Stacks and Categories in Geometry, Topology, and Algebra
About this Title
Tony Pantev, University of Pennsylvania, Philadelphia, PA, Carlos Simpson, Université Nice Sophia Antipolis, Nice, France, Bertrand Toën, Université de Montpellier 2, Montpellier, France, Michel Vaquié, Université Paul Sabatier, Toulouse, France and Gabriele Vezzosi, Università degli Studi di Firenze, Firenze, Italy, Editors
Publication: Contemporary Mathematics
Publication Year 2015: Volume 643
ISBNs: 978-1-4704-1557-0 (print); 978-1-4704-2568-5 (online)
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.
Graduate 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
- Damien Calaque – Lagrangian structures on mapping stacks and semi-classical 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 dg-Lie algebroids
- Oren Ben-Bassat – Multiple derived Lagrangian intersections
- Dennis Gaitsgory – Sheaves of categories and the notion of 1-affineness
- D. Kaledin – Trace theories and localization
- George Dimitrov and Ludmil Katzarkov – Non-semistable exceptional objects in hereditary categories: some remarks and conjectures
- Anatoly Preygel – Ind-coherent complexes on loop spaces and connections