Maximal Functions, LittlewoodPaley Theory, Riesz Transforms and Atomic Decomposition in the Multi-Parameter Flag Setting PDF Download
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Author: Yongsheng Han
Publisher: American Mathematical Society
ISBN: 1470453452
Category : Mathematics
Languages : en
Pages : 118
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Author: Yongsheng Han
Publisher: American Mathematical Society
ISBN: 1470453452
Category : Mathematics
Languages : en
Pages : 118
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Book Description
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Author: Anand P. Patel
Publisher: American Mathematical Society
ISBN: 1470461579
Category : Mathematics
Languages : en
Pages : 114
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Book Description
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Author: Michael Artin
Publisher: American Mathematical Society
ISBN: 1470471116
Category : Mathematics
Languages : en
Pages : 104
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Book Description
This book is an introduction to the geometry of complex algebraic varieties. It is intended for students who have learned algebra, analysis, and topology, as taught in standard undergraduate courses. So it is a suitable text for a beginning graduate course or an advanced undergraduate course. The book begins with a study of plane algebraic curves, then introduces affine and projective varieties, going on to dimension and constructibility. $mathcal{O}$-modules (quasicoherent sheaves) are defined without reference to sheaf theory, and their cohomology is defined axiomatically. The Riemann-Roch Theorem for curves is proved using projection to the projective line. Some of the points that aren't always treated in beginning courses are Hensel's Lemma, Chevalley's Finiteness Theorem, and the Birkhoff-Grothendieck Theorem. The book contains extensive discussions of finite group actions, lines in $mathbb{P}^3$, and double planes, and it ends with applications of the Riemann-Roch Theorem.
Author: Hideto Asashiba
Publisher: American Mathematical Society
ISBN: 1470464845
Category : Mathematics
Languages : en
Pages : 282
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Book Description
This book gives a self-contained account of applications of category theory to the theory of representations of algebras. Its main focus is on 2-categorical techniques, including 2-categorical covering theory. The book has few prerequisites beyond linear algebra and elementary ring theory, but familiarity with the basics of representations of quivers and of category theory will be helpful. In addition to providing an introduction to category theory, the book develops useful tools such as quivers, adjoints, string diagrams, and tensor products over a small category; gives an exposition of new advances such as a 2-categorical generalization of Cohen-Montgomery duality in pseudo-actions of a group; and develops the moderation level of categories, first proposed by Levy, to avoid the set theoretic paradox in category theory. The book is accessible to advanced undergraduate and graduate students who would like to study the representation theory of algebras, and it contains many exercises. It can be used as the textbook for an introductory course on the category theoretic approach with an emphasis on 2-categories, and as a reference for researchers in algebra interested in derived equivalences and covering theory.
Author: Srikanth B. Iyengar
Publisher: American Mathematical Society
ISBN: 1470471590
Category : Mathematics
Languages : en
Pages : 108
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Book Description
This book is aimed to provide an introduction to local cohomology which takes cognizance of the breadth of its interactions with other areas of mathematics. It covers topics such as the number of defining equations of algebraic sets, connectedness properties of algebraic sets, connections to sheaf cohomology and to de Rham cohomology, Gröbner bases in the commutative setting as well as for $D$-modules, the Frobenius morphism and characteristic $p$ methods, finiteness properties of local cohomology modules, semigroup rings and polyhedral geometry, and hypergeometric systems arising from semigroups. The book begins with basic notions in geometry, sheaf theory, and homological algebra leading to the definition and basic properties of local cohomology. Then it develops the theory in a number of different directions, and draws connections with topology, geometry, combinatorics, and algorithmic aspects of the subject.
Author: Tomasz Downarowicz
Publisher: American Mathematical Society
ISBN: 1470455870
Category : Mathematics
Languages : en
Pages : 108
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Book Description
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Author: Jacob Bedrossian
Publisher: American Mathematical Society
ISBN: 1470472252
Category : Mathematics
Languages : en
Pages : 148
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Book Description
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Author: D. Kaledin
Publisher: American Mathematical Society
ISBN: 1470455366
Category : Mathematics
Languages : en
Pages : 104
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Book Description
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Author: Kannan Soundararajan
Publisher: American Mathematical Society
ISBN: 1470469308
Category : Mathematics
Languages : en
Pages : 100
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Book Description
This book uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. It constructs all finite fields from scratch and shows that they are unique up to isomorphism. As a payoff, several combinatorial applications of finite fields are given: Sidon sets and perfect difference sets, de Bruijn sequences and a magic trick of Persi Diaconis, and the polynomial time algorithm for primality testing due to Agrawal, Kayal and Saxena. The book forms the basis for a one term intensive course with students meeting weekly for multiple lectures and a discussion session. Readers can expect to develop familiarity with ideas in algebra (groups, rings and fields), and elementary number theory, which would help with later classes where these are developed in greater detail. And they will enjoy seeing the AKS primality test application tying together the many disparate topics from the book. The pre-requisites for reading this book are minimal: familiarity with proof writing, some linear algebra, and one variable calculus is assumed. This book is aimed at incoming undergraduate students with a strong interest in mathematics or computer science.
Author: João C. A. Barata
Publisher: American Mathematical Society
ISBN: 147045548X
Category : Mathematics
Languages : en
Pages : 282
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Book Description
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