derived algebraic geometry oor Spaans
derived algebraic geometry
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geometría algebraica derivada
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branch of mathematics
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He is best known for his work, starting with his thesis, on infinity-categories and derived algebraic geometry.
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He earned his Ph.D. from the Massachusetts Institute of Technology under supervision of Michael J. Hopkins, in 2004 with a thesis on derived algebraic geometry.
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Derived algebraic geometry is a way of infusing homotopical methods into algebraic geometry, with two purposes: deeper insight into algebraic geometry (e.g. into intersection theory) and the use of methods of algebraic geometry in stable homotopy theory.
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1957 onwards: Grothendieck extends sheaf theory in line with the needs of algebraic geometry, introducing: schemes and general sheaves on them, local cohomology, derived categories (with Verdier), and Grothendieck topologies.
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In an address to the 1994 International Congress of Mathematicians in Zürich, Kontsevich (1994) speculated that mirror symmetry for a pair of Calabi–Yau manifolds X and Y could be explained as an equivalence of a triangulated category constructed from the algebraic geometry of X (the derived category of coherent sheaves on X) and another triangulated category constructed from the symplectic geometry of Y (the derived Fukaya category).
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Other research interests include tame and in particular derived tame algebras, and the geometry of varieties related to the representation theory of finite-dimensional associative algebras.
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His derivation of the estimates is a tour de force and the applications in algebraic geometry are beautiful.
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Our graduates gain sufficient knowledge to conduct basic research in such areas as algebra, geometry, differential equations and differential equations with partial derivatives.
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Aptitude for applying knowledge towards linear algebra, geometry, differential geometry, differential and integral calculus, differential equations and in partial derivatives, numerical methods, numerical algorithms, statistics, and optimization.
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Aptitude for applying knowledge about linear algebra, geometry, differential geometry, differential and integral calculus, differential equations and in partial derivatives, numerical methods, numerical algorithms, statistics, and optimization.
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On the other hand, the geometry of the algebraic surfaces and their moduli spaces is studied, and the surfaces K3 in relation to derived categories.
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The derived category of coherent sheaves is constructed using tools from complex geometry, a branch of mathematics that describes geometric curves in algebraic terms and solves geometric problems using algebraic equations.
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Aptitude to apply knowledge on: linear algebra; geometry, differential geometry; differential and integral calculus; differential equations and partial derivatives; numerical methods; numerical algorithms; statistics and optimisation. Understanding and mastery of basic concepts on the general laws of mechanics, thermodynamics, fields and waves and electromagnetism and their application for solving engineering problems.
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Available under License Creative Commons Attribution Non-commercial No Derivatives. 5MB mathematics teachers have to supplement their classes with dynamic geometry software like GeoGebra, a useful teaching tool for the subjects of geometry, calculus, algebra and trigonometry.
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