Multiplicative Invariant Fields Of Dimension Leq 6
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Author | : Akinari Hoshi |
Publisher | : American Mathematical Society |
Total Pages | : 150 |
Release | : 2023-03-09 |
Genre | : Mathematics |
ISBN | : 147046022X |
Download Multiplicative Invariant Fields of Dimension $leq 6$ Book in PDF, Epub and Kindle
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Author | : Peter Bürgisser |
Publisher | : Springer Science & Business Media |
Total Pages | : 630 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 3662033380 |
Download Algebraic Complexity Theory Book in PDF, Epub and Kindle
The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under standing of the intrinsic computational difficulty of problems.
Author | : Robert R. Bruner |
Publisher | : Springer |
Total Pages | : 396 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540397787 |
Download H Ring Spectra and Their Applications Book in PDF, Epub and Kindle
Author | : Mikhail Gersh Katz |
Publisher | : American Mathematical Soc. |
Total Pages | : 238 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 0821841777 |
Download Systolic Geometry and Topology Book in PDF, Epub and Kindle
The systole of a compact metric space $X$ is a metric invariant of $X$, defined as the least length of a noncontractible loop in $X$. When $X$ is a graph, the invariant is usually referred to as the girth, ever since the 1947 article by W. Tutte. The first nontrivial results for systoles of surfaces are the two classical inequalities of C. Loewner and P. Pu, relying on integral-geometric identities, in the case of the two-dimensional torus and real projective plane, respectively. Currently, systolic geometry is a rapidly developing field, which studies systolic invariants in their relation to other geometric invariants of a manifold. This book presents the systolic geometry of manifolds and polyhedra, starting with the two classical inequalities, and then proceeding to recent results, including a proof of M. Gromov's filling area conjecture in a hyperelliptic setting. It then presents Gromov's inequalities and their generalisations, as well as asymptotic phenomena for systoles of surfaces of large genus, revealing a link both to ergodic theory and to properties of congruence subgroups of arithmetic groups. The author includes results on the systolic manifestations of Massey products, as well as of the classical Lusternik-Schnirelmann category.
Author | : Maria Gorelik |
Publisher | : Springer Nature |
Total Pages | : 553 |
Release | : 2019-10-18 |
Genre | : Mathematics |
ISBN | : 3030235319 |
Download Representations and Nilpotent Orbits of Lie Algebraic Systems Book in PDF, Epub and Kindle
This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.
Author | : K. Erdmann |
Publisher | : Springer Science & Business Media |
Total Pages | : 254 |
Release | : 2006-09-28 |
Genre | : Mathematics |
ISBN | : 1846284902 |
Download Introduction to Lie Algebras Book in PDF, Epub and Kindle
Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous worked examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions. Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics.
Author | : Akinari Hoshi |
Publisher | : American Mathematical Soc. |
Total Pages | : 228 |
Release | : 2017-07-13 |
Genre | : Mathematics |
ISBN | : 1470424096 |
Download Rationality Problem for Algebraic Tori Book in PDF, Epub and Kindle
The authors give the complete stably rational classification of algebraic tori of dimensions and over a field . In particular, the stably rational classification of norm one tori whose Chevalley modules are of rank and is given. The authors show that there exist exactly (resp. , resp. ) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension , and there exist exactly (resp. , resp. ) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension . The authors make a procedure to compute a flabby resolution of a -lattice effectively by using the computer algebra system GAP. Some algorithms may determine whether the flabby class of a -lattice is invertible (resp. zero) or not. Using the algorithms, the suthors determine all the flabby and coflabby -lattices of rank up to and verify that they are stably permutation. The authors also show that the Krull-Schmidt theorem for -lattices holds when the rank , and fails when the rank is ...
Author | : |
Publisher | : |
Total Pages | : 308 |
Release | : 2008 |
Genre | : Dissertations, Academic |
ISBN | : |
Download Index to Theses with Abstracts Accepted for Higher Degrees by the Universities of Great Britain and Ireland and the Council for National Academic Awards Book in PDF, Epub and Kindle
Author | : Ellis Robert Kolchin |
Publisher | : |
Total Pages | : 271 |
Release | : 1985 |
Genre | : Differential algebraic groups |
ISBN | : 9780124176409 |
Download Pure and Applied Mathematics Book in PDF, Epub and Kindle
Author | : Fedor Bogomolov |
Publisher | : Springer Science & Business Media |
Total Pages | : 324 |
Release | : 2013-05-17 |
Genre | : Mathematics |
ISBN | : 146146482X |
Download Birational Geometry, Rational Curves, and Arithmetic Book in PDF, Epub and Kindle
This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.