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Stacks and catetories in geometry, topology, and algebra / [edited by] Tony Pantev...[et al.].

By: Contributor(s): Material type: TextTextSeries: Contemporary mathematics ; 643.Publication details: Providence : American Mathematical Society, 2015.Description: viii, 323 p. : illustrations ; 26 cmISBN:
  • 9781470415570 (pbk. : acidfree paper)
Subject(s): DDC classification:
  • 510 23 Am512c
Contents:
Lagrangian structures on mapping stacks and semi-classical TFTs -- Cluster categories for topologists -- Crossed simplicial groups and structured surfaces -- A model structure on relative dg-Lie algebroids -- Multiple derived Lagrangian intersections -- Sheaves of categories and the notion of 1-affineness -- Trace theories and localization -- Non-semistable exceptional objects in hereditary categories: some remarks and conjectures -- Ind-coherent complexes on loop spaces and connections.
Summary: 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, ind-coherent complexes and 1-affineness showing up in geometric Langlands, branching out to many related topics along the way.
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Includes bibliographical references.

Lagrangian structures on mapping stacks and semi-classical TFTs --
Cluster categories for topologists --
Crossed simplicial groups and structured surfaces --
A model structure on relative dg-Lie algebroids --
Multiple derived Lagrangian intersections --
Sheaves of categories and the notion of 1-affineness --
Trace theories and localization --
Non-semistable exceptional objects in hereditary categories: some remarks and conjectures --
Ind-coherent complexes on loop spaces and connections.

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, ind-coherent complexes and 1-affineness showing up in geometric Langlands, branching out to many related topics along the way.

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