Motivic Homotopy Theory And Refined Enumerative Geometry

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Motivic Homotopy Theory and Refined Enumerative Geometry

Federico Binda,Marc Levine,Manh Toan Nguyen,Oliver Röndigs
Motivic Homotopy Theory and Refined Enumerative Geometry Book PDF

Author : Federico Binda,Marc Levine,Manh Toan Nguyen,Oliver Röndigs
Publisher : American Mathematical Soc.
Page : 267 pages
File Size : 42,6 Mb
Release : 2020-03-09
Category : Education
ISBN : 9781470448981

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Motivic Homotopy Theory and Refined Enumerative Geometry by Federico Binda,Marc Levine,Manh Toan Nguyen,Oliver Röndigs Pdf

This volume contains the proceedings of the Workshop on Motivic Homotopy Theory and Refined Enumerative Geometry, held from May 14–18, 2018, at the Universität Duisburg-Essen, Essen, Germany. It constitutes an accessible yet swift introduction to a new and active area within algebraic geometry, which connects well with classical intersection theory. Combining both lecture notes aimed at the graduate student level and research articles pointing towards the manifold promising applications of this refined approach, it broadly covers refined enumerative algebraic geometry.

Homotopy Theory and Arithmetic Geometry – Motivic and Diophantine Aspects

Frank Neumann,Ambrus Pál
Homotopy Theory and Arithmetic Geometry Motivic and Diophantine Aspects Book PDF

Author : Frank Neumann,Ambrus Pál
Publisher : Springer Nature
Page : 223 pages
File Size : 55,6 Mb
Release : 2021-09-29
Category : Mathematics
ISBN : 9783030789770

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Homotopy Theory and Arithmetic Geometry – Motivic and Diophantine Aspects by Frank Neumann,Ambrus Pál Pdf

This book provides an introduction to state-of-the-art applications of homotopy theory to arithmetic geometry. The contributions to this volume are based on original lectures by leading researchers at the LMS-CMI Research School on ‘Homotopy Theory and Arithmetic Geometry - Motivic and Diophantine Aspects’ and the Nelder Fellow Lecturer Series, which both took place at Imperial College London in the summer of 2018. The contribution by Brazelton, based on the lectures by Wickelgren, provides an introduction to arithmetic enumerative geometry, the notes of Cisinski present motivic sheaves and new cohomological methods for intersection theory, and Schlank’s contribution gives an overview of the use of étale homotopy theory for obstructions to the existence of rational points on algebraic varieties. Finally, the article by Asok and Østvær, based in part on the Nelder Fellow lecture series by Østvær, gives a survey of the interplay between motivic homotopy theory and affine algebraic geometry, with a focus on contractible algebraic varieties. Now a major trend in arithmetic geometry, this volume offers a detailed guide to the fascinating circle of recent applications of homotopy theory to number theory. It will be invaluable to research students entering the field, as well as postdoctoral and more established researchers.

Homotopy Theory and Arithmetic Geometry - Motivic and Diophantine Aspects

Frank Neumann,Ambrus Pál
Homotopy Theory and Arithmetic Geometry Motivic and Diophantine Aspects Book PDF

Author : Frank Neumann,Ambrus Pál
Publisher : Unknown
Page : 0 pages
File Size : 43,9 Mb
Release : 2021
Category : Electronic
ISBN : 3030789780

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Homotopy Theory and Arithmetic Geometry - Motivic and Diophantine Aspects by Frank Neumann,Ambrus Pál Pdf

This book provides an introduction to state-of-the-art applications of homotopy theory to arithmetic geometry. The contributions to this volume are based on original lectures by leading researchers at the LMS-CMI Research School on 'Homotopy Theory and Arithmetic Geometry - Motivic and Diophantine Aspects' and the Nelder Fellow Lecturer Series, which both took place at Imperial College London in the summer of 2018. The contribution by Brazelton, based on the lectures by Wickelgren, provides an introduction to arithmetic enumerative geometry, the notes of Cisinski present motivic sheaves and new cohomological methods for intersection theory, and Schlank's contribution gives an overview of the use of étale homotopy theory for obstructions to the existence of rational points on algebraic varieties. Finally, the article by Asok and Østvær, based in part on the Nelder Fellow lecture series by Østvær, gives a survey of the interplay between motivic homotopy theory and affine algebraic geometry, with a focus on contractible algebraic varieties. Now a major trend in arithmetic geometry, this volume offers a detailed guide to the fascinating circle of recent applications of homotopy theory to number theory. It will be invaluable to research students entering the field, as well as postdoctoral and more established researchers.

Motivic Homotopy Theory

Bjorn Ian Dundas,Marc Levine,P.A. Østvær,Oliver Röndigs,Vladimir Voevodsky
Motivic Homotopy Theory Book PDF

Author : Bjorn Ian Dundas,Marc Levine,P.A. Østvær,Oliver Röndigs,Vladimir Voevodsky
Publisher : Springer Science & Business Media
Page : 228 pages
File Size : 49,6 Mb
Release : 2007-07-11
Category : Mathematics
ISBN : 9783540458975

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Motivic Homotopy Theory by Bjorn Ian Dundas,Marc Levine,P.A. Østvær,Oliver Röndigs,Vladimir Voevodsky Pdf

This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.

Trends in Set Theory

Samuel Coskey,Grigor Sargsyan
Trends in Set Theory Book PDF

Author : Samuel Coskey,Grigor Sargsyan
Publisher : American Mathematical Soc.
Page : 207 pages
File Size : 55,8 Mb
Release : 2020-06-18
Category : Education
ISBN : 9781470443320

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Trends in Set Theory by Samuel Coskey,Grigor Sargsyan Pdf

This volume contains the proceedings of Simon Fest, held in honor of Simon Thomas's 60th birthday, from September 15–17, 2017, at Rutgers University, Piscataway, New Jersey. The topics covered showcase recent advances from a variety of main areas of set theory, including descriptive set theory, forcing, and inner model theory, in addition to several applications of set theory, including ergodic theory, combinatorics, and model theory.

K-theory in Algebra, Analysis and Topology

Guillermo Cortiñas,Charles A. Weibel
K theory in Algebra Analysis and Topology Book PDF

Author : Guillermo Cortiñas,Charles A. Weibel
Publisher : American Mathematical Soc.
Page : 388 pages
File Size : 51,6 Mb
Release : 2024-07-01
Category : Education
ISBN : 9781470450267

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K-theory in Algebra, Analysis and Topology by Guillermo Cortiñas,Charles A. Weibel Pdf

This volume contains the proceedings of the ICM 2018 satellite school and workshop K-theory conference in Argentina. The school was held from July 16–20, 2018, in La Plata, Argentina, and the workshop was held from July 23–27, 2018, in Buenos Aires, Argentina. The volume showcases current developments in K-theory and related areas, including motives, homological algebra, index theory, operator algebras, and their applications and connections. Papers cover topics such as K-theory of group rings, Witt groups of real algebraic varieties, coarse homology theories, topological cyclic homology, negative K-groups of monoid algebras, Milnor K-theory and regulators, noncommutative motives, the classification of C∗-algebras via Kasparov's K-theory, the comparison between full and reduced C∗-crossed products, and a proof of Bott periodicity using almost commuting matrices.

75 Years of Mathematics of Computation

Susanne C. Brenner,Igor E. Shparlinski,Chi-Wang Shu,Daniel Szyld
75 Years of Mathematics of Computation Book PDF

Author : Susanne C. Brenner,Igor E. Shparlinski,Chi-Wang Shu,Daniel Szyld
Publisher : American Mathematical Soc.
Page : 364 pages
File Size : 54,6 Mb
Release : 2020-07-29
Category : Education
ISBN : 9781470451639

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75 Years of Mathematics of Computation by Susanne C. Brenner,Igor E. Shparlinski,Chi-Wang Shu,Daniel Szyld Pdf

The year 2018 marked the 75th anniversary of the founding of Mathematics of Computation, one of the four primary research journals published by the American Mathematical Society and the oldest research journal devoted to computational mathematics. To celebrate this milestone, the symposium “Celebrating 75 Years of Mathematics of Computation” was held from November 1–3, 2018, at the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island. The sixteen papers in this volume, written by the symposium speakers and editors of the journal, include both survey articles and new contributions. On the discrete side, there are four papers covering topics in computational number theory and computational algebra. On the continuous side, there are twelve papers covering topics in machine learning, high dimensional approximations, nonlocal and fractional elliptic problems, gradient flows, hyperbolic conservation laws, Maxwell's equations, Stokes's equations, a posteriori error estimation, and iterative methods. Together they provide a snapshot of significant achievements in the past quarter century in computational mathematics and also in important current trends.

Categorical, Homological and Combinatorial Methods in Algebra

Ashish K. Srivastava,André Leroy,Ivo Herzog,Pedro A. Guil Asensio
Categorical Homological and Combinatorial Methods in Algebra Book PDF

Author : Ashish K. Srivastava,André Leroy,Ivo Herzog,Pedro A. Guil Asensio
Publisher : American Mathematical Soc.
Page : 357 pages
File Size : 43,5 Mb
Release : 2020-06-23
Category : Education
ISBN : 9781470443689

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Categorical, Homological and Combinatorial Methods in Algebra by Ashish K. Srivastava,André Leroy,Ivo Herzog,Pedro A. Guil Asensio Pdf

This book contains the proceedings of the AMS Special Session, in honor of S. K. Jain's 80th birthday, on Categorical, Homological and Combinatorial Methods in Algebra held from March 16–18, 2018, at Ohio State University, Columbus, Ohio. The articles contained in this volume aim to showcase the current state of art in categorical, homological and combinatorial aspects of algebra.

Polytopes and Discrete Geometry

Gabriel Cunningham,Mark Mixer,Egon Schulte
Polytopes and Discrete Geometry Book PDF

Author : Gabriel Cunningham,Mark Mixer,Egon Schulte
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 41,5 Mb
Release : 2021-04-06
Category : Education
ISBN : 9781470448974

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Polytopes and Discrete Geometry by Gabriel Cunningham,Mark Mixer,Egon Schulte Pdf

The papers showcase the breadth of discrete geometry through many new methods and results in a variety of topics. Also included are survey articles on some important areas of active research. This volume is aimed at researchers in discrete and convex geometry and researchers who work with abstract polytopes or string C C-groups. It is also aimed at early career mathematicians, including graduate students and postdoctoral fellows, to give them a glimpse of the variety and beauty of these research areas. Topics covered in this volume include: the combinatorics, geometry, and symmetries of convex polytopes; tilings; discrete point sets; the combinatorics of Eulerian posets and interval posets; symmetries of surfaces and maps on surfaces; self-dual polytopes; string C C-groups; hypertopes; and graph coloring.

Representations of Algebras, Geometry and Physics

Kiyoshi Igusa,Alex Martsinkovsky,Gordana Todorov
Representations of Algebras Geometry and Physics Book PDF

Author : Kiyoshi Igusa,Alex Martsinkovsky,Gordana Todorov
Publisher : American Mathematical Soc.
Page : 241 pages
File Size : 44,6 Mb
Release : 2021-05-17
Category : Education
ISBN : 9781470452308

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Representations of Algebras, Geometry and Physics by Kiyoshi Igusa,Alex Martsinkovsky,Gordana Todorov Pdf

This volume contains selected expository lectures delivered at the 2018 Maurice Auslander Distinguished Lectures and International Conference, held April 25–30, 2018, at the Woods Hole Oceanographic Institute, Woods Hole, MA. Reflecting recent developments in modern representation theory of algebras, the selected topics include an introduction to a new class of quiver algebras on surfaces, called “geodesic ghor algebras”, a detailed presentation of Feynman categories from a representation-theoretic viewpoint, connections between representations of quivers and the structure theory of Coxeter groups, powerful new applications of approximable triangulated categories, new results on the heart of a t t-structure, and an introduction to methods of constructive category theory.

Advances in Harmonic Analysis and Partial Differential Equations

Donatella Danielli,Irina Mitrea
Advances in Harmonic Analysis and Partial Differential Equations Book PDF

Author : Donatella Danielli,Irina Mitrea
Publisher : American Mathematical Soc.
Page : 200 pages
File Size : 49,7 Mb
Release : 2020-04-09
Category : Education
ISBN : 9781470448967

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Advances in Harmonic Analysis and Partial Differential Equations by Donatella Danielli,Irina Mitrea Pdf

This volume contains the proceedings of the AMS Special Session on Harmonic Analysis and Partial Differential Equations, held from April 21–22, 2018, at Northeastern University, Boston, Massachusetts. The book features a series of recent developments at the interface between harmonic analysis and partial differential equations and is aimed toward the theoretical and applied communities of researchers working in real, complex, and harmonic analysis, partial differential equations, and their applications. The topics covered belong to the general areas of the theory of function spaces, partial differential equations of elliptic, parabolic, and dissipative types, geometric optics, free boundary problems, and ergodic theory, and the emphasis is on a host of new concepts, methods, and results.

Geometry at the Frontier: Symmetries and Moduli Spaces of Algebraic Varieties

Paola Comparin,Eduardo Esteves,Herbert Lange,Sebastián Reyes-Carocca,Rubí E. Rodríguez
Geometry at the Frontier Symmetries and Moduli Spaces of Algebraic Varieties Book PDF

Author : Paola Comparin,Eduardo Esteves,Herbert Lange,Sebastián Reyes-Carocca,Rubí E. Rodríguez
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 42,6 Mb
Release : 2021-04-23
Category : Education
ISBN : 9781470453275

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Geometry at the Frontier: Symmetries and Moduli Spaces of Algebraic Varieties by Paola Comparin,Eduardo Esteves,Herbert Lange,Sebastián Reyes-Carocca,Rubí E. Rodríguez Pdf

Articles in this volume are based on lectures given at three conferences on Geometry at the Frontier, held at the Universidad de la Frontera, Pucón, Chile in 2016, 2017, and 2018. The papers cover recent developments on the theory of algebraic varieties—in particular, of their automorphism groups and moduli spaces. They will be of interest to anyone working in the area, as well as young mathematicians and students interested in complex and algebraic geometry.

Representation Theory and Beyond

Jan Šťovíček,Jan Trlifaj
Representation Theory and Beyond Book PDF

Author : Jan Šťovíček,Jan Trlifaj
Publisher : American Mathematical Soc.
Page : 298 pages
File Size : 42,6 Mb
Release : 2020-11-13
Category : Education
ISBN : 9781470451318

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Representation Theory and Beyond by Jan Šťovíček,Jan Trlifaj Pdf

This volume contains the proceedings of the Workshop and 18th International Conference on Representations of Algebras (ICRA 2018) held from August 8–17, 2018, in Prague, Czech Republic. It presents several themes of contemporary representation theory together with some new tools, such as stable ∞ ∞-categories, stable derivators, and contramodules. In the first part, expanded lecture notes of four courses delivered at the workshop are presented, covering the representation theory of finite sets with correspondences, geometric theory of quiver Grassmannians, recent applications of contramodules to tilting theory, as well as symmetries in the representation theory over an abstract stable homotopy theory. The second part consists of six more-advanced papers based on plenary talks of the conference, presenting selected topics from contemporary representation theory: recollements and purity, maximal green sequences, cohomological Hall algebras, Hochschild cohomology of associative algebras, cohomology of local selfinjective algebras, and the higher Auslander–Reiten theory studied via homotopy theory.

Lie Groups, Number Theory, and Vertex Algebras

Dražen Adamović,Andrej Dujella,Antun Milas,Pavle Pandžić
Lie Groups Number Theory and Vertex Algebras Book PDF

Author : Dražen Adamović,Andrej Dujella,Antun Milas,Pavle Pandžić
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 41,9 Mb
Release : 2021-05-10
Category : Education
ISBN : 9781470453510

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Lie Groups, Number Theory, and Vertex Algebras by Dražen Adamović,Andrej Dujella,Antun Milas,Pavle Pandžić Pdf

This volume contains the proceedings of the conference Representation Theory XVI, held from June 25–29, 2019, in Dubrovnik, Croatia. The articles in the volume address selected aspects of representation theory of reductive Lie groups and vertex algebras, and are written by prominent experts in the field as well as junior researchers. The three main topics of these articles are Lie theory, number theory, and vertex algebras.

Abelian Varieties and Number Theory

Moshe Jarden,Tony Shaska
Abelian Varieties and Number Theory Book PDF

Author : Moshe Jarden,Tony Shaska
Publisher : American Mathematical Soc.
Page : 200 pages
File Size : 53,5 Mb
Release : 2021-05-03
Category : Education
ISBN : 9781470452070

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Abelian Varieties and Number Theory by Moshe Jarden,Tony Shaska Pdf

This book is a collection of articles on Abelian varieties and number theory dedicated to Gerhard Frey's 75th birthday. It contains original articles by experts in the area of arithmetic and algebraic geometry. The articles cover topics on Abelian varieties and finitely generated Galois groups, ranks of Abelian varieties and Mordell-Lang conjecture, Tate-Shafarevich group and isogeny volcanoes, endomorphisms of superelliptic Jacobians, obstructions to local-global principles over semi-global fields, Drinfeld modular varieties, representations of etale fundamental groups and specialization of algebraic cycles, Deuring's theory of constant reductions, etc. The book will be a valuable resource to graduate students and experts working on Abelian varieties and related areas.