invariant theory and the connection is drawn from a modern standpoint. The Hilbert Basis Theorem and the Nullstellenstatz were considered lemmas for classical invariant theory. The Groebner basis is a modern tool used and is implemented with the computer …
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A survey of some problems in affine algebraic geometry
We describe the status of the following two questions: What are the automorphisms of the affine n-space An? Given m < n, is there a unique way (up to automorphisms of An) to embed Am in A n?
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Algebraic Geometry and Its Application to Error-Correcting Codes
… this end that we are studying the usefulness of algebraic geometry in making more efficient codes. We will be discussing how these codes are created and their parameters. We will then compare these geometric codes with their traditional counterparts.
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Algebraic geometry and representation theory in the Verlinde category
This thesis studies algebraic geometry and the representation theory of group schemes in the setting of symmetric tensor categories over algebraically closed fields of positive characteristic. A specific focus is paid to the Verlinde category, a symmetric fusion category in characteristic p that …
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Algebraic geometry for tensor networks, matrix multiplication, and flag matroids
… We use methods from nonlinear algebra and algebraic geometry to answer questions about topology, defining equations, and identifiability of uniform matrix product states. By an interplay of theorems from algebra, geometry, and quantum physics we answer several questions and conjectures …
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Interactions between combinatorics, lie theory and algebraic geometry via the Bruhat orders
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1981.
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Enumerative algebraic geometry via techniques of symplectic topology and analysis of local obstructions
Enumerative geometry of algebraic varieties is a fascinating field of mathematics that dates back to the nineteenth century. We introduce new computational tools into this field that are motivated by recent progress in symplectic topology and its influence on enumerative geometry. The most …
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Techniques in interpolation problems
… interpolation problem goes back to the origin of algebraic geometry and is still far from being solved. We approach it using algebraic geometry techniques, by systematically exploiting degenerations of the projective plane. Degenerating the plane into a union of planes we prove the planar case of …
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Resolution of Stratifolds and Connection to Mather's Abstract Pre-Stratified Spaces
Many spaces which naturally occur in topology and algebraic geometry are not manifolds, but have a decomposition as a disjoint union of manifolds. Examples include algebraic varieties, orbit spaces of proper smooth group actions on manifolds and mappings cylinders of maps between manifolds. In 1998 …
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FROM DG-CATEGORIES OVER K TO K-LINEAR STABLE INFINITY-CATEGORIES
… This result is a meeting point between algebraic topology and algebraic geometry. In 2013 L. Cohn proved it in a preprint, and in 2016, he updated the preprint to its latest version. Since then the ∞-category theory and the spectral algebraic geometry theory have made progress: …
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Enumerative problems in intersection theory
… of the basic tools of intersection theory in algebraic geometry. Some classical enumerative problems are then solved using these methods. In particular, we discuss the Fano variety of a cubic in surface in P3 , determinantal varieties, and the number of conics tangent to five conics in P2 .
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