Download or read book A Celebration of the Mathematical Legacy of Raoul Bott written by Peter Robert Kotiuga and published by American Mathematical Soc.. This book was released on 2010-01-01 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A History in Sum written by Steve Nadis and published by Harvard University Press. This book was released on 2013-11-01 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the twentieth century, American mathematicians began to make critical advances in a field previously dominated by Europeans. Harvard’s mathematics department was at the center of these developments. A History in Sum is an inviting account of the pioneers who trailblazed a distinctly American tradition of mathematics—in algebraic geometry and topology, complex analysis, number theory, and a host of esoteric subdisciplines that have rarely been written about outside of journal articles or advanced textbooks. The heady mathematical concepts that emerged, and the men and women who shaped them, are described here in lively, accessible prose. The story begins in 1825, when a precocious sixteen-year-old freshman, Benjamin Peirce, arrived at the College. He would become the first American to produce original mathematics—an ambition frowned upon in an era when professors largely limited themselves to teaching. Peirce’s successors—William Fogg Osgood and Maxime Bôcher—undertook the task of transforming the math department into a world-class research center, attracting to the faculty such luminaries as George David Birkhoff. Birkhoff produced a dazzling body of work, while training a generation of innovators—students like Marston Morse and Hassler Whitney, who forged novel pathways in topology and other areas. Influential figures from around the world soon flocked to Harvard, some overcoming great challenges to pursue their elected calling. A History in Sum elucidates the contributions of these extraordinary minds and makes clear why the history of the Harvard mathematics department is an essential part of the history of mathematics in America and beyond.
Download or read book Introductory Lectures on Equivariant Cohomology written by Loring W. Tu and published by Princeton University Press. This book was released on 2020-03-03 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Research in History and Philosophy of Mathematics written by Maria Zack and published by Springer Nature. This book was released on 2024-01-18 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 8 papers that have been collected by the Canadian Society for History and Philosophy of Mathematics. It showcases rigorously reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics.Some of the topics explored include: A way to rethink how logic is taught to philosophy students by using a rejuvenated version of the Aristotelian idea of an argument schema A quantitative approach using data from Wikipedia to study collaboration between nineteenth-century British mathematicians The depiction and perception of Émilie Du Châtelet’s scientific contributions as viewed through the frontispieces designed for books written by or connected to her A study of the Cambridge Women’s Research Club, a place where British women were able to participate in scholarly scientific discourse in the middle of the twentieth century An examination of the research and writing process of mathematicians by looking at their drafts and other preparatory notes A global history of al-Khwārāzmī’s Kitāb al-jabr wa-l-muqābala as obtained by tracing its reception through numerous translations and commentaries Written by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.
Download or read book Peter Lax Mathematician written by Reuben Hersh and published by American Mathematical Soc.. This book was released on 2014-12-29 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a biography of one of the most famous and influential living mathematicians, Peter Lax. He is virtually unique as a preeminent leader in both pure and applied mathematics, fields which are often seen as competing and incompatible. Although he has been an academic for all of his adult life, his biography is not without drama and tragedy. Lax and his family barely escaped to the U.S. from Budapest before the Holocaust descended. He was one of the youngest scientists to work on the Manhattan Project. He played a leading role in coping with the infamous "kidnapping" of the NYU mathematics department's computer, in 1970. The list of topics in which Lax made fundamental and long-lasting contributions is remarkable: scattering theory, solitons, shock waves, and even classical analysis, to name a few. His work has been honored many times, including the Abel Prize in 2005. The book concludes with an account of his most important mathematical contributions, made accessible without heavy prerequisites. Reuben Hersh has written extensively on mathematics. His book with Philip Davis, The Mathematical Experience, won the National Book Award in science. Hersh is emeritus professor of mathematics at the University of New Mexico.
Download or read book Noncommutative Geometry And Physics 3 Proceedings Of The Noncommutative Geometry And Physics 2008 On K theory And D branes Proceedings Of The Rims Thematic Year 2010 On Perspectives In Deformation Quantization And Noncommutative Geometry written by Giuseppe Dito and published by World Scientific. This book was released on 2013-01-11 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative differential geometry is a novel approach to geometry, aimed in part at applications in physics. It was founded in the early eighties by the 1982 Fields Medalist Alain Connes on the basis of his fundamental works in operator algebras. It is now a very active branch of mathematics with actual and potential applications to a variety of domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field. It is an important topic both for mathematics and physics.
Download or read book String Math 2013 written by Ron Donagi, Michael R. Douglas and published by American Mathematical Soc.. This book was released on 2014-12-02 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference `String-Math 2013' which was held June 17-21, 2013 at the Simons Center for Geometry and Physics at Stony Brook University. This was the third in a series of annual meetings devoted to the interface of mathematics and string theory. Topics include the latest developments in supersymmetric and topological field theory, localization techniques, the mathematics of quantum field theory, superstring compactification and duality, scattering amplitudes and their relation to Hodge theory, mirror symmetry and two-dimensional conformal field theory, and many more. This book will be important reading for researchers and students in the area, and for all mathematicians and string theorists who want to update themselves on developments in the math-string interface.
Download or read book Mathematical Foundations of Quantum Field Theory and Perturbative String Theory written by Hisham Sati and published by American Mathematical Soc.. This book was released on 2011-12-07 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conceptual progress in fundamental theoretical physics is linked with the search for the suitable mathematical structures that model the physical systems. Quantum field theory (QFT) has proven to be a rich source of ideas for mathematics for a long time. However, fundamental questions such as ``What is a QFT?'' did not have satisfactory mathematical answers, especially on spaces with arbitrary topology, fundamental for the formulation of perturbative string theory. This book contains a collection of papers highlighting the mathematical foundations of QFT and its relevance to perturbative string theory as well as the deep techniques that have been emerging in the last few years. The papers are organized under three main chapters: Foundations for Quantum Field Theory, Quantization of Field Theories, and Two-Dimensional Quantum Field Theories. An introduction, written by the editors, provides an overview of the main underlying themes that bind together the papers in the volume.
Download or read book Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes written by Boyan Sirakov and published by World Scientific. This book was released on 2019-02-27 with total page 5393 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Download or read book Coherent Sheaves Superconnections and Riemann Roch Grothendieck written by Jean-Michel Bismut and published by Springer Nature. This book was released on 2023-12-15 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph addresses two significant related questions in complex geometry: the construction of a Chern character on the Grothendieck group of coherent sheaves of a compact complex manifold with values in its Bott-Chern cohomology, and the proof of a corresponding Riemann-Roch-Grothendieck theorem. One main tool used is the equivalence of categories established by Block between the derived category of bounded complexes with coherent cohomology and the homotopy category of antiholomorphic superconnections. Chern-Weil theoretic techniques are then used to construct forms that represent the Chern character. The main theorem is then established using methods of analysis, by combining local index theory with the hypoelliptic Laplacian. Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck is an important contribution to both the geometric and analytic study of complex manifolds and, as such, it will be a valuable resource for many researchers in geometry, analysis, and mathematical physics.
Download or read book Interactions Between Hyperbolic Geometry Quantum Topology and Number Theory written by Abhijit Champanerkar and published by American Mathematical Soc.. This book was released on 2011 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a 10-day workshop given by leading experts in hyperbolic geometry, quantum topology and number theory, in June 2009 at Columbia University. Each speaker gave a minicourse consisting of three or four lectures aimed at graduate students and recent PhDs. The proceedings of this enormously successful workshop can serve as an introduction to this active research area in a way that is expository and broadly accessible to graduate students. Although many ideas overlap, the twelve expository/research papers in this volume can be grouped into four rough categories: (1) different approaches to the Volume Conjecture, and relations between the main quantum and geometric invariants; (2) the geometry associated to triangulations of hyperbolic 3-manifolds; (3) arithmetic invariants of hyperbolic 3-manifolds; (4) quantum invariants associated to knots and hyperbolic 3-manifolds. The workshop, the conference that followed, and these proceedings continue a long tradition in quantum and geometric topology of bringing together ideas from diverse areas of mathematics and physics, and highlights the importance of collaborative research in tackling big problems that require expertise in disparate disciplines.
Download or read book Global Homotopy Theory written by Stefan Schwede and published by Cambridge University Press. This book was released on 2018-09-06 with total page 847 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, self-contained approach to global equivariant homotopy theory, with many detailed examples and sample calculations.
Download or read book Lectures on Field Theory and Topology written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 2019-08-23 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.
Download or read book Women in Topology written by Maria Basterra and published by American Mathematical Soc.. This book was released on 2015-05-21 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the WIT: Women in Topology workshop, held from August 18-23, 2013, at the Banff International Research Station, Banff, Alberta, Canada. The Women in Topology workshop was devoted primarily to active collaboration by teams of five to seven participants, each including senior and junior researchers, as well as graduate students. This volume contains papers based on the results obtained by team projects in homotopy theory, including -infinity structures, equivariant homotopy theory, functor calculus, model categories, orbispaces, and topological Hochschild homology.
Download or read book Topological Groups Yesterday Today Tomorrow written by Sidney A. Morris and published by MDPI. This book was released on 2018-09-27 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Topological Groups: Yesterday, Today, Tomorrow" that was published in Axioms
Download or read book Analysis Geometry and Quantum Field Theory written by Clara L. Aldana and published by American Mathematical Soc.. This book was released on 2012 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference ``Analysis, Geometry and Quantum Field Theory'' held at Potsdam University in September 2011, which honored Steve Rosenberg's 60th birthday. The papers in this volume cover a wide range of areas, including Quantum Field Theory, Deformation Quantization, Gerbes, Loop Spaces, Index Theory, Determinants of Elliptic Operators, K-theory, Infinite Rank Bundles and Mathematical Biology.
Download or read book Algebraic Geometry and Number Theory written by Hussein Mourtada and published by Birkhäuser. This book was released on 2017-05-07 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
