New contexts for stable homotopy theory

Programme theme

The versatility of stable homotopy theory and its associated range of cohomological techniques has made it an important branch of mathematics. Recently there have been several fundamental developments which have been used to solve a number of longstanding questions. This programme aims to consolidate the advances within homotopy theory itself which have led to these results, to open the way to substantial further developments within the subject, to expose a diversity of new applications and to bring practitioners of these subjects into contact with each other and with practising homotopy theorists. The programme will be designed around specialist workshops, but the aim will be to maximize contact between all parties by means of a number of introductory short courses.

Recent developments have culminated in several stable homotopy constructions which are homotopy theoretic enrichments of the category of abelian groups (``spectral algebra''). These new stable homotopy categories are useful for studying a wide range of phenomena, from algebraic K-theory and arithmetic to the elliptic cohomology phenomena introduced by Witten. In algebraic geometry the motivic homotopy category of Voevodsky and Morel has already been used in Voevodsky's proof of the Milnor conjecture in algebraic K-theory. In algebraic topology, the work of Hopkins et al on elliptic cohomology has led to geometric applications and topological refinements of modular forms.

y means of a series of workshops, seminars and short courses on the themes of

axiomatic and enriched homotopy theory
homotopy theory of geometric categories
K-theory and arithmetic
Elliptic cohomology and chromatic phenomena

it is hoped to promote further applications of the latest stable homotopy theoretic techniques.

Click here to download the programme's final scientific report

Preprints

Title	Year	Programme
Stark's conjecture and new Stickelberger phenomena Authors: VP Snaith Download PDF	2002	NST	21 October 2016
Explicit Brauer induction and the Glauberman correspondence Authors: V Snaith, A Case Download PDF	2002	NST	21 October 2016
Explicit Brauer induction for symplectic and and orthogonal representations Authors: V Snaith, O Neisse Download PDF	2002	NST	21 October 2016
Cubical homotopy theory: a beginning Authors: Rick Jardine Download PDF	2002	NST	21 October 2016
Galois cohomology of Witt vectors of algebraic integers Authors: Lars Hesselholt Download PDF	2002	NST	21 October 2016
Refined and $l$-adic Euler characteristics of nearly perfect complexes Authors: D Burns, B Kock, V Snaith Download PDF	2002	NST	21 October 2016
Generalised sheaf cohomology theories Authors: Rick Jardine Download PDF	2002	NST	21 October 2016
The upper triangular group and operations in algebraic K-theory Authors: VP Snaith Download PDF	2002	NST	21 October 2016
Relative $K_0$, annihilators, Fitting ideals and the Stickelberger phenomena Authors: VP Snaith Download PDF	2002	NST	21 October 2016
Cosimplicial objects and little $\it n$-cubes.I. Authors: Jeff Smith, James (Jim) McClure Download PDF	2002	NST	21 October 2016
Galois structure of vanishing cycles Authors: V Snaith Download PDF	2002	NST	21 October 2016
Rational torus-equivariant stable homotopy I calculating groups of stable maps Authors: JPC Greenlees Download PDF	2002	NST	21 October 2016
Rational torus-equivariant stable homotopy II the algebra of localization and inflation Authors: JPC Greenlees Download PDF	2002	NST	21 October 2016
Simplicial approximation Authors: Rick Jardine Download PDF	2002	NST	21 October 2016
The sigma orientation for analytic circle equivariant elliptic cohomology Authors: Matthew Ando Download PDF	2002	NST	21 October 2016
$\Gamma$-Cohomology of rings of numerical polynomials and E$\infty$ structures on K-theory Authors: B Richter, Andrew Baker Download PDF	2002	NST	21 October 2016
The de Rham-Witt complex and ${\it p}$-adic vanishing cycles Authors: Lars Hesselholt, T Geisser Download PDF	2002	NST	21 October 2016
The syntomic regular for ${\it k}$-theory of fields Authors: Rob de Jeu, Amnon Besser Download PDF	2002	NST	21 October 2016

Workshops

NSTW01

Seminars

Thursday 26th September 2002
14:00 to 15:00	Nobuaki Yagita Algebraic cobordism of simply connected Lie groups	Room 2
15:15 to 16:15	Grzegorz Banaszak Adam Mickiewicz University Non-torsion elements in algebraic k-theory of number fields, Mordell-Weil groups and l-adic representations	Room 2

Friday 27th September 2002
14:00 to 15:00	Bruno Kahn Informal geometry seminar series: Birational motives	Room 1

Wednesday 9th October 2002
16:00 to 17:00	Mark Mahowald Northwestern University tmf(3) and other tmf module spectra	Room 1

Thursday 10th October 2002
16:00 to 17:00	Masaki Hanamura Kyushu University Blow-ups and mixed motives	Room 1

Thursday 17th October 2002
14:00 to 15:00	K-theory and derived equivalences	Room 1
16:00 to 17:00	Douglas Ravenel University of Rochester The status of the telescope conjecture	Room 1

Thursday 24th October 2002
14:00 to 15:00	Mark Hovey Wesleyan University The structure of E$(n)_*E(n)$ comodules	Room 1
16:00 to 17:00	Marian Anton University of Kentucky General linear group homology	Room 1

Thursday 31st October 2002
14:00 to 15:00	Matthew Ando University of Illinois at Urbana-Champaign Guises of the second Chern class: the circle-equivariant sigma orientation	Room 1
16:00 to 17:00	Rob De Jeu University of Durham The rank conjecture for fields, and higher Chow groups	Room 1

Wednesday 6th November 2002
14:00 to 15:00	Euler characteristics of nearly perfect complexes	Room 1

Thursday 7th November 2002
14:00 to 15:00	Rational torus-equivariant cohomology theories	Room 1

Thursday 14th November 2002
14:00 to 15:00	Neil Strickland University of Sheffield Equivariant formal groups	Room 1

Thursday 21st November 2002
14:00 to 15:00	Rick Jardine University of Western Ontario Higher order stacks	Room 1

Thursday 28th November 2002
14:00 to 15:00	The Bass conjecture and acyclic groups	Room 1
16:00 to 17:00	John McCleary Vassar College Hochschild homology and closed geodesics	Room 1

Thursday 5th December 2002
14:00 to 15:00	Andrew (Andy) Baker University of Glasgow Minimal atomic complexes	Room 1
16:00 to 17:00	John Rognes University of Oslo Algebraic K-theory of topological K-theory	Room 1

Organisers

John Greenlees University of Sheffield
Haynes Miller Acclarogen Limited

Speakers

Matthew Ando University of Illinois at Urbana-Champaign
Marian Anton University of Kentucky
Andrew (Andy) Baker University of Glasgow
Grzegorz Banaszak Adam Mickiewicz University
Rob De Jeu University of Durham
Masaki Hanamura Kyushu University
Mark Hovey Wesleyan University
Rick Jardine University of Western Ontario
Bruno Kahn
Mark Mahowald Northwestern University
John McCleary Vassar College
Douglas Ravenel University of Rochester
John Rognes University of Oslo
Neil Strickland University of Sheffield
Nobuaki Yagita

Show All

New contexts for stable homotopy theory

Programme theme

Preprints

Stark's conjecture and new Stickelberger phenomena

Explicit Brauer induction and the Glauberman correspondence

Explicit Brauer induction for symplectic and and orthogonal representations

Cubical homotopy theory: a beginning

Galois cohomology of Witt vectors of algebraic integers

Refined and $l$-adic Euler characteristics of nearly perfect complexes

Generalised sheaf cohomology theories

The upper triangular group and operations in algebraic K-theory

Relative $K_0$, annihilators, Fitting ideals and the Stickelberger phenomena

Cosimplicial objects and little $\it n$-cubes.I.

Galois structure of vanishing cycles

Rational torus-equivariant stable homotopy I calculating groups of stable maps

Rational torus-equivariant stable homotopy II the algebra of localization and inflation

Simplicial approximation

The sigma orientation for analytic circle equivariant elliptic cohomology

$\Gamma$-Cohomology of rings of numerical polynomials and E$\infty$ structures on K-theory

The de Rham-Witt complex and ${\it p}$-adic vanishing cycles

The syntomic regular for ${\it k}$-theory of fields

Workshops

Axiomatic, enriched and motivic homotopy theory

Homotopy theory of geometric categories

K-theory and arithmetic

Elliptic cohomology and chromatic chenomena & higher chromatic phenomena

Seminars

Organisers

Speakers

Supported By

New contexts for stable homotopy theory

Programme theme

Preprints

Stark's conjecture and new Stickelberger phenomena

Explicit Brauer induction and the Glauberman correspondence

Explicit Brauer induction for symplectic and and orthogonal representations

Cubical homotopy theory: a beginning

Galois cohomology of Witt vectors of algebraic integers

Refined and $l$-adic Euler characteristics of nearly perfect complexes

Generalised sheaf cohomology theories

The upper triangular group and operations in algebraic K-theory

Relative $K_0$, annihilators, Fitting ideals and the Stickelberger phenomena

Cosimplicial objects and little $\it n$-cubes.I.

Galois structure of vanishing cycles

Rational torus-equivariant stable homotopy I calculating groups of stable maps

Rational torus-equivariant stable homotopy II the algebra of localization and inflation

Simplicial approximation

The sigma orientation for analytic circle equivariant elliptic cohomology

$\Gamma$-Cohomology of rings of numerical polynomials and E$\infty$ structures on K-theory

The de Rham-Witt complex and ${\it p}$-adic vanishing cycles

The syntomic regular for ${\it k}$-theory of fields

Workshops

Axiomatic, enriched and motivic homotopy theory

Homotopy theory of geometric categories

K-theory and arithmetic

Elliptic cohomology and chromatic chenomena & higher chromatic phenomena

Seminars

Organisers

Speakers

Supported By

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