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Author: Pierre Cartier
Publisher: Springer
ISBN: 0817645764
Category : Mathematics
Languages : en
Pages : 499
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Book Description
This three-volume work contains articles collected on the occasion of Alexander Grothendieck’s sixtieth birthday and originally published in 1990. The articles were offered as a tribute to one of the world’s greatest living mathematicians. Many of the groundbreaking contributions in these volumes contain material that is now considered foundational to the subject. Topics addressed by these top-notch contributors match the breadth of Grothendieck’s own interests, including: functional analysis, algebraic geometry, algebraic topology, number theory, representation theory, K-theory, category theory, and homological algebra.
Author: Pierre Cartier
Publisher: Springer
ISBN: 0817645764
Category : Mathematics
Languages : en
Pages : 499
Get Book Here
Book Description
This three-volume work contains articles collected on the occasion of Alexander Grothendieck’s sixtieth birthday and originally published in 1990. The articles were offered as a tribute to one of the world’s greatest living mathematicians. Many of the groundbreaking contributions in these volumes contain material that is now considered foundational to the subject. Topics addressed by these top-notch contributors match the breadth of Grothendieck’s own interests, including: functional analysis, algebraic geometry, algebraic topology, number theory, representation theory, K-theory, category theory, and homological algebra.
Author: Pierre Cartier
Publisher:
ISBN:
Category : Geometry, Algebraic
Languages : en
Pages : 518
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Book Description
Author: Pierre Cartier
Publisher: Springer Science & Business Media
ISBN: 0817645748
Category : Mathematics
Languages : en
Pages : 514
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Book Description
This three-volume work contains articles collected on the occasion of Alexander Grothendieck’s sixtieth birthday and originally published in 1990. The articles were offered as a tribute to one of the world’s greatest living mathematicians. Many of the groundbreaking contributions in these volumes contain material that is now considered foundational to the subject. Topics addressed by these top-notch contributors match the breadth of Grothendieck’s own interests, including: functional analysis, algebraic geometry, algebraic topology, number theory, representation theory, K-theory, category theory, and homological algebra.
Author: Peter H. Kropholler
Publisher: Cambridge University Press
ISBN: 131662322X
Category : Mathematics
Languages : en
Pages : 277
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Book Description
Surveys the state of the art in geometric and cohomological group theory. Ideal entry point for young researchers.
Author: William Fulton
Publisher: Springer
ISBN: 3540698043
Category : Mathematics
Languages : en
Pages : 158
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Book Description
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.
Author: Yves André
Publisher: Birkhäuser
ISBN: 3034883366
Category : Mathematics
Languages : en
Pages : 223
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Book Description
"...A nice feature of the book [is] that at various points the authors provide examples, or rather counterexamples, that clearly show what can go wrong...This is a nicely-written book [that] studies algebraic differential modules in several variables." --Mathematical Reviews
Author: Takeo Ohsawa
Publisher: Springer Nature
ISBN: 9811515883
Category : Mathematics
Languages : en
Pages : 438
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Book Description
This volume originated in the workshop held at Nagoya University, August 28–30, 2015, focusing on the surprising and mysterious Ohkawa's theorem: the Bousfield classes in the stable homotopy category SH form a set. An inspiring, extensive mathematical story can be narrated starting with Ohkawa's theorem, evolving naturally with a chain of motivational questions: Ohkawa's theorem states that the Bousfield classes of the stable homotopy category SH surprisingly forms a set, which is still very mysterious. Are there any toy models where analogous Bousfield classes form a set with a clear meaning? The fundamental theorem of Hopkins, Neeman, Thomason, and others states that the analogue of the Bousfield classes in the derived category of quasi-coherent sheaves Dqc(X) form a set with a clear algebro-geometric description. However, Hopkins was actually motivated not by Ohkawa's theorem but by his own theorem with Smith in the triangulated subcategory SHc, consisting of compact objects in SH. Now the following questions naturally occur: (1) Having theorems of Ohkawa and Hopkins-Smith in SH, are there analogues for the Morel-Voevodsky A1-stable homotopy category SH(k), which subsumes SH when k is a subfield of C?, (2) Was it not natural for Hopkins to have considered Dqc(X)c instead of Dqc(X)? However, whereas there is a conceptually simple algebro-geometrical interpretation Dqc(X)c = Dperf(X), it is its close relative Dbcoh(X) that traditionally, ever since Oka and Cartan, has been intensively studied because of its rich geometric and physical information. This book contains developments for the rest of the story and much more, including the chromatics homotopy theory, which the Hopkins–Smith theorem is based upon, and applications of Lurie's higher algebra, all by distinguished contributors.
Author: Jianxun Hu
Publisher: Springer Nature
ISBN: 9811574510
Category : Mathematics
Languages : en
Pages : 367
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Book Description
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.
Author: Athanase Papadopoulos
Publisher: European Mathematical Society
ISBN: 9783037190296
Category : Mathematics
Languages : en
Pages : 812
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Book Description
The Teichmuller space of a surface was introduced by O. Teichmuller in the 1930s. It is a basic tool in the study of Riemann's moduli spaces and the mapping class groups. These objects are fundamental in several fields of mathematics, including algebraic geometry, number theory, topology, geometry, and dynamics. The original setting of Teichmuller theory is complex analysis. The work of Thurston in the 1970s brought techniques of hyperbolic geometry to the study of Teichmuller space and its asymptotic geometry. Teichmuller spaces are also studied from the point of view of the representation theory of the fundamental group of the surface in a Lie group $G$, most notably $G=\mathrm{PSL}(2,\mathbb{R})$ and $G=\mathrm{PSL}(2,\mathbb{C})$. In the 1980s, there evolved an essentially combinatorial treatment of the Teichmuller and moduli spaces involving techniques and ideas from high-energy physics, namely from string theory. The current research interests include the quantization of Teichmuller space, the Weil-Petersson symplectic and Poisson geometry of this space as well as gauge-theoretic extensions of these structures. The quantization theories can lead to new invariants of hyperbolic 3-manifolds. The purpose of this handbook is to give a panorama of some of the most important aspects of Teichmuller theory. The handbook should be useful to specialists in the field, to graduate students, and more generally to mathematicians who want to learn about the subject. All the chapters are self-contained and have a pedagogical character. They are written by leading experts in the subject.
Author: Thomas Lam
Publisher: Springer
ISBN: 1493906828
Category : Mathematics
Languages : en
Pages : 226
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Book Description
This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems. Affine Schubert calculus lies at the crossroads of combinatorics, geometry, and representation theory. Its modern development is motivated by two seemingly unrelated directions. One is the introduction of k-Schur functions in the study of Macdonald polynomial positivity, a mostly combinatorial branch of symmetric function theory. The other direction is the study of the Schubert bases of the (co)homology of the affine Grassmannian, an algebro-topological formulation of a problem in enumerative geometry. This is the first introductory text on this subject. It contains many examples in Sage, a free open source general purpose mathematical software system, to entice the reader to investigate the open problems. This book is written for advanced undergraduate and graduate students, as well as researchers, who want to become familiar with this fascinating new field.
