Superschool On Derived Categories And D Branes

Author : Matthew Ballard,Charles Doran,David Favero,Eric Sharpe
Publisher : Springer
Page : 260 pages
File Size : 45,8 Mb
Release : 2018-08-21
Category : Mathematics
ISBN : 9783319916262

Get Book

Superschool on Derived Categories and D-branes by Matthew Ballard,Charles Doran,David Favero,Eric Sharpe Pdf

This book consists of a series of introductory lectures on mirror symmetry and its surrounding topics. These lectures were provided by participants in the PIMS Superschool for Derived Categories and D-branes in July 2016. Together, they form a comprehensive introduction to the field that integrates perspectives from mathematicians and physicists alike. These proceedings provide a pleasant and broad introduction into modern research topics surrounding string theory and mirror symmetry that is approachable to readers new to the subjects. These topics include constructions of various mirror pairs, approaches to mirror symmetry, connections to homological algebra, and physical motivations. Of particular interest is the connection between GLSMs, D-branes, birational geometry, and derived categories, which is explained both from a physical and mathematical perspective. The introductory lectures provided herein highlight many features of this emerging field and give concrete connections between the physics and the math. Mathematical readers will come away with a broader perspective on this field and a bit of physical intuition, while physicists will gain an introductory overview of the developing mathematical realization of physical predictions.

Author : Łukasz Piątek,Soon Heng Lim,Chien Ming Wang,Rutger de Graaf-van Dinther
Publisher : Springer Nature
Page : 518 pages
File Size : 43,6 Mb
Release : 2021-08-05
Category : Technology & Engineering
ISBN : 9789811622564

Get Book

WCFS2020 by Łukasz Piątek,Soon Heng Lim,Chien Ming Wang,Rutger de Graaf-van Dinther Pdf

This book highlights state-of-the-art research findings on floating developments in both inland and coastal waters with focus on living, recreation and working offshore. It includes six themes: (1) business case and real estate development, (2) spatial planning and architecture, (3) food and energy production, (4) ecological impact and nature-based solutions, (5) governance and social impact and (6) design and engineering of (infra)structures. The book presents key issues addressed when utilizing water space. It gives an overview of findings and discussions from the world’s leading experts from the industry, policymakers, entrepreneurs, researchers and identifies new opportunities as well as fosters collaboration on floating projects for a more climate-adaptive, socially inclusive, sustainable and better world.

Author : Noriko Yui
Publisher : American Mathematical Soc.
Page : 320 pages
File Size : 47,9 Mb
Release : 2008
Category : Duality (Mathematics)
ISBN : 9780821844847

Get Book

Modular Forms and String Duality by Noriko Yui Pdf

"This book is a testimony to the BIRS Workshop, and it covers a wide range of topics at the interface of number theory and string theory, with special emphasis on modular forms and string duality. They include the recent advances as well as introductory expositions on various aspects of modular forms, motives, differential equations, conformal field theory, topological strings and Gromov-Witten invariants, mirror symmetry, and homological mirror symmetry. The contributions are roughly divided into three categories: arithmetic and modular forms, geometric and differential equations, and physics and string theory. The book is suitable for researchers working at the interface of number theory and string theory."--BOOK JACKET.

Author : Jerzy Kowalski-Glikman
Publisher : Springer
Page : 376 pages
File Size : 55,8 Mb
Release : 2008-01-11
Category : Science
ISBN : 9783540466345

Get Book

Towards Quantum Gravity by Jerzy Kowalski-Glikman Pdf

The aim of this book is to give graduate students an overview of quantum gravity but it also covers related topics from astrophysics. Some well-written contributions can serve as an introduction into basic conceptual concepts like time in quantum gravity or the emergence of a classical world from quantum cosmology. This makes the volume attractive to philosophers of science, too. Other topics are black holes, gravitational waves and non-commutative extensions of physical theories.

Author : Matt Kerr,Gregory Pearlstein
Publisher : Cambridge University Press
Page : 533 pages
File Size : 51,5 Mb
Release : 2016-02-04
Category : Mathematics
ISBN : 9781107546295

Get Book

Recent Advances in Hodge Theory by Matt Kerr,Gregory Pearlstein Pdf

Combines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.

Author : Vincent Bouchard:,Charles Doran,Stefan Méndez-Diez,Callum Quigley
Publisher : American Mathematical Soc.
Page : 396 pages
File Size : 48,8 Mb
Release : 2016-06-10
Category : $K$-theory
ISBN : 9781470419929

Get Book

String-Math 2014 by Vincent Bouchard:,Charles Doran,Stefan Méndez-Diez,Callum Quigley Pdf

The conference String-Math 2014 was held from June 9–13, 2014, at the University of Alberta. This edition of String-Math is the first to include satellite workshops: “String-Math Summer School” (held from June 2–6, 2014, at the University of British Columbia), “Calabi-Yau Manifolds and their Moduli” (held from June 14–18, 2014, at the University of Alberta), and “Quantum Curves and Quantum Knot Invariants” (held from June 16–20, 2014, at the Banff International Research Station). This volume presents the proceedings of the conference and satellite workshops. For mathematics, string theory has been a source of many significant inspirations, ranging from Seiberg-Witten theory in four-manifolds, to enumerative geometry and Gromov-Witten theory in algebraic geometry, to work on the Jones polynomial in knot theory, to recent progress in the geometric Langlands program and the development of derived algebraic geometry and n-category theory. In the other direction, mathematics has provided physicists with powerful tools, ranging from powerful differential geometric techniques for solving or analyzing key partial differential equations, to toric geometry, to K-theory and derived categories in D-branes, to the analysis of Calabi-Yau manifolds and string compactifications, to modular forms and other arithmetic techniques. Articles in this book address many of these topics.

Author : Chen Ning Yang,Mo-lin Ge,Yang-hui He
Publisher : World Scientific
Page : 231 pages
File Size : 45,6 Mb
Release : 2019-01-09
Category : Science
ISBN : 9789813278684

Get Book

Topology And Physics by Chen Ning Yang,Mo-lin Ge,Yang-hui He Pdf

'The book is an engaging and influential collection of significant contributions from an assembly of world expert leaders and pioneers from different fields, working at the interface between topology and physics or applications of topology to physical systems … The book explores many interesting and novel topics that lie at the intersection between gravity, quantum fields, condensed matter, physical cosmology and topology … A rich, well-organized, and comprehensive overview of remarkable and insightful connections between physics and topology is here made available to the physics reader.'Contemporary PhysicsSince its birth in Poincaré's seminal 1894 'Analysis Situs', topology has become a cornerstone of mathematics. As with all beautiful mathematical concepts, topology inevitably — resonating with that Wignerian principle of the effectiveness of mathematics in the natural sciences — finds its prominent role in physics. From Chern-Simons theory to topological quantum field theory, from knot invariants to Calabi-Yau compactification in string theory, from spacetime topology in cosmology to the recent Nobel Prize winning work on topological insulators, the interactions between topology and physics have been a triumph over the past few decades.In this eponymous volume, we are honoured to have contributions from an assembly of grand masters of the field, guiding us with their world-renowned expertise on the subject of the interplay between 'Topology' and 'Physics'. Beginning with a preface by Chen Ning Yang on his recollections of the early days, we proceed to a novel view of nuclei from the perspective of complex geometry by Sir Michael Atiyah and Nick Manton, followed by an entrée toward recent developments in two-dimensional gravity and intersection theory on the moduli space of Riemann surfaces by Robbert Dijkgraaf and Edward Witten; a study of Majorana fermions and relations to the Braid group by Louis H Kauffman; a pioneering investigation on arithmetic gauge theory by Minhyong Kim; an anecdote-enriched review of singularity theorems in black-hole physics by Sir Roger Penrose; an adventure beyond anyons by Zhenghan Wang; an aperçu on topological insulators from first-principle calculations by Haijun Zhang and Shou-Cheng Zhang; finishing with synopsis on quantum information theory as one of the four revolutions in physics and the second quantum revolution by Xiao-Gang Wen. We hope that this book will serve to inspire the research community.

Author : Radu Laza,Matthias Schütt,Noriko Yui
Publisher : Springer Science & Business Media
Page : 613 pages
File Size : 45,8 Mb
Release : 2013-06-12
Category : Mathematics
ISBN : 9781461464037

Get Book

Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds by Radu Laza,Matthias Schütt,Noriko Yui Pdf

In recent years, research in K3 surfaces and Calabi–Yau varieties has seen spectacular progress from both arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics—in particular, in string theory. The workshop on Arithmetic and Geometry of K3 surfaces and Calabi–Yau threefolds, held at the Fields Institute (August 16-25, 2011), aimed to give a state-of-the-art survey of these new developments. This proceedings volume includes a representative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometry to mathematical physics, the papers are naturally related by the common theme of Calabi–Yau varieties. With the big variety of branches of mathematics and mathematical physics touched upon, this area reveals many deep connections between subjects previously considered unrelated. Unlike most other conferences, the 2011 Calabi–Yau workshop started with 3 days of introductory lectures. A selection of 4 of these lectures is included in this volume. These lectures can be used as a starting point for the graduate students and other junior researchers, or as a guide to the subject.

Author : Radu Laza,Matthias Schütt,Noriko Yui
Publisher : Springer
Page : 547 pages
File Size : 55,9 Mb
Release : 2015-08-27
Category : Mathematics
ISBN : 9781493928309

Get Book

Calabi-Yau Varieties: Arithmetic, Geometry and Physics by Radu Laza,Matthias Schütt,Noriko Yui Pdf

This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area. The contributions in this book are based on lectures that took place during workshops with the following thematic titles: “Modular Forms Around String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics Around Mirror Symmetry,” “Hodge Theory in String Theory.” The book is ideal for graduate students and researchers learning about Calabi–Yau varieties as well as physics students and string theorists who wish to learn the mathematics behind these varieties.

Author : John McKay
Publisher : American Mathematical Soc.
Page : 280 pages
File Size : 43,8 Mb
Release : 2001
Category : Finite groups
ISBN : 9780821828793

Get Book

Proceedings on Moonshine and Related Topics by John McKay Pdf

This volume contains the proceedings of the Moonshine workshop held at the Centre de Recherches Mathematiques (CRM) in Montreal. In this volume, all the classical Moonshine themes are presented, namely the Monster simple group and other finite groups, automorphic functions and forms and related congruence groups, and vertex algebras and their representations. These topics appear in either a pure form or in a blend of algebraic geometry dealing with algebraic surfaces, Picard-Fuchsequations, and hypergeometric functions.

Author : Jan Arthur Christophersen,Kristian Ranestad
Publisher : Springer
Page : 0 pages
File Size : 55,5 Mb
Release : 2018-11-24
Category : Mathematics
ISBN : 3319948806

Get Book

Geometry of Moduli by Jan Arthur Christophersen,Kristian Ranestad Pdf

The proceedings from the Abel Symposium on Geometry of Moduli, held at Svinøya Rorbuer, Svolvær in Lofoten, in August 2017, present both survey and research articles on the recent surge of developments in understanding moduli problems in algebraic geometry. Written by many of the main contributors to this evolving subject, the book provides a comprehensive collection of new methods and the various directions in which moduli theory is advancing. These include the geometry of moduli spaces, non-reductive geometric invariant theory, birational geometry, enumerative geometry, hyper-kähler geometry, syzygies of curves and Brill-Noether theory and stability conditions. Moduli theory is ubiquitous in algebraic geometry, and this is reflected in the list of moduli spaces addressed in this volume: sheaves on varieties, symmetric tensors, abelian differentials, (log) Calabi-Yau varieties, points on schemes, rational varieties, curves, abelian varieties and hyper-Kähler manifolds.

Author : Gavril Farkas,Ian Morrison
Publisher : Unknown
Page : 594 pages
File Size : 47,7 Mb
Release : 2013
Category : Moduli theory
ISBN : 1571462589

Get Book

Handbook of Moduli by Gavril Farkas,Ian Morrison Pdf

Author : Hussein Mourtada,Celal Cem Sarıoğlu,Christophe Soulé,Ayberk Zeytin
Publisher : Birkhäuser
Page : 232 pages
File Size : 53,5 Mb
Release : 2017-05-16
Category : Mathematics
ISBN : 3319477781

Get Book

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 : Alexander Givental
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 55,9 Mb
Release : 2001
Category : Algebras, Linear
ISBN : 0821828509

Get Book

Linear Algebra and Differential Equations by Alexander Givental Pdf

The material presented in this book corresponds to a semester-long course, ``Linear Algebra and Differential Equations'', taught to sophomore students at UC Berkeley. In contrast with typical undergraduate texts, the book offers a unifying point of view on the subject, namely that linear algebra solves several clearly-posed classification problems about such geometric objects as quadratic forms and linear transformations. This attractive viewpoint on the classical theory agrees well with modern tendencies in advanced mathematics and is shared by many research mathematicians. However, the idea of classification seldom finds its way to basic programs in mathematics, and is usually unfamiliar to undergraduates. To meet the challenge, the book first guides the reader through the entire agenda of linear algebra in the elementary environment of two-dimensional geometry, and prior to spelling out the general idea and employing it in higher dimensions, shows how it works in applications such as linear ODE systems or stability of equilibria. Appropriate as a text for regular junior and honors sophomore level college classes, the book is accessible to high school students familiar with basic calculus, and can also be useful to engineering graduate students.

Author : Daniel Huybrechts
Publisher : Cambridge University Press
Page : 499 pages
File Size : 40,6 Mb
Release : 2016-09-26
Category : Mathematics
ISBN : 9781107153042

Get Book

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.