Classical Algebraic Geometry: A Modern View
by Igor V. Dolgachev
Publisher: Cambridge University Press 2012
Number of pages: 721
The main purpose of the present treatise is to give an account of some of the topics in algebraic geometry which while having occupied the minds of many mathematicians in previous generations have fallen out of fashion in modern times.
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by Alexander Kleshchev - University of Oregon
Contents: General Algebra; Commutative Algebra; Affine and Projective Algebraic Sets; Varieties; Morphisms; Tangent spaces; Complete Varieties; Basic Concepts; Lie algebra of an algebraic group; Quotients; Semisimple and unipotent elements; etc.
by Olivia Dumitrescu, Motohico Mulase - arXiv
The paper aims at giving an introduction to the notion of quantum curves. The main purpose is to describe the discovery of the relation between the topological recursion and the quantization of Hitchin spectral curves associated with Higgs bundles.
by Robert Hermann - Math Sci Press
Systems theory offers a unified mathematical framework to solve problems in a wide variety of fields. This mathematics is not of the traditional sort involved in engineering education, but involves virtually every field of modern mathematics.
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This is survey of recent developments in, and a tutorial on, the approach to P v. NP and related questions called Geometric Complexity Theory. The article is written to be accessible to graduate students. Numerous open questions are presented.