Schubert Varieties, Equivariant Cohomology and Characteristic Classes

Schubert Varieties, Equivariant Cohomology and Characteristic Classes

Author: Jarosław Buczyński

Publisher:

Published: 2018

Total Pages: 354

ISBN-13: 9783037196823

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IMPANGA stands for the activities of Algebraic Geometers at the Institute of Mathematics, Polish Academy of Sciences, including one of the most important seminars in algebraic geometry in Poland. The topics of the lectures usually fit within the framework of complex algebraic geometry and neighboring areas of mathematics. This volume is a collection of contributions by the participants of the conference IMPANGA15, organized by participants of the seminar, as well as notes from the major lecture series of the seminar in the period 2010-2015. Both original research papers and self-contained expository surveys can be found here. The articles circulate around a broad range of topics within algebraic geometry such as vector bundles, Schubert varieties, degeneracy loci, homogeneous spaces, equivariant cohomology, Thom polynomials, characteristic classes, symmetric functions and polynomials, and algebraic geometry in positive characteristic.


Book Synopsis Schubert Varieties, Equivariant Cohomology and Characteristic Classes by : Jarosław Buczyński

Download or read book Schubert Varieties, Equivariant Cohomology and Characteristic Classes written by Jarosław Buczyński and published by . This book was released on 2018 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: IMPANGA stands for the activities of Algebraic Geometers at the Institute of Mathematics, Polish Academy of Sciences, including one of the most important seminars in algebraic geometry in Poland. The topics of the lectures usually fit within the framework of complex algebraic geometry and neighboring areas of mathematics. This volume is a collection of contributions by the participants of the conference IMPANGA15, organized by participants of the seminar, as well as notes from the major lecture series of the seminar in the period 2010-2015. Both original research papers and self-contained expository surveys can be found here. The articles circulate around a broad range of topics within algebraic geometry such as vector bundles, Schubert varieties, degeneracy loci, homogeneous spaces, equivariant cohomology, Thom polynomials, characteristic classes, symmetric functions and polynomials, and algebraic geometry in positive characteristic.

Schubert Calculus and Its Applications in Combinatorics and Representation Theory

Schubert Calculus and Its Applications in Combinatorics and Representation Theory

Author: Jianxun Hu

Publisher: Springer Nature

Published: 2020-10-24

Total Pages: 367

ISBN-13: 9811574510

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This book gathers research papers and surveys on the latest advances in Schubert Calculus, presented at the International Festival in Schubert Calculus, held in Guangzhou, China on November 6–10, 2017. With roots in enumerative geometry and Hilbert's 15th problem, modern Schubert Calculus studies classical and quantum intersection rings on spaces with symmetries, such as flag manifolds. The presence of symmetries leads to particularly rich structures, and it connects Schubert Calculus to many branches of mathematics, including algebraic geometry, combinatorics, representation theory, and theoretical physics. For instance, the study of the quantum cohomology ring of a Grassmann manifold combines all these areas in an organic way. The book is useful for researchers and graduate students interested in Schubert Calculus, and more generally in the study of flag manifolds in relation to algebraic geometry, combinatorics, representation theory and mathematical physics.


Book Synopsis Schubert Calculus and Its Applications in Combinatorics and Representation Theory by : Jianxun Hu

Download or read book Schubert Calculus and Its Applications in Combinatorics and Representation Theory written by Jianxun Hu and published by Springer Nature. This book was released on 2020-10-24 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers research papers and surveys on the latest advances in Schubert Calculus, presented at the International Festival in Schubert Calculus, held in Guangzhou, China on November 6–10, 2017. With roots in enumerative geometry and Hilbert's 15th problem, modern Schubert Calculus studies classical and quantum intersection rings on spaces with symmetries, such as flag manifolds. The presence of symmetries leads to particularly rich structures, and it connects Schubert Calculus to many branches of mathematics, including algebraic geometry, combinatorics, representation theory, and theoretical physics. For instance, the study of the quantum cohomology ring of a Grassmann manifold combines all these areas in an organic way. The book is useful for researchers and graduate students interested in Schubert Calculus, and more generally in the study of flag manifolds in relation to algebraic geometry, combinatorics, representation theory and mathematical physics.

Facets of Algebraic Geometry: Volume 2

Facets of Algebraic Geometry: Volume 2

Author: Paolo Aluffi

Publisher: Cambridge University Press

Published: 2022-04-07

Total Pages: 396

ISBN-13: 1108890547

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Written to honor the 80th birthday of William Fulton, the articles collected in this volume (the second of a pair) present substantial contributions to algebraic geometry and related fields, with an emphasis on combinatorial algebraic geometry and intersection theory. Featured include commutative algebra, moduli spaces, quantum cohomology, representation theory, Schubert calculus, and toric and tropical geometry. The range of these contributions is a testament to the breadth and depth of Fulton's mathematical influence. The authors are all internationally recognized experts, and include well-established researchers as well as rising stars of a new generation of mathematicians. The text aims to stimulate progress and provide inspiration to graduate students and researchers in the field.


Book Synopsis Facets of Algebraic Geometry: Volume 2 by : Paolo Aluffi

Download or read book Facets of Algebraic Geometry: Volume 2 written by Paolo Aluffi and published by Cambridge University Press. This book was released on 2022-04-07 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written to honor the 80th birthday of William Fulton, the articles collected in this volume (the second of a pair) present substantial contributions to algebraic geometry and related fields, with an emphasis on combinatorial algebraic geometry and intersection theory. Featured include commutative algebra, moduli spaces, quantum cohomology, representation theory, Schubert calculus, and toric and tropical geometry. The range of these contributions is a testament to the breadth and depth of Fulton's mathematical influence. The authors are all internationally recognized experts, and include well-established researchers as well as rising stars of a new generation of mathematicians. The text aims to stimulate progress and provide inspiration to graduate students and researchers in the field.

Schubert Varieties and Degeneracy Loci

Schubert Varieties and Degeneracy Loci

Author: William Fulton

Publisher: Springer

Published: 2006-11-13

Total Pages: 158

ISBN-13: 3540698043

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Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks. These notes, from a summer school in Thurnau, aim to give an introduction to these topics, and to describe recent progress on these problems. There are interesting interactions with the algebra of symmetric functions and combinatorics, as well as the geometry of flag manifolds and intersection theory and algebraic geometry.


Book Synopsis Schubert Varieties and Degeneracy Loci by : William Fulton

Download or read book Schubert Varieties and Degeneracy Loci written by William Fulton and published by Springer. This book was released on 2006-11-13 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks. These notes, from a summer school in Thurnau, aim to give an introduction to these topics, and to describe recent progress on these problems. There are interesting interactions with the algebra of symmetric functions and combinatorics, as well as the geometry of flag manifolds and intersection theory and algebraic geometry.

Equivariant Cohomology in Algebraic Geometry

Equivariant Cohomology in Algebraic Geometry

Author: David Anderson

Publisher: Cambridge University Press

Published: 2023-10-26

Total Pages: 464

ISBN-13: 1009349961

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Intended for first- or second-year graduate students in mathematics, as well as researchers working in algebraic geometry or combinatorics, this text introduces techniques that are essential in several areas of modern mathematics. With numerous exercises and examples, it covers the core notions and applications of equivariant cohomology.


Book Synopsis Equivariant Cohomology in Algebraic Geometry by : David Anderson

Download or read book Equivariant Cohomology in Algebraic Geometry written by David Anderson and published by Cambridge University Press. This book was released on 2023-10-26 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for first- or second-year graduate students in mathematics, as well as researchers working in algebraic geometry or combinatorics, this text introduces techniques that are essential in several areas of modern mathematics. With numerous exercises and examples, it covers the core notions and applications of equivariant cohomology.

Representation Theories and Algebraic Geometry

Representation Theories and Algebraic Geometry

Author: A. Broer

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 455

ISBN-13: 9401591318

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The 12 lectures presented in Representation Theories and Algebraic Geometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology. The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.


Book Synopsis Representation Theories and Algebraic Geometry by : A. Broer

Download or read book Representation Theories and Algebraic Geometry written by A. Broer and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 12 lectures presented in Representation Theories and Algebraic Geometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology. The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.

Handbook of Geometry and Topology of Singularities III

Handbook of Geometry and Topology of Singularities III

Author: José Luis Cisneros-Molina

Publisher: Springer Nature

Published: 2022-06-06

Total Pages: 822

ISBN-13: 3030957608

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This is the third volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I and II, such as, for instance, Zariski’s equisingularity, the interplay between isolated complex surface singularities and 3-manifold theory, stratified Morse theory, constructible sheaves, the topology of the non-critical levels of holomorphic functions, and intersection cohomology. Other chapters bring in new subjects, such as the Thom–Mather theory for maps, characteristic classes for singular varieties, mixed Hodge structures, residues in complex analytic varieties, nearby and vanishing cycles, and more. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.


Book Synopsis Handbook of Geometry and Topology of Singularities III by : José Luis Cisneros-Molina

Download or read book Handbook of Geometry and Topology of Singularities III written by José Luis Cisneros-Molina and published by Springer Nature. This book was released on 2022-06-06 with total page 822 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I and II, such as, for instance, Zariski’s equisingularity, the interplay between isolated complex surface singularities and 3-manifold theory, stratified Morse theory, constructible sheaves, the topology of the non-critical levels of holomorphic functions, and intersection cohomology. Other chapters bring in new subjects, such as the Thom–Mather theory for maps, characteristic classes for singular varieties, mixed Hodge structures, residues in complex analytic varieties, nearby and vanishing cycles, and more. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Singularities and Their Interaction with Geometry and Low Dimensional Topology

Singularities and Their Interaction with Geometry and Low Dimensional Topology

Author: Javier Fernández de Bobadilla

Publisher: Springer Nature

Published: 2021-05-27

Total Pages: 332

ISBN-13: 3030619583

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The book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory. The papers, written by leading researchers working on various topics of the above fields, are the outcome of the “Némethi60: Geometry and Topology of Singularities” conference held at the Alfréd Rényi Institute of Mathematics in Budapest, from May 27 to 31, 2019. Both the conference and this resulting volume are in honor of Professor András Némethi, on the occasion of his 60th birthday, whose work plays a decisive and influential role in the interactions between the above fields. The book should serve as a valuable resource for graduate students and researchers to deepen the new perspectives, methods, and connections between geometry and topology regarding singularities.


Book Synopsis Singularities and Their Interaction with Geometry and Low Dimensional Topology by : Javier Fernández de Bobadilla

Download or read book Singularities and Their Interaction with Geometry and Low Dimensional Topology written by Javier Fernández de Bobadilla and published by Springer Nature. This book was released on 2021-05-27 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory. The papers, written by leading researchers working on various topics of the above fields, are the outcome of the “Némethi60: Geometry and Topology of Singularities” conference held at the Alfréd Rényi Institute of Mathematics in Budapest, from May 27 to 31, 2019. Both the conference and this resulting volume are in honor of Professor András Némethi, on the occasion of his 60th birthday, whose work plays a decisive and influential role in the interactions between the above fields. The book should serve as a valuable resource for graduate students and researchers to deepen the new perspectives, methods, and connections between geometry and topology regarding singularities.

Singularities - Kagoshima 2017: Proceedings Of The 5th Franco-japanese-vietnamese Symposium On Singularities

Singularities - Kagoshima 2017: Proceedings Of The 5th Franco-japanese-vietnamese Symposium On Singularities

Author:

Publisher: World Scientific

Published: 2020-06-15

Total Pages: 312

ISBN-13: 981120604X

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This is a proceedings of the 5th Franco-Japanese-Vietnamese Symposium on Singularities held in Kagoshima during 27th October - 3rd November, 2017. The main theme of the symposium was Singularity Theory in a broad sense, including complex and real algebraic varieties, functions and mappings, and topology of singularities. The symposium was based on long-term interaction of singularity theorists in France, Japan, Vietnam and other countries. This volume includes three surveys of recent trends based on the lectures in the mini-school organized in the first two days of the symposium and articles presenting recent progress in Singularity Theory.


Book Synopsis Singularities - Kagoshima 2017: Proceedings Of The 5th Franco-japanese-vietnamese Symposium On Singularities by :

Download or read book Singularities - Kagoshima 2017: Proceedings Of The 5th Franco-japanese-vietnamese Symposium On Singularities written by and published by World Scientific. This book was released on 2020-06-15 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a proceedings of the 5th Franco-Japanese-Vietnamese Symposium on Singularities held in Kagoshima during 27th October - 3rd November, 2017. The main theme of the symposium was Singularity Theory in a broad sense, including complex and real algebraic varieties, functions and mappings, and topology of singularities. The symposium was based on long-term interaction of singularity theorists in France, Japan, Vietnam and other countries. This volume includes three surveys of recent trends based on the lectures in the mini-school organized in the first two days of the symposium and articles presenting recent progress in Singularity Theory.

Intersection Homology & Perverse Sheaves

Intersection Homology & Perverse Sheaves

Author: Laurenţiu G. Maxim

Publisher: Springer Nature

Published: 2019-11-30

Total Pages: 270

ISBN-13: 3030276449

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This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. Those looking to delve further into the abstract theory will find ample references to facilitate navigation of both classic and recent literature. Beginning with an introduction to intersection homology from a geometric and topological viewpoint, the text goes on to develop the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief discussion of constructibility opens onto an in-depth exploration of perverse sheaves. Highlights from the following chapters include a detailed account of the proof of the Beilinson–Bernstein–Deligne–Gabber (BBDG) decomposition theorem, applications of perverse sheaves to hypersurface singularities, and a discussion of Hodge-theoretic aspects of intersection homology via Saito’s deep theory of mixed Hodge modules. An epilogue offers a succinct summary of the literature surrounding some recent applications. Intersection Homology & Perverse Sheaves is suitable for graduate students with a basic background in topology and algebraic geometry. By building context and familiarity with examples, the text offers an ideal starting point for those entering the field. This classroom-tested approach opens the door to further study and to current research.


Book Synopsis Intersection Homology & Perverse Sheaves by : Laurenţiu G. Maxim

Download or read book Intersection Homology & Perverse Sheaves written by Laurenţiu G. Maxim and published by Springer Nature. This book was released on 2019-11-30 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. Those looking to delve further into the abstract theory will find ample references to facilitate navigation of both classic and recent literature. Beginning with an introduction to intersection homology from a geometric and topological viewpoint, the text goes on to develop the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief discussion of constructibility opens onto an in-depth exploration of perverse sheaves. Highlights from the following chapters include a detailed account of the proof of the Beilinson–Bernstein–Deligne–Gabber (BBDG) decomposition theorem, applications of perverse sheaves to hypersurface singularities, and a discussion of Hodge-theoretic aspects of intersection homology via Saito’s deep theory of mixed Hodge modules. An epilogue offers a succinct summary of the literature surrounding some recent applications. Intersection Homology & Perverse Sheaves is suitable for graduate students with a basic background in topology and algebraic geometry. By building context and familiarity with examples, the text offers an ideal starting point for those entering the field. This classroom-tested approach opens the door to further study and to current research.