Algebraic Topology: Applications and New Directions
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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.
Table of Contents
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Front/Back Matter
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 _n\mathbb $, mapping class groups, and $\mathrm (F_n)$
- William Dwyer and Kathryn Hess – The Boardman-Vogt tensor product of operadic bimodules
- Søren Galatius and Oscar Randal-Williams – 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 co-compact 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 non-commutative toric variety
- Nitu Kitchloo – The Stable Symplectic Category and Quantization
- Graeme Segal – A geometric perspective on quantum field theory
- Mikael Vejdemo-Johansson – Sketches of a platypus: a survey of persistent homology and its algebraic foundations
- Kirsten Wickelgren – Cartier’s first theorem for Witt vectors on $\mathbb _<\geq 0>^n - 0$
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