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Softcover ISBN:  9781470415570 
Product Code:  CONM/643 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
eBook ISBN:  9781470425685 
Product Code:  CONM/643.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470415570 
eBook ISBN:  9781470425685 
Product Code:  CONM/643.B 
List Price:  $255.00 $192.50 
MAA Member Price:  $229.50 $173.25 
AMS Member Price:  $204.00 $154.00 

Book DetailsContemporary MathematicsVolume: 643; 2015; 323 ppMSC: Primary 14; 18; 55; 57; 81;
This volume contains the proceedings of the CATS4 Conference on Higher Categorical Structures and their Interactions with Algebraic Geometry, Algebraic Topology and Algebra, held from July 2–7, 2012, at CIRM in Luminy, France.
Over the past several years, the CATS conference series has brought together top level researchers from around the world interested in relative and higher category theory and its applications to classical mathematical domains.
Included in this volume is a collection of articles covering the applications of categories and stacks to geometry, topology and algebra. Techniques such as localization, model categories, simplicial objects, sheaves of categories, mapping stacks, dg structures, hereditary categories, and derived stacks, are applied to give new insight on cluster algebra, Lagrangians, trace theories, loop spaces, structured surfaces, stability, indcoherent complexes and 1affineness showing up in geometric Langlands, branching out to many related topics along the way.
ReadershipGraduate students and research mathematicians interested in category theory and its applications in algebraic geometry, algebraic topology, representation theory, symplectic geometry, and mathematical physics.

Table of Contents

Articles

Damien Calaque — Lagrangian structures on mapping stacks and semiclassical TFTs

Julia E. Bergner and Marcy Robertson — Cluster categories for topologists

T. Dyckerhoff and M. Kapranov — Crossed simplicial groups and structured surfaces

Gabriele Vezzosi — A model structure on relative dgLie algebroids

Oren BenBassat — Multiple derived Lagrangian intersections

Dennis Gaitsgory — Sheaves of categories and the notion of 1affineness

D. Kaledin — Trace theories and localization

George Dimitrov and Ludmil Katzarkov — Nonsemistable exceptional objects in hereditary categories: some remarks and conjectures

Anatoly Preygel — Indcoherent complexes on loop spaces and connections


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This volume contains the proceedings of the CATS4 Conference on Higher Categorical Structures and their Interactions with Algebraic Geometry, Algebraic Topology and Algebra, held from July 2–7, 2012, at CIRM in Luminy, France.
Over the past several years, the CATS conference series has brought together top level researchers from around the world interested in relative and higher category theory and its applications to classical mathematical domains.
Included in this volume is a collection of articles covering the applications of categories and stacks to geometry, topology and algebra. Techniques such as localization, model categories, simplicial objects, sheaves of categories, mapping stacks, dg structures, hereditary categories, and derived stacks, are applied to give new insight on cluster algebra, Lagrangians, trace theories, loop spaces, structured surfaces, stability, indcoherent complexes and 1affineness showing up in geometric Langlands, branching out to many related topics along the way.
Graduate students and research mathematicians interested in category theory and its applications in algebraic geometry, algebraic topology, representation theory, symplectic geometry, and mathematical physics.

Articles

Damien Calaque — Lagrangian structures on mapping stacks and semiclassical TFTs

Julia E. Bergner and Marcy Robertson — Cluster categories for topologists

T. Dyckerhoff and M. Kapranov — Crossed simplicial groups and structured surfaces

Gabriele Vezzosi — A model structure on relative dgLie algebroids

Oren BenBassat — Multiple derived Lagrangian intersections

Dennis Gaitsgory — Sheaves of categories and the notion of 1affineness

D. Kaledin — Trace theories and localization

George Dimitrov and Ludmil Katzarkov — Nonsemistable exceptional objects in hereditary categories: some remarks and conjectures

Anatoly Preygel — Indcoherent complexes on loop spaces and connections