Snowbird Lectures In Algebraic Geometry

Author : Ravi Vakil
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 51,7 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821837191

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Snowbird Lectures in Algebraic Geometry by Ravi Vakil Pdf

A significant part of the 2004 Summer Research Conference on Algebraic Geometry (Snowbird, UT) was devoted to lectures introducing the participants, in particular, graduate students and recent Ph.D.'s, to a wide swathe of algebraic geometry and giving them a working familiarity with exciting, rapidly developing parts of the field. One of the main goals of the organizers was to allow the participants to broaden their horizons beyond the narrow area in which they are working. A fine selection of topics and a noteworthy list of contributors made the resulting collection of articles a useful resource for everyone interested in getting acquainted with the modern topic of algebraic geometry. The book consists of ten articles covering, among others, the following topics: the minimal model program, derived categories of sheaves on algebraic varieties, Kobayashi hyperbolicity, groupoids and quotients in algebraic geometry, rigid analytic varieties, and equivariant cohomology. Suitable for independent study, this unique volume is intended for graduate students and researchers interested in algebraic geometry.

Author : Katrin Becker
Publisher : American Mathematical Soc.
Page : 120 pages
File Size : 48,6 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821836637

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Snowbird Lectures on String Geometry by Katrin Becker Pdf

The interaction and cross-fertilization of mathematics and physics is ubiquitous in the history of both disciplines. In particular, the recent developments of string theory have led to some relatively new areas of common interest among mathematicians and physicists, some of which are explored in the papers in this volume. These papers provide a reasonably comprehensive sampling of the potential for fruitful interaction between mathematicians and physicists that exists as a result of string theory.

Author : Anonim
Publisher : American Mathematical Soc.
Page : 104 pages
File Size : 48,9 Mb
Release : 2006
Category : Calabi-Yau manifolds
ISBN : 0821857339

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Snowbird Lectures on String Geometry by Anonim Pdf

Author : Hussein Mourtada,Celal Cem Sarıoğlu,Christophe Soulé,Ayberk Zeytin
Publisher : Birkhäuser
Page : 232 pages
File Size : 42,6 Mb
Release : 2017-05-07
Category : Mathematics
ISBN : 9783319477794

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Algebraic Geometry and Number Theory by Hussein Mourtada,Celal Cem Sarıoğlu,Christophe Soulé,Ayberk Zeytin Pdf

This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.

Author : Igor V. Dolgachev,JongHae Keum,Shigeyuki Kondō
Publisher : American Mathematical Soc.
Page : 256 pages
File Size : 43,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821842010

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Algebraic Geometry by Igor V. Dolgachev,JongHae Keum,Shigeyuki Kondō Pdf

This volume contains the proceedings of the Korea-Japan Conference on Algebraic Geometry in honor of Igor Dolgachev on his sixtieth birthday. The articles in this volume explore a wide variety of problems that illustrate interactions between algebraic geometry and other branches of mathematics. Among the topics covered by this volume are algebraic curve theory, algebraic surface theory, moduli space, automorphic forms, Mordell-Weil lattices, and automorphisms of hyperkahler manifolds. This book is an excellent and rich reference source for researchers.

Author : Sudhir Ghorpade
Publisher : American Mathematical Soc.
Page : 192 pages
File Size : 50,5 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821836293

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Commutative Algebra and Algebraic Geometry by Sudhir Ghorpade Pdf

The first Joint AMS-India Mathematics Meeting was held in Bangalore (India). This book presents articles written by speakers from a special session on commutative algebra and algebraic geometry. Included are contributions from some leading researchers around the world in this subject area. The volume contains new and original research papers and survey articles suitable for graduate students and researchers interested in commutative algebra and algebraic geometry.

Author : Daniel Huybrechts
Publisher : Cambridge University Press
Page : 499 pages
File Size : 47,7 Mb
Release : 2016-09-26
Category : Mathematics
ISBN : 9781107153042

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Lectures on K3 Surfaces by Daniel Huybrechts Pdf

Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.

Author : Arnaud Beauville,Brendan Hassett,Alexander Kuznetsov,Alessandro Verra
Publisher : Springer
Page : 170 pages
File Size : 47,6 Mb
Release : 2016-12-06
Category : Mathematics
ISBN : 9783319462097

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Rationality Problems in Algebraic Geometry by Arnaud Beauville,Brendan Hassett,Alexander Kuznetsov,Alessandro Verra Pdf

Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It offers a comprehensive introduction to this fascinating topic, and will certainly become an essential reference for anybody working in the field. Rationality problems are of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems motivated significant developments in the theory of abelian integrals, Riemann surfaces and the Abel–Jacobi map, among other areas, and they have strong links with modern notions such as moduli spaces, Hodge theory, algebraic cycles and derived categories. This text is aimed at researchers and graduate students in algebraic geometry.

Author : Georgia Benkart
Publisher : American Mathematical Soc.
Page : 270 pages
File Size : 55,7 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821839249

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Representations of Algebraic Groups, Quantum Groups, and Lie Algebras by Georgia Benkart Pdf

Covers various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie super algebras. This book outlines connections among irreducible representations of certain blocks of reduced enveloping algebras of semi-simple Lie algebras in positive characteristic.

Author : Loring W. Tu
Publisher : Princeton University Press
Page : 200 pages
File Size : 45,5 Mb
Release : 2020-03-03
Category : Mathematics
ISBN : 9780691197487

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Introductory Lectures on Equivariant Cohomology by Loring W. Tu Pdf

This book gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology. Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, or in other words, with symmetries of spaces. First defined in the 1950s, it has been introduced into K-theory and algebraic geometry, but it is in algebraic topology that the concepts are the most transparent and the proofs are the simplest. One of the most useful applications of equivariant cohomology is the equivariant localization theorem of Atiyah-Bott and Berline-Vergne, which converts the integral of an equivariant differential form into a finite sum over the fixed point set of the group action, providing a powerful tool for computing integrals over a manifold. Because integrals and symmetries are ubiquitous, equivariant cohomology has found applications in diverse areas of mathematics and physics. Assuming readers have taken one semester of manifold theory and a year of algebraic topology, Loring Tu begins with the topological construction of equivariant cohomology, then develops the theory for smooth manifolds with the aid of differential forms. To keep the exposition simple, the equivariant localization theorem is proven only for a circle action. An appendix gives a proof of the equivariant de Rham theorem, demonstrating that equivariant cohomology can be computed using equivariant differential forms. Examples and calculations illustrate new concepts. Exercises include hints or solutions, making this book suitable for self-study.

Author : Andrew Markoe
Publisher : American Mathematical Soc.
Page : 176 pages
File Size : 54,7 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821837559

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Integral Geometry and Tomography by Andrew Markoe Pdf

This volume consists of a collection of papers that brings together fundamental research in Radon transforms, integral geometry, and tomography. It grew out of the Special Session at a Sectional Meeting of the American Mathematical Society in 2004. The book contains very recent work of some of the top researchers in the field. The articles in the book deal with the determination of properties of functions on a manifold by integral theoretic methods, or by determining the geometricstructure of subsets of a manifold by analytic methods. Of particular concern are ways of reconstructing an unknown function from some of its projections. Radon transforms were developed at the beginning of the twentieth century by researchers who were motivated by problems in differential geometry,mathematical physics, and partial differential equations. Later, medical applications of these transforms produced breakthroughs in imaging technology that resulted in the 1979 Nobel Prize in Physiology and Medicine for the development of computerized tomography. Today the subject boasts substantial cross-disciplinary interactions, both in pure and applied mathematics as well as medicine, engineering, biology, physics, geosciences, and industrial testing. Therefore, this volume should be ofinterest to a wide spectrum of researchers both in mathematics and in other fields.

Author : Fabio Ancona
Publisher : American Mathematical Soc.
Page : 416 pages
File Size : 45,9 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821837665

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Control Methods in PDE-Dynamical Systems by Fabio Ancona Pdf

While rooted in controlled PDE systems, this 2005 AMS-IMS-SIAM Summer Research Conference sought to reach out to a rather distinct, yet scientifically related, research community in mathematics interested in PDE-based dynamical systems. Indeed, this community is also involved in the study of dynamical properties and asymptotic long-time behavior (in particular, stability) of PDE-mixed problems. It was the editors' conviction that the time had become ripe and the circumstances propitious for these two mathematical communities--that of PDE control and optimization theorists and that of dynamical specialists--to come together in order to share recent advances and breakthroughs in their respective disciplines. This conviction was further buttressed by recent discoveries that certain energy methods, initially devised for control-theoretic a-priori estimates, once combined with dynamical systems techniques, yield wholly new asymptotic results on well-established, nonlinear PDE systems, particularly hyperb These expectations are now particularly well reflected in the contributions to this volume, which involve nonlinear parabolic, as well as hyperbolic, equations and their attractors; aero-elasticity, elastic systems; Euler-Korteweg models; thin-film equations; Schrodinger equations; beam equations; etc. in addition, the static topics of Helmholtz and Morrey potentials are also prominently featured. A special component of the present volume focuses on hyperbolic conservation laws, to take advantage of recent theoretical advances with significant implications also on applied problems. in all these areas, the reader will find state-of-the-art accounts as stimulating starting points for further research.

Author : Sylvie Paycha,Bernardo Uribe
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 42,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821840627

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Geometric and Topological Methods for Quantum Field Theory by Sylvie Paycha,Bernardo Uribe Pdf

This volume, based on lectures and short communications at a summer school in Villa de Leyva, Colombia (July 2005), offers an introduction to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. It is aimed at graduate students in physics or mathematics who might want insight in the following topics (covered in five survey lectures): Anomalies and noncommutative geometry, Deformation quantisation and Poisson algebras, Topological quantum field theory and orbifolds. These lectures are followed by nine articles on various topics at the borderline of mathematics and physics ranging from quasicrystals to invariant instantons through black holes, and involving a number of mathematical tools borrowed from geometry, algebra and analysis.

Author : Richard Douglas Canary
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 49,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821842270

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In the Tradition of Ahlfors-Bers, IV by Richard Douglas Canary Pdf

The Ahlfors-Bers Colloquia commemorate the mathematical legacy of Lars Ahlfors and Lipman Bers. The core of this legacy lies in the fields of geometric function theory, Teichmuller theory, hyperbolic manifolds, and partial differential equations. However, the work of Ahlfors and Bers has impacted and created interactions with many other fields, such as algebraic geometry, mathematical physics, dynamics, geometric group theory, number theory, and topology. The triannual Ahlford-Bers colloquia serve as a venue to disseminate the relevant work to the wider mathematical community and bring the key participants together to ponder future directions in the field. The present volume includes a wide range of articles in the fields central to this legacy. The majority of articles present new results, but there are expository articles as well.

Author : Gui-Qiang Chen,Elton P. Hsu,Mark A. Pinsky
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 47,9 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821840597

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Stochastic Analysis and Partial Differential Equations by Gui-Qiang Chen,Elton P. Hsu,Mark A. Pinsky Pdf

This book is a collection of original research papers and expository articles from the scientific program of the 2004-05 Emphasis Year on Stochastic Analysis and Partial Differential Equations at Northwestern University. Many well-known mathematicians attended the events and submitted their contributions for this volume. Topics from stochastic analysis discussed in this volume include stochastic analysis of turbulence, Markov processes, microscopic lattice dynamics, microscopic interacting particle systems, and stochastic analysis on manifolds. Topics from partial differential equations include kinetic equations, hyperbolic conservation laws, Navier-Stokes equations, and Hamilton-Jacobi equations. A variety of methods, such as numerical analysis, homogenization, measure-theoretical analysis, entropy analysis, weak convergence analysis, Fourier analysis, and Ito's calculus, are further developed and applied. All these topics are naturally interrelated and represent a cross-section of the most significant recent advances and current trends and directions in stochastic analysis and partial differential equations. This volume is suitable for researchers and graduate students interested in stochastic analysis, partial differential equations, and related analysis and applications.