Algebraic topology : applications and new directions : Stanford Symposium on Algebraic Topology: Applications and New Directions, July 23--27, 2012, Stanford University, Stanford, CA / Ulrike Tillmann, Soren Galatius, Dev Sinha, editors.

Format:

Book

Conference/Event

Contributor:

Tillmann, U. L. (Ulrike Luise), 1962- editor.

Galatius, Søren, 1976- editor.

Sinha, Dev (Dev Prakash), 1971- editor.

Conference Name:

Stanford Symposium on Algebraic Topology: Applications and New Directions (2012 : Stanford, California)

Stanford Symposium on Algebraic Topology: Applications and New Directions (2012 : Stanford, Calif.)

Series:

Contemporary mathematics, 0271-4132 620

Contemporary mathematics, 1098-3627 ; 620 0271-4132

Language:

English

Subjects (All):

Algebraic topology--Congresses.

Algebraic topology.

Physical Description:

1 online resource (328 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2014.

Language Note:

English

Summary:

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.

Contents:

Preface

Scientific Programme

List of Participants and Conference Photo

Representation stability in cohomology and asymptotics for families of varieties over finite fields

1. Introduction

2. The twisted Grothendieck-Lefschetz Formula

3. Hyperplane arrangements, their cohomology, and combinatorics of squarefree polynomials

4. Statistics of squarefree polynomials and the cohomology of the pure braid group

5. Maximal tori in ...

References

A stability conjecture for the unstable cohomology of .... mapping class groups, and...

2. Stability in the unstable cohomology of

3. Stability in the unstable cohomology of mapping class groups

4. Stability in the unstable cohomology of .....

The Boardman-Vogt tensor product of operadic bimodules

Introduction

1. Lifting the Boardman-Vogt tensor product

2. The algebra of the divided powers functor

Appendix A. Proofs of Proposition 1.20 and Theorem 1.22

Detecting and realising characteristic classes of manifold bundles

1. Introduction and statement of results

2. Proof of Theorem 1.1

3. Proof of Theorem 1.4

4. Proof of Proposition 1.3

Controlled Algebraic -theory, II

2. Continuous Control for Filtered Modules

3. Continuously Controlled -theory

4. The Localization Homotopy Fibration

5. Controlled Excision Theorems

More examples of discrete co-compact group actions

1. Groups with periodic cohomology

2. Homotopy theoretic commutative algebra

3. Extended powers and indexed monoidal products

4. Equivariant multiplicative closure

Topology of random simplicial complexes: a survey

2. Random graphs

3. Random 2-complexes

4. Random flag complexes

5. Comments

Acknowledgements

The definition of a non-commutative toric variety

2. Classical Toric Varieties

3. Non-commutative Geometry

4. Variations on Diffeology

5. LVM-theory

6. Non-commutative Toric Varieties.

Notes:

Description based upon print version of record.

Includes bibliographical references at the end of each chapters.

Description based on print version record.

ISBN:

1-4704-1855-X