Lectures on Geometric Methods in Mathematical Physics
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Ja n 20 09 Toric geometry and local Calabi - Yau varieties
These lecture notes are an introduction to toric geometry. Particular focus is put on the description of toric local Calabi-Yau varieties, such as needed in applications to the AdS/CFT correspondence in string theory. The point of view taken in these lectures is mostly algebro-geometric but no prior knowledge of algebraic geometry is assumed. After introducing the necessary mathematical definit...
متن کامل8 M ay 2 00 9 Toric geometry and local Calabi - Yau varieties
These lecture notes are an introduction to toric geometry. Particular focus is put on the description of toric local Calabi-Yau varieties, such as needed in applications to the AdS/CFT correspondence in string theory. The point of view taken in these lectures is mostly algebro-geometric but no prior knowledge of algebraic geometry is assumed. After introducing the necessary mathematical definit...
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These notes are a rough write-up of lectures presented at the workshop on “Geometry and Integrability”, held at the University of Melbourne, 6-15 Feb, 2008. My interest in Geometric Representation Theory stems from recent developments in the Geometric Langlands program. These lectures are an introduction into material which are a prerequisite to anyone interested in studying the Geometric Langl...
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Introduction: Geometric distortion is a major shortcoming of magnetic resonance imaging (MRI), which has an important influence on the accuracy of volumetric measurements, an important parameter in neurology and oncology. Our goal is to design and construct a new three- dimensional phantom using a 3D printer in order to measure geometric distortion and its reproducibility in...
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In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as “why mathematicians are/should be interested in algebraic quantum field theory” would be equally fitting. Besides a presentation of the framework and the main results of local quantum physics these notes may ser...
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