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Electronic ISBN:  9781470418557 
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Book DetailsContemporary MathematicsVolume: 620; 2014; 328 ppMSC: Primary 14; 18; 19; 55; 57; 60;
This volume contains the proceedings of the Stanford Symposium on Algebraic Topology: Applications and New Directions, held from July 23–27, 2012, at Stanford University, Stanford, California. The symposium was held in honor of Gunnar Carlsson, Ralph Cohen and Ib Madsen, who celebrated their 60th and 70th birthdays that year. It showcased current research in Algebraic Topology reflecting the celebrants' broad interests and profound influence on the subject.
The topics varied broadly from stable equivariant homotopy theory to persistent homology and application in data analysis, covering topological aspects of quantum physics such as string topology and geometric quantization, examining homology stability in algebraic and geometric contexts, including algebraic \(K\)theory and the theory of operads.ReadershipGraduate students and research mathematicians interested in algebraic topology and its applications.

Table of Contents

Articles

Thomas Church, Jordan S. Ellenberg and Benson Farb  Representation stability in cohomology and asymptotics for families of varieties over finite fields

Thomas Church, Benson Farb and Andrew Putman  A stability conjecture for the unstable cohomology of $\mathrm {SL}_n\mathbb {Z}$, mapping class groups, and $\mathrm {Aut}(F_n)$

William Dwyer and Kathryn Hess  The BoardmanVogt tensor product of operadic bimodules

Søren Galatius and Oscar RandalWilliams  Detecting and realising characteristic classes of manifold bundles

Boris Goldfarb and Timothy K. Lance  Controlled Algebraic $G$theory, II

Ian Hambleton and Erik K. Pedersen  More examples of discrete cocompact group actions

Lars Hesselholt  On the $K$theory of planar cuspical curves and a new family of polytopes

M. A. Hill and M. J. Hopkins  Equivariant multiplicative closure

Matthew Kahle  Topology of random simplicial complexes: a survey

Ludmil Katzarkov, Ernesto Lupercio, Laurent Meersseman and Alberto Verjovsky  The definition of a noncommutative toric variety

Nitu Kitchloo  The Stable Symplectic Category and Quantization

Graeme Segal  A geometric perspective on quantum field theory

Mikael VejdemoJohansson  Sketches of a platypus: a survey of persistent homology and its algebraic foundations

Kirsten Wickelgren  Cartier’s first theorem for Witt vectors on $\mathbb {Z}_{\geq 0}^n  0$


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This volume contains the proceedings of the Stanford Symposium on Algebraic Topology: Applications and New Directions, held from July 23–27, 2012, at Stanford University, Stanford, California. The symposium was held in honor of Gunnar Carlsson, Ralph Cohen and Ib Madsen, who celebrated their 60th and 70th birthdays that year. It showcased current research in Algebraic Topology reflecting the celebrants' broad interests and profound influence on the subject.
The topics varied broadly from stable equivariant homotopy theory to persistent homology and application in data analysis, covering topological aspects of quantum physics such as string topology and geometric quantization, examining homology stability in algebraic and geometric contexts, including algebraic \(K\)theory and the theory of operads.
Graduate students and research mathematicians interested in algebraic topology and its applications.

Articles

Thomas Church, Jordan S. Ellenberg and Benson Farb  Representation stability in cohomology and asymptotics for families of varieties over finite fields

Thomas Church, Benson Farb and Andrew Putman  A stability conjecture for the unstable cohomology of $\mathrm {SL}_n\mathbb {Z}$, mapping class groups, and $\mathrm {Aut}(F_n)$

William Dwyer and Kathryn Hess  The BoardmanVogt tensor product of operadic bimodules

Søren Galatius and Oscar RandalWilliams  Detecting and realising characteristic classes of manifold bundles

Boris Goldfarb and Timothy K. Lance  Controlled Algebraic $G$theory, II

Ian Hambleton and Erik K. Pedersen  More examples of discrete cocompact group actions

Lars Hesselholt  On the $K$theory of planar cuspical curves and a new family of polytopes

M. A. Hill and M. J. Hopkins  Equivariant multiplicative closure

Matthew Kahle  Topology of random simplicial complexes: a survey

Ludmil Katzarkov, Ernesto Lupercio, Laurent Meersseman and Alberto Verjovsky  The definition of a noncommutative toric variety

Nitu Kitchloo  The Stable Symplectic Category and Quantization

Graeme Segal  A geometric perspective on quantum field theory

Mikael VejdemoJohansson  Sketches of a platypus: a survey of persistent homology and its algebraic foundations

Kirsten Wickelgren  Cartier’s first theorem for Witt vectors on $\mathbb {Z}_{\geq 0}^n  0$