Abel Symposia – serie
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33 produkter
33 produkter
Del 13 - Abel Symposia
Computation and Combinatorics in Dynamics, Stochastics and Control
The Abel Symposium, Rosendal, Norway, August 2016
Inbunden, Engelska, 2019
1 828 kr
Skickas inom 10-15 vardagar
The Abel Symposia volume at hand contains a collection of high-quality articles written by the world’s leading experts, and addressing all mathematicians interested in advances in deterministic and stochastic dynamical systems, numerical analysis, and control theory.In recent years we have witnessed a remarkable convergence between individual mathematical disciplines that approach deterministic and stochastic dynamical systems from mathematical analysis, computational mathematics and control theoretical perspectives. Breakthrough developments in these fields now provide a common mathematical framework for attacking many different problems related to differential geometry, analysis and algorithms for stochastic and deterministic dynamics. In the Abel Symposium 2016, which took place from August 16-19 in Rosendal near Bergen, leading researchers in the fields of deterministic and stochastic differential equations, control theory, numerical analysis, algebra and random processes presented and discussed the current state of the art in these diverse fields.The current Abel Symposia volume may serve as a point of departure for exploring these related but diverse fields of research, as well as an indicator of important current and future developments in modern mathematics.
Del 15 - Abel Symposia
Topological Data Analysis
The Abel Symposium 2018
Inbunden, Engelska, 2020
2 434 kr
Skickas inom 10-15 vardagar
This book gathers the proceedings of the 2018 Abel Symposium, which was held in Geiranger, Norway, on June 4-8, 2018. The symposium offered an overview of the emerging field of "Topological Data Analysis". This volume presents papers on various research directions, notably including applications in neuroscience, materials science, cancer biology, and immune response. Providing an essential snapshot of the status quo, it represents a valuable asset for practitioners and those considering entering the field.
Del 15 - Abel Symposia
Topological Data Analysis
The Abel Symposium 2018
Häftad, Engelska, 2021
2 434 kr
Skickas inom 10-15 vardagar
This book gathers the proceedings of the 2018 Abel Symposium, which was held in Geiranger, Norway, on June 4-8, 2018. The symposium offered an overview of the emerging field of "Topological Data Analysis". This volume presents papers on various research directions, notably including applications in neuroscience, materials science, cancer biology, and immune response. Providing an essential snapshot of the status quo, it represents a valuable asset for practitioners and those considering entering the field.
Del 16 - Abel Symposia
Geometry, Lie Theory and Applications
The Abel Symposium 2019
Inbunden, Engelska, 2022
1 935 kr
Skickas inom 10-15 vardagar
This book consists of contributions from the participants of the Abel Symposium 2019 held in Ålesund, Norway. It was centered about applications of the ideas of symmetry and invariance, including equivalence and deformation theory of geometric structures, classification of differential invariants and invariant differential operators, integrability analysis of equations of mathematical physics, progress in parabolic geometry and mathematical aspects of general relativity.The chapters are written by leading international researchers, and consist of both survey and research articles. The book gives the reader an insight into the current research in differential geometry and Lie theory, as well as applications of these topics, in particular to general relativity and string theory.
Del 16 - Abel Symposia
Geometry, Lie Theory and Applications
The Abel Symposium 2019
Häftad, Engelska, 2023
1 935 kr
Skickas inom 10-15 vardagar
This book consists of contributions from the participants of the Abel Symposium 2019 held in Ålesund, Norway. It was centered about applications of the ideas of symmetry and invariance, including equivalence and deformation theory of geometric structures, classification of differential invariants and invariant differential operators, integrability analysis of equations of mathematical physics, progress in parabolic geometry and mathematical aspects of general relativity.The chapters are written by leading international researchers, and consist of both survey and research articles. The book gives the reader an insight into the current research in differential geometry and Lie theory, as well as applications of these topics, in particular to general relativity and string theory.
Del 17 - Abel Symposia
Triangulated Categories in Representation Theory and Beyond
The Abel Symposium 2022
Inbunden, Engelska, 2024
2 685 kr
Skickas inom 5-8 vardagar
In recent years, triangulated categories have proved very successful as a common mathematical framework for formulating important advances in various fields, and at the same time for the interaction between different subject areas. The purpose of the symposium was therefore not only the study of triangulated categories in itself, but rather fruitful exchanges between disciplines. The symposium brought together established researchers who have made important contributions involving triangulated categories. Many participants came from representation theory, but there were also participants with backgrounds in commutative algebra, geometry and algebraic topology.
Del 17 - Abel Symposia
Triangulated Categories in Representation Theory and Beyond
The Abel Symposium 2022
Häftad, Engelska, 2025
2 685 kr
Skickas inom 10-15 vardagar
In recent years, triangulated categories have proved very successful as a common mathematical framework for formulating important advances in various fields, and at the same time for the interaction between different subject areas. The purpose of the symposium was therefore not only the study of triangulated categories in itself, but rather fruitful exchanges between disciplines. The symposium brought together established researchers who have made important contributions involving triangulated categories. Many participants came from representation theory, but there were also participants with backgrounds in commutative algebra, geometry and algebraic topology.
Del 18 - Abel Symposia
Partial Differential Equations: Waves, Nonlinearities and Nonlocalities
The Abel Symposium 2023
Inbunden, Engelska, 2025
2 685 kr
Skickas inom 10-15 vardagar
This volume in the renowned Abel Symposia series contains the peer-reviewed proceedings of the Abel Symposium 2023 on Partial Differential Equations: Waves, Nonlinearities and Nonlocalities, held at Bårdshaug Mansion in Orkanger outside Trondheim, Norway, June 13–16, 2023.Research in nonlinear partial differential equations has been undergoing an intense development, with new phenomena modelled by increasingly complicated systems integrating nonlocal effects, and with the solution of previously unsolved problems, such as the Onsager conjecture. Comprising fifteen articles written by leading researchers, covering a wide range of topics, this book takes readers to the forefront of a highly active subject.
Del 9 - Abel Symposia
Operator-Related Function Theory and Time-Frequency Analysis
The Abel Symposium 2012
Inbunden, Engelska, 2014
1 078 kr
Skickas inom 10-15 vardagar
This book collects the proceedings of the 2012 Abel Symposium, held at the Norwegian Academy of Science and Letters, Oslo. The Symposium, and this book, are focused on two important fields of modern mathematical analysis: operator-related function theory and time-frequency analysis; and the profound interplay between them.Among the original contributions and overview lectures gathered here are a paper presenting multifractal analysis as a bridge between geometric measure theory and signal processing; local and global geometry of Prony systems and Fourier reconstruction of piecewise-smooth functions; Bernstein's problem on weighted polynomial approximation; singular distributions and symmetry of the spectrum; and many others.Offering a selection of the latest and most exciting results obtained by world-leading researchers, the book will benefit scientists working in Harmonic and Complex Analysis, Mathematical Physics and Signal Processing.
Del 10 - Abel Symposia
Complex Geometry and Dynamics
The Abel Symposium 2013
Inbunden, Engelska, 2015
1 078 kr
Skickas inom 10-15 vardagar
This book focuses on complex geometry and covers highly active topics centered around geometric problems in several complex variables and complex dynamics, written by some of the world’s leading experts in their respective fields.This book features research and expository contributions from the 2013 Abel Symposium, held at the Norwegian University of Science and Technology Trondheim on July 2-5, 2013. The purpose of the symposium was to present the state of the art on the topics, and to discuss future research directions.
Del 11 - Abel Symposia
Statistical Analysis for High-Dimensional Data
The Abel Symposium 2014
Inbunden, Engelska, 2016
1 614 kr
Skickas inom 10-15 vardagar
This book features research contributions fromThe Abel Symposium on Statistical Analysis for High Dimensional Data, held inNyvågar, Lofoten, Norway, in May 2014.The focus of the symposium was on statisticaland machine learning methodologies specifically developed for inference in “bigdata” situations, with particular reference to genomic applications. Thecontributors, who are among the most prominent researchers on the theory ofstatistics for high dimensional inference, present new theories and methods, aswell as challenging applications and computational solutions. Specific themesinclude, among others, variable selection and screening, penalised regression,sparsity, thresholding, low dimensional structures, computational challenges,non-convex situations, learning graphical models, sparse covariance andprecision matrices, semi- and non-parametric formulations, multiple testing,classification, factor models, clustering, and preselection.Highlighting cutting-edge researchand casting light on future research directions, the contributions will benefitgraduate students and researchers in computational biology, statistics and themachine learning community.
Häftad, Engelska, 2016
1 435 kr
Skickas inom 5-8 vardagar
This book collects the proceedings of the 2012 Abel Symposium, held at the Norwegian Academy of Science and Letters, Oslo. The Symposium, and this book, are focused on two important fields of modern mathematical analysis: operator-related function theory and time-frequency analysis; and the profound interplay between them.Among the original contributions and overview lectures gathered here are a paper presenting multifractal analysis as a bridge between geometric measure theory and signal processing; local and global geometry of Prony systems and Fourier reconstruction of piecewise-smooth functions; Bernstein's problem on weighted polynomial approximation; singular distributions and symmetry of the spectrum; and many others.Offering a selection of the latest and most exciting results obtained by world-leading researchers, the book will benefit scientists working in Harmonic and Complex Analysis, Mathematical Physics and Signal Processing.
Del 10 - Abel Symposia
Complex Geometry and Dynamics
The Abel Symposium 2013
Häftad, Engelska, 2016
1 078 kr
Skickas inom 10-15 vardagar
This book focuses on complex geometry and covers highly active topics centered around geometric problems in several complex variables and complex dynamics, written by some of the world’s leading experts in their respective fields.This book features research and expository contributions from the 2013 Abel Symposium, held at the Norwegian University of Science and Technology Trondheim on July 2-5, 2013. The purpose of the symposium was to present the state of the art on the topics, and to discuss future research directions.
Del 12 - Abel Symposia
Operator Algebras and Applications
The Abel Symposium 2015
Inbunden, Engelska, 2016
2 364 kr
Skickas inom 10-15 vardagar
Like the first Abel Symposium, held in 2004, the Abel Symposium 2015 focused on operator algebras. It is interesting to see the remarkable advances that have been made in operator algebras over these years, which strikingly illustrate the vitality of the field. A total of 26 talks were given at the symposium on a variety of themes, all highlighting the richness of the subject.The field of operator algebras was created in the 1930s and was motivated by problems of quantum mechanics. It has subsequently developed well beyond its initial intended realm of applications and expanded into such diverse areas of mathematics as representation theory, dynamical systems, differential geometry, number theory and quantum algebra. One branch, known as “noncommutative geometry”, has become a powerful tool for studying phenomena that are beyond the reach of classical analysis.This volume includes research papers that present new results, surveys that discuss the development of a specific line of research, and articles that offer a combination of survey and research. These contributions provide a multifaceted portrait of beautiful mathematics that both newcomers to the field of operator algebras and seasoned researchers alike will appreciate.
Del 11 - Abel Symposia
Statistical Analysis for High-Dimensional Data
The Abel Symposium 2014
Häftad, Engelska, 2018
1 662 kr
Skickas inom 10-15 vardagar
This book features research contributions fromThe Abel Symposium on Statistical Analysis for High Dimensional Data, held inNyvågar, Lofoten, Norway, in May 2014.The focus of the symposium was on statisticaland machine learning methodologies specifically developed for inference in “bigdata” situations, with particular reference to genomic applications. Thecontributors, who are among the most prominent researchers on the theory ofstatistics for high dimensional inference, present new theories and methods, aswell as challenging applications and computational solutions. Specific themesinclude, among others, variable selection and screening, penalised regression,sparsity, thresholding, low dimensional structures, computational challenges,non-convex situations, learning graphical models, sparse covariance andprecision matrices, semi- and non-parametric formulations, multiple testing,classification, factor models, clustering, and preselection.Highlighting cutting-edge researchand casting light on future research directions, the contributions will benefitgraduate students and researchers in computational biology, statistics and themachine learning community.
Del 12 - Abel Symposia
Operator Algebras and Applications
The Abel Symposium 2015
Häftad, Engelska, 2018
2 364 kr
Skickas inom 10-15 vardagar
Like the first Abel Symposium, held in 2004, the Abel Symposium 2015 focused on operator algebras. It is interesting to see the remarkable advances that have been made in operator algebras over these years, which strikingly illustrate the vitality of the field. A total of 26 talks were given at the symposium on a variety of themes, all highlighting the richness of the subject.The field of operator algebras was created in the 1930s and was motivated by problems of quantum mechanics. It has subsequently developed well beyond its initial intended realm of applications and expanded into such diverse areas of mathematics as representation theory, dynamical systems, differential geometry, number theory and quantum algebra. One branch, known as “noncommutative geometry”, has become a powerful tool for studying phenomena that are beyond the reach of classical analysis.This volume includes research papers that present new results, surveys that discuss the development of a specific line of research, and articles that offer a combination of survey and research. These contributions provide a multifaceted portrait of beautiful mathematics that both newcomers to the field of operator algebras and seasoned researchers alike will appreciate.
Del 14 - Abel Symposia
Geometry of Moduli
Inbunden, Engelska, 2018
2 149 kr
Skickas inom 10-15 vardagar
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.
Del 1 - Abel Symposia
Operator Algebras
The Abel Symposium 2004
Inbunden, Engelska, 2006
1 078 kr
Skickas inom 10-15 vardagar
The theme of this symposium was operator algebras in a wide sense. In the last 40 years operator algebras has developed from a rather special dis- pline within functional analysis to become a central ?eld in mathematics often described as “non-commutative geometry” (see for example the book “Non-Commutative Geometry” by the Fields medalist Alain Connes). It has branched out in several sub-disciplines and made contact with other subjects like for example mathematical physics, algebraic topology, geometry, dyn- ical systems, knot theory, ergodic theory, wavelets, representations of groups and quantum groups. Norway has a relatively strong group of researchers in the subject, which contributed to the award of the ?rst symposium in the series of Abel Symposia to this group. The contributions to this volume give a state-of-the-art account of some of these sub-disciplines and the variety of topics re?ect to some extent how the subject has branched out. We are happy that some of the top researchers in the ?eld were willing to contribute. The basic ?eld of operator algebras is classi?ed within mathematics as part of functional analysis. Functional analysis treats analysis on in?nite - mensional spaces by using topological concepts. A linear map between two such spaces is called an operator. Examples are di?erential and integral - erators. An important feature is that the composition of two operators is a non-commutative operation.
Inbunden, Engelska, 2008
543 kr
Skickas inom 10-15 vardagar
The 2006 Abel symposium is focusing on contemporary research involving interaction between computer science, computational science and mathematics. In recent years, computation has been affecting pure mathematics in fundamental ways. Conversely, ideas and methods of pure mathematics are becoming increasingly important within computational and applied mathematics. At the core of computer science is the study of computability and complexity for discrete mathematical structures. Studying the foundations of computational mathematics raises similar questions concerning continuous mathematical structures. There are several reasons for these developments. The exponential growth of computing power is bringing computational methods into ever new application areas.Equally important is the advance of software and programming languages, which to an increasing degree allows the representation of abstract mathematical structures in program code. Symbolic computing is bringing algorithms from mathematical analysis into the hands of pure and applied mathematicians, and the combination of symbolic and numerical techniques is becoming increasingly important both in computational science and in areas of pure mathematics.
Del 2 - Abel Symposia
Stochastic Analysis and Applications
The Abel Symposium 2005
Inbunden, Engelska, 2007
1 614 kr
Skickas inom 10-15 vardagar
Kiyosi Ito, the founder of stochastic calculus, is one of the few central figures of the twentieth century mathematics who reshaped the mathematical world. Today stochastic calculus is a central research field with applications in several other mathematical disciplines, for example physics, engineering, biology, economics and finance.The Abel Symposium 2005 was organized as a tribute to the work of Kiyosi Ito on the occasion of his 90th birthday. Distinguished researchers from all over the world were invited to present the newest developments within the exciting and fast growing field of stochastic analysis. The present volume combines both papers from the invited speakers and contributions by the presenting lecturers. A special feature is the Memoirs that Kiyoshi Ito wrote for this occasion. These are valuable pages for both young and established researchers in the field.
Del 5 - Abel Symposia
Differential Equations - Geometry, Symmetries and Integrability
The Abel Symposium 2008
Inbunden, Engelska, 2009
1 078 kr
Skickas inom 10-15 vardagar
The Abel Symposium 2008 focused on the modern theory of differential equations and their applications in geometry, mechanics, and mathematical physics. Following the tradition of Monge, Abel and Lie, the scientific program emphasized the role of algebro-geometric methods, which nowadays permeate all mathematical models in natural and engineering sciences. The ideas of invariance and symmetry are of fundamental importance in the geometric approach to differential equations, with a serious impact coming from the area of integrable systems and field theories. This volume consists of original contributions and broad overview lectures of the participants of the Symposium. The papers in this volume present the modern approach to this classical subject.
Del 4 - Abel Symposia
Algebraic Topology
The Abel Symposium 2007
Inbunden, Engelska, 2009
2 149 kr
Skickas inom 10-15 vardagar
The 2007 Abel Symposium took place at the University of Oslo in August 2007. The goal of the symposium was to bring together mathematicians whose research efforts have led to recent advances in algebraic geometry, algebraic K-theory, algebraic topology, and mathematical physics. A common theme of this symposium was the development of new perspectives and new constructions with a categorical flavor. As the lectures at the symposium and the papers of this volume demonstrate, these perspectives and constructions have enabled a broadening of vistas, a synergy between once-differentiated subjects, and solutions to mathematical problems both old and new.
Del 1 - Abel Symposia
Operator Algebras
The Abel Symposium 2004
Häftad, Engelska, 2010
1 078 kr
Skickas inom 10-15 vardagar
The theme of this symposium was operator algebras in a wide sense. In the last 40 years operator algebras has developed from a rather special dis- pline within functional analysis to become a central ?eld in mathematics often described as “non-commutative geometry” (see for example the book “Non-Commutative Geometry” by the Fields medalist Alain Connes). It has branched out in several sub-disciplines and made contact with other subjects like for example mathematical physics, algebraic topology, geometry, dyn- ical systems, knot theory, ergodic theory, wavelets, representations of groups and quantum groups. Norway has a relatively strong group of researchers in the subject, which contributed to the award of the ?rst symposium in the series of Abel Symposia to this group. The contributions to this volume give a state-of-the-art account of some of these sub-disciplines and the variety of topics re?ect to some extent how the subject has branched out. We are happy that some of the top researchers in the ?eld were willing to contribute. The basic ?eld of operator algebras is classi?ed within mathematics as part of functional analysis. Functional analysis treats analysis on in?nite - mensional spaces by using topological concepts. A linear map between two such spaces is called an operator. Examples are di?erential and integral - erators. An important feature is that the composition of two operators is a non-commutative operation.
Häftad, Engelska, 2010
543 kr
Skickas inom 10-15 vardagar
The 2006 Abel symposium is focusing on contemporary research involving interaction between computer science, computational science and mathematics. In recent years, computation has been affecting pure mathematics in fundamental ways. Conversely, ideas and methods of pure mathematics are becoming increasingly important within computational and applied mathematics. At the core of computer science is the study of computability and complexity for discrete mathematical structures. Studying the foundations of computational mathematics raises similar questions concerning continuous mathematical structures. There are several reasons for these developments. The exponential growth of computing power is bringing computational methods into ever new application areas.Equally important is the advance of software and programming languages, which to an increasing degree allows the representation of abstract mathematical structures in program code. Symbolic computing is bringing algorithms from mathematical analysis into the hands of pure and applied mathematicians, and the combination of symbolic and numerical techniques is becoming increasingly important both in computational science and in areas of pure mathematics.
Del 2 - Abel Symposia
Stochastic Analysis and Applications
The Abel Symposium 2005
Häftad, Engelska, 2010
1 614 kr
Skickas inom 10-15 vardagar
Kiyosi Ito, the founder of stochastic calculus, is one of the few central figures of the twentieth century mathematics who reshaped the mathematical world. Today stochastic calculus is a central research field with applications in several other mathematical disciplines, for example physics, engineering, biology, economics and finance.The Abel Symposium 2005 was organized as a tribute to the work of Kiyosi Ito on the occasion of his 90th birthday. Distinguished researchers from all over the world were invited to present the newest developments within the exciting and fast growing field of stochastic analysis. The present volume combines both papers from the invited speakers and contributions by the presenting lecturers. A special feature is the Memoirs that Kiyoshi Ito wrote for this occasion. These are valuable pages for both young and established researchers in the field.
Del 6 - Abel Symposia
Combinatorial Aspects of Commutative Algebra and Algebraic Geometry
The Abel Symposium 2009
Inbunden, Engelska, 2011
1 614 kr
Skickas inom 10-15 vardagar
The Abel Symposium 2009 "Combinatorial aspects of Commutative Algebra and Algebraic Geometry", held at Voss, Norway, featured talks by leading researchers in the field. This is the proceedings of the Symposium, presenting contributions on syzygies, tropical geometry, Boij-Söderberg theory, Schubert calculus, and quiver varieties. The volume also includes an introductory survey on binomial ideals with applications to hypergeometric series, combinatorial games and chemical reactions. The contributions pose interesting problems, and offer up-to-date research on some of the most active fields of commutative algebra and algebraic geometry with a combinatorial flavour.
Inbunden, Engelska, 2012
1 614 kr
Skickas inom 10-15 vardagar
The topic of the 2010 Abel Symposium, hosted at the Norwegian Academy of Science and Letters, Oslo, was Nonlinear Partial Differential Equations, the study of which is of fundamental importance in mathematics and in almost all of natural sciences, economics, and engineering. This area of mathematics is currently in the midst of an unprecedented development worldwide. Differential equations are used to model phenomena of increasing complexity, and in areas that have traditionally been outside the realm of mathematics. New analytical tools and numerical methods are dramatically improving our understanding of nonlinear models. Nonlinearity gives rise to novel effects reflected in the appearance of shock waves, turbulence, material defects, etc., and offers challenging mathematical problems. On the other hand, new mathematical developments provide new insight in many applications. These proceedings present a selection of the latest exciting results by world leading researchers.
Del 4 - Abel Symposia
Algebraic Topology
The Abel Symposium 2007
Häftad, Engelska, 2012
2 149 kr
Skickas inom 10-15 vardagar
The 2007 Abel Symposium took place at the University of Oslo in August 2007. The goal of the symposium was to bring together mathematicians whose research efforts have led to recent advances in algebraic geometry, algebraic K-theory, algebraic topology, and mathematical physics. A common theme of this symposium was the development of new perspectives and new constructions with a categorical flavor. As the lectures at the symposium and the papers of this volume demonstrate, these perspectives and constructions have enabled a broadening of vistas, a synergy between once-differentiated subjects, and solutions to mathematical problems both old and new.
Del 6 - Abel Symposia
Combinatorial Aspects of Commutative Algebra and Algebraic Geometry
The Abel Symposium 2009
Häftad, Engelska, 2013
1 614 kr
Skickas inom 10-15 vardagar
The Abel Symposium 2009 "Combinatorial aspects of Commutative Algebra and Algebraic Geometry", held at Voss, Norway, featured talks by leading researchers in the field. This is the proceedings of the Symposium, presenting contributions on syzygies, tropical geometry, Boij-Söderberg theory, Schubert calculus, and quiver varieties. The volume also includes an introductory survey on binomial ideals with applications to hypergeometric series, combinatorial games and chemical reactions. The contributions pose interesting problems, and offer up-to-date research on some of the most active fields of commutative algebra and algebraic geometry with a combinatorial flavour.
Del 5 - Abel Symposia
Differential Equations - Geometry, Symmetries and Integrability
The Abel Symposium 2008
Häftad, Engelska, 2012
1 078 kr
Skickas inom 10-15 vardagar
The Abel Symposium 2008 focused on the modern theory of differential equations and their applications in geometry, mechanics, and mathematical physics. Following the tradition of Monge, Abel and Lie, the scientific program emphasized the role of algebro-geometric methods, which nowadays permeate all mathematical models in natural and engineering sciences. The ideas of invariance and symmetry are of fundamental importance in the geometric approach to differential equations, with a serious impact coming from the area of integrable systems and field theories. This volume consists of original contributions and broad overview lectures of the participants of the Symposium. The papers in this volume present the modern approach to this classical subject.