C Algebraic Geometry With Corners

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C Algebraic Geometry With Corners

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Author : Kelli Francis-Staite
language : en
Publisher: Cambridge University Press
Release Date : 2024-01-04

C Algebraic Geometry With Corners written by Kelli Francis-Staite and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-04 with Mathematics categories.

Crossing the boundary between differential and algebraic geometry in order to study singular spaces, this book introduces 'C∞-schemes with corners'.

C Algebraic Geometry With Corners

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Author : Kelli Francis-Staite
language : en
Publisher: Cambridge University Press
Release Date : 2024-01-04

C Algebraic Geometry With Corners written by Kelli Francis-Staite and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-04 with Mathematics categories.

Schemes in algebraic geometry can have singular points, whereas differential geometers typically focus on manifolds which are nonsingular. However, there is a class of schemes, 'C∞-schemes', which allow differential geometers to study a huge range of singular spaces, including 'infinitesimals' and infinite-dimensional spaces. These are applied in synthetic differential geometry, and derived differential geometry, the study of 'derived manifolds'. Differential geometers also study manifolds with corners. The cube is a 3-dimensional manifold with corners, with boundary the six square faces. This book introduces 'C∞-schemes with corners', singular spaces in differential geometry with good notions of boundary and corners. They can be used to define 'derived manifolds with corners' and 'derived orbifolds with corners'. These have applications to major areas of symplectic geometry involving moduli spaces of J-holomorphic curves. This work will be a welcome source of information and inspiration for graduate students and researchers working in differential or algebraic geometry.

Algebraic Geometry Over C Rings

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Author : Dominic Joyce
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-09-05

Algebraic Geometry Over C Rings written by Dominic Joyce and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-05 with Mathematics categories.

If X is a manifold then the R-algebra C∞(X) of smooth functions c:X→R is a C∞-ring. That is, for each smooth function f:Rn→R there is an n-fold operation Φf:C∞(X)n→C∞(X) acting by Φf:(c1,…,cn)↦f(c1,…,cn), and these operations Φf satisfy many natural identities. Thus, C∞(X) actually has a far richer structure than the obvious R-algebra structure. The author explains the foundations of a version of algebraic geometry in which rings or algebras are replaced by C∞-rings. As schemes are the basic objects in algebraic geometry, the new basic objects are C∞-schemes, a category of geometric objects which generalize manifolds and whose morphisms generalize smooth maps. The author also studies quasicoherent sheaves on C∞-schemes, and C∞-stacks, in particular Deligne-Mumford C∞-stacks, a 2-category of geometric objects generalizing orbifolds. Many of these ideas are not new: C∞-rings and C∞ -schemes have long been part of synthetic differential geometry. But the author develops them in new directions. In earlier publications, the author used these tools to define d-manifolds and d-orbifolds, “derived” versions of manifolds and orbifolds related to Spivak's “derived manifolds”.

C Infinity Algebraic Geometry With Corners

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Author : Kelli L. Francis-Staite
language : en
Publisher:
Release Date : 2019

C Infinity Algebraic Geometry With Corners written by Kelli L. Francis-Staite and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.

C Infinity Algebraic Geometry With Corners

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Author : Kelli L. Francis-Staite
language : en
Publisher:
Release Date : 2019

C Infinity Algebraic Geometry With Corners written by Kelli L. Francis-Staite and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.

Groups And Graphs Designs And Dynamics

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Author : R. A. Bailey
language : en
Publisher: Cambridge University Press
Release Date : 2024-05-30

Groups And Graphs Designs And Dynamics written by R. A. Bailey and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-30 with Mathematics categories.

This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.

Surveys In Combinatorics 2024

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Author : Felix Fischer
language : en
Publisher: Cambridge University Press
Release Date : 2024-06-13

Surveys In Combinatorics 2024 written by Felix Fischer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-13 with Mathematics categories.

This volume contains surveys of current research directions in combinatorics written by leading researchers in their fields.

Operator Algebras Quantization And Noncommutative Geometry

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Author : Robert S. Doran
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Operator Algebras Quantization And Noncommutative Geometry written by Robert S. Doran and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Computers categories.

John von Neumann and Marshall Stone were two giants of Twentieth Century mathematics. In honor of the 100th anniversary of their births, a mathematical celebration was organized featuring developments in fields where both men were major influences. This volume contains articles from the AMS Special Session, Operator Algebras, Quantization and Noncommutative Geometry: A Centennial Celebration in Honor of John von Neumann and Marshall H. Stone. Papers range from expository and refereed and cover a broad range of mathematical topics reflecting the fundamental ideas of von Neumann and Stone. Most contributions are expanded versions of the talks and were written exclusively for this volume. Included, among Also featured is a reprint of P.R. Halmos's The Legend of John von Neumann. The book is suitable for graduate students and researchers interested in operator algebras and applications, including noncommutative geometry.

Real Algebraic Geometry And Ordered Structures

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Author : Charles N. Delzell
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

Real Algebraic Geometry And Ordered Structures written by Charles N. Delzell and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

This volume contains 16 carefully refereed articles by participants in the Special Semester and the AMS Special Session on Real Algebraic Geometry and Ordered Structures held at Louisiana State University and Southern University (Baton Rouge). The 23 contributors to this volume were among the 75 mathematicians from 15 countries who participated in the special semester. Topics include the topology of real algebraic curves (Hilbert's 16th problem), moduli of real algebraic curves, effective sums of squares of real forms (Hilbert's 17th problem), efficient real quantifier elimination, subanalytic sets and stratifications, semialgebraic singularity theory, radial vector fields, exponential functions and valuations on nonarchimedean ordered fields, valued field extensions, partially ordered and lattice-ordered rings, rings of continuous functions, spectra of rings, and abstract spaces of (higher-level) orderings and real places. This volume provides a good overview of the state of the art in this area in the 1990s. It includes both expository and original research papers by top workers in this thriving field. The authors and editors strived to make the volume useful to a wide audience (including students and researchers) interested in real algebraic geometry and ordered structures-two subjects that are obviously related, but seldom brought together.

Algebraic Geometry

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Author : Dan Abramovich
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

Algebraic Geometry written by Dan Abramovich and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

This volume contains research and expository papers by some of the speakers at the 2005 AMS Summer Institute on Algebraic Geometry. Numerous papers delve into the geometry of various moduli spaces, including those of stable curves, stable maps, coherent sheaves, and abelian varieties.