Noncommutative geometry

Programme theme

Noncommutative geometry aims to carry over geometrical concepts to a new class of spaces whose algebras of functions are no longer commutative. The central idea goes back to quantum mechanics, where classical observables such as position and momenta no longer commute. In recent years it has become appreciated that such noncommutative spaces retain a rich topology and geometry expressed first of all in K-theory and K-homology, as well as in finer aspects of the theory. The subject has also been approached from a more algebraic side with the advent of quantum groups and their quantum homogeneous spaces.

The subject in its modern form has also been connected with developments in several different fields of both pure mathematics and mathematical physics. In mathematics these include fruitful interactions with analysis, number theory, category theory and representation theory. In mathematical physics, developments include the quantum Hall effect, applications to the standard model in particle physics and to renormalization in quantum field theory, models of spacetimes with noncommuting coordinates. Noncommutative geometry also appears naturally in string/M-theory. The programme will be devoted to bringing together these different streams and instances of noncommutative geometry, as well as identifying new emerging directions.

Three main themes of the programme will be reflected in workshops in July, September and December of 2006, covering noncommutative geometry and cyclic cohomology, noncommutative geometry and fundamental physics, and new directions in noncommutative geometry respectively.

Click here to download the programme's final scientific report

Preprints

Title	Year	Programme	Publication Date
Geometrization of the strong Novikov conjecture for residually finite groups Authors: Q Wang, G Yu, G Gong Download PDF	2006	NCG	21 October 2016
Dyson Schwinger equations: From Hopf algebras to number theory Authors: Dirk Kreimer Download PDF	2006	NCG	21 October 2016
Noncommutative Batalin-Vilkovisky geometry and matrix integrals Authors: S Barannikov Download PDF	2006	NCG	21 October 2016
The isospectral Dirac operator on the 4-dimensional quantum euclidean sphere Authors: Francesco D'Andrea, Ludwik Dabrowski, G Landi Download PDF	2006	NCG	21 October 2016
Noncommutative resolutions and rational singularities Authors: J Toby Stafford, Michel van den Bergh Download PDF	2006	NCG	21 October 2016
A class of noncommutative projective surfaces Authors: Daniel Rogalski, J Toby Stafford Download PDF	2006	NCG	21 October 2016
Naive noncommutative blowups at zero-dimensional schemes Authors: J Toby Stafford, Daniel Rogalski Download PDF	2006	NCG	21 October 2016
Matched pairs approach to set theoretic solutions of the Yang-Baxter equation Authors: Shahn Majid, Tatiana Gateva-Ivanova Download PDF	2006	NCG	21 October 2016
Bar categories and star operations Authors: Shahn Majid, Edwin Beggs Download PDF	2006	NCG	21 October 2016
Quantisation of twistor theory by cocycle twist Authors: Shahn Majid, SJ Brain Download PDF	2006	NCG	21 October 2016
Set theoretic solutions of the Yang-Baxter equation, graphs and computations Authors: Shahn Majid, Tatiana Gateva-Ivanova Download PDF	2006	NCG	21 October 2016
$\ast$-compatible connections in noncommutative Riemannian geometry Authors: Shahn Majid, Edwin Beggs Download PDF	2006	NCG	21 October 2016

Workshops

NCGW01

NCGW04

16 April 2012 to 20 April 2012

Seminars

Thursday 27th July 2006
14:00 to 15:00	Tom Hadfield Queen Mary University of London Braided Homology of Quantum Groups	Room 2

Friday 28th July 2006
14:00 to 15:00	Poincare duality in Hochschild (co)homology and smoothness	Room 2
15:30 to 16:30	Piotr Mieczyslaw Hajac Noncommutative geometry approach to principal and associated bundles	Room 2

Wednesday 9th August 2006
14:00 to 15:00	Zinaida Lykova University of Newcastle upon Tyne Cyclic cohomology of projective limits of topological algebras	Room 1

Thursday 10th August 2006
16:30 to 17:30	Ryszard Nest Københavns Universitet (University of Copenhagen) Baum-Connes isomorphism for certain quantum groups II	Room 1

Tuesday 15th August 2006
15:30 to 16:30	Iain Gordon University of Edinburgh Existence of symplectic resolutions through noncommutative algebra	Room 1

Wednesday 16th August 2006
15:30 to 16:30	Stanislaw Lech Woronowicz Quantum Ax+B. Where does the quantisation of $\hbar$ come from?	Room 1

Tuesday 22nd August 2006
15:00 to 16:00	Stephane Launois University of Edinburgh Unique factorisation domain and quantum algebras	Room 1

Wednesday 23rd August 2006
15:00 to 16:00	Mariusz Wodzicki University of California Differential operators on multiple points	Room 1

Wednesday 30th August 2006
15:00 to 16:00	Mikael Pichot The space of triangle buildings	Room 1

Thursday 31st August 2006
15:30 to 16:30	Victor Gayral Københavns Universitet (University of Copenhagen) Spectral triples and Berezin-Toeplitz quantization	Room 1

Friday 1st September 2006
15:30 to 16:30	Vadim Vologodsky University of Chicago On cristalline Deligne cohomology	Room 1

Monday 11th September 2006
11:30 to 12:30	A Lorentzian version of the non-commutative geometry of the standard model of particle physics	Room 2
14:00 to 15:00	Catherine Meusburger Perimeter Institute for Theoretical Physics (2+1)-dimensional gravity in the geometrical and in the Chern-Simons formulation	Room 2
15:00 to 16:00	Andrzej Sitarz On spin structures in non-commutative geometry and shadows of non-commutativity	Room 2

Tuesday 12th September 2006
15:00 to 16:00	Joachim Cuntz Universität Münster On a C*-algebra associated with the set of prime numbers	Room 2
16:30 to 17:30	Ping Xu Pennsylvania State University Chern character for twisted K-theory of orbifolds	Room 2

Wednesday 13th September 2006
15:00 to 16:00	Quantum principal bundles in twistor theory	Room 2

Thursday 14th September 2006
15:00 to 16:00	Franz Luef From signal analysis and coherent states to projective modules over non-commutative tori	Room 2

Monday 18th September 2006
15:00 to 16:00	Marc Rieffel University of California Physicists say "Matrix algebras converge to the sphere"	Room 2

Tuesday 19th September 2006
15:00 to 16:00	Mariusz Wodzicki University of California Differential operators on multiple points, part II	Room 2

Thursday 21st September 2006
15:00 to 16:00	Twisted conformal symmetry and instantons	Room 2

Monday 25th September 2006
15:00 to 16:00	Michael Farber University of Durham Homology of planar linkages	Room 1

Tuesday 26th September 2006
15:00 to 16:00	Noncommutative Batalin-Vilkovisky geometry and stable ribbon graphs	Room 1

Wednesday 27th September 2006
15:00 to 16:00	Marc Rieffel University of California Vector bundles and Gromov-Hausdorff distance	Room 1

Friday 29th September 2006
15:00 to 16:00	Mariusz Wodzicki University of California Differential operators, part III: operators of negative order \& exceptional Lie algebras $\frak g_2$, $\frak f_4$, $\frak e_8$	Room 1

Monday 2nd October 2006
14:00 to 16:00	Alain Connes IHES Spectral action and gravity coupled with matter	Room 2

Wednesday 4th October 2006
14:30 to 15:30	George Wilson University of Oxford Algebras with many mad subalgebras	Room 2

Friday 6th October 2006
14:30 to 15:30	Homogeneous coordinate rings of non-commutative spaces	Room 1

Monday 9th October 2006
14:00 to 16:00	Alain Connes IHES Spectral action and gravity coupled with matter	Room 1

Tuesday 10th October 2006
14:30 to 15:30	Dimitri Gurevich Noncummutative dynamical models with quantum symmetries	Room 1

Wednesday 11th October 2006
11:00 to 13:00	Alain Connes IHES Spectral action and gravity coupled with matter	Room 1

Thursday 12th October 2006
14:30 to 15:30	Jorge Plazas Arithmetic structures on noncommutative tori with real multiplication	Room 1

Wednesday 18th October 2006
14:30 to 15:30	Edwin Beggs University of Wales, Swansea Star Bar categories in noncommutative geometry	Room 1

Thursday 19th October 2006
14:00 to 15:00	Monoidal categories and WDW equation NCG in collaboration with COW seminar	Room 2
15:45 to 16:30	Recent progress in the minimal model program NCG in collaboration with COW seminar	Room 2
16:30 to 17:30	Alexey Bondal TBA NCG in collaboration with COW seminar	Room 2

Tuesday 24th October 2006
14:30 to 15:30	Cherednik algebras from braidings on Coxeter groups	Room 1

Wednesday 25th October 2006
14:30 to 15:30	Roger Plymen University of Manchester Affine Hecke algebras, Langlands duality and geometric structure	Room 1

Thursday 26th October 2006
14:30 to 15:30	Zinaida Lykova University of Newcastle upon Tyne Topologically pure extensions of Frechet algebras and applications to homology	Room 1

Tuesday 31st October 2006
14:30 to 15:30	Jacques Alev Poisson versus Hochschild homology for some quotient varieties	Room 2

Wednesday 1st November 2006
14:30 to 15:30	Calder Daenzer University of Pennsylvania On refining noncommutative T-duality	Room 2

Thursday 2nd November 2006
14:30 to 15:30	Tatiana Gateva-Ivanova Bulgarian Academy of Sciences Matched pairs approach to set-theoretic solutions of the YBE	Room 2

Monday 6th November 2006
14:00 to 16:00	Alain Connes IHES Spectral action and gravity coupled with matter	Room 1

Wednesday 8th November 2006
14:00 to 16:00	Alain Connes IHES Spectral action and gravity coupled with matter	Room 1

Thursday 9th November 2006
14:30 to 15:30	J Toby Stafford University of Michigan Noncommutative resolutions and rational singularities	Room 1

Tuesday 21st November 2006
14:30 to 15:30	Noncommutative Hirzebruch surfaces	Room 2

Thursday 23rd November 2006
14:30 to 15:30	David Kyed Københavns Universitet (University of Copenhagen) L$^2$-homology for compact quantum groups	Room 2

Tuesday 28th November 2006
14:30 to 15:30	Johannes Aastrup Leibniz Universität Hannover Deformation quantization of endomorphism bundles	Room 1

Thursday 30th November 2006
14:30 to 15:30	John Hunton University of Leicester Aperiodic patterns	Room 1

Monday 4th December 2006
10:30 to 11:15	Antony Wassermann Minicourse on Bott Periodicity and Index Theorems	Room 1
11:30 to 12:30	Antony Wassermann Minicourse on Bott Periodicity and Index Theorems	Room 1

Wednesday 6th December 2006
10:30 to 11:15	Antony Wassermann Minicourse on Bott Periodicity and Index Theorems	Room 1
11:30 to 12:30	Antony Wassermann Minicourse on Bott Periodicity and Index Theorems	Room 1
14:30 to 15:30	Vladimir Retakh On a class of algebras associated with directed graphs	Room 1

Friday 8th December 2006
10:30 to 11:15	Antony Wassermann Minicourse on Bott Periodicity and Index Theorems	Room 1
11:30 to 12:30	Antony Wassermann Minicourse on Bott Periodicity and Index Theorems	Room 1
14:30 to 15:30	Ryszard Nest Københavns Universitet (University of Copenhagen) Atiyah-Singer Index Theorem on R$^n$	Room 1

Tuesday 12th December 2006
14:30 to 15:30	Modular invariants, subfactors and twisted K-theory	Room 2

Wednesday 13th December 2006
14:30 to 15:30	Vladimir Manuilov Institute of Mechanics of Moscow State University On homotopy non-invertibility of C*-extensions	Room 2

Friday 15th December 2006
10:00 to 11:30	Masoud Khalkhali Hopf cyclic cohomology: why and how	Room 2
11:30 to 12:30	Twisted spectral triples and covariant differential calculi	Room 2
14:30 to 15:30	Tom Hadfield Queen Mary University of London K-theoretic construction of noncommutative instantons	Room 2
16:00 to 17:00	Nahum Zobin Functional integral approach to noncommutative quantum gauge theory	Room 2

Organisers

Alain Connes IHES
Shahn Majid
Albert Schwarz University of California

Speakers

Johannes Aastrup Leibniz Universität Hannover
Jacques Alev
Edwin Beggs University of Wales, Swansea
Alexey Bondal
Alain Connes IHES
Joachim Cuntz Universität Münster
Calder Daenzer University of Pennsylvania
Michael Farber University of Durham
Tatiana Gateva-Ivanova Bulgarian Academy of Sciences
Victor Gayral Københavns Universitet (University of Copenhagen)
Iain Gordon University of Edinburgh
Dimitri Gurevich
Tom Hadfield Queen Mary University of London
Piotr Mieczyslaw Hajac
John Hunton University of Leicester
Masoud Khalkhali
David Kyed Københavns Universitet (University of Copenhagen)
Stephane Launois University of Edinburgh
Franz Luef
Zinaida Lykova University of Newcastle upon Tyne
Vladimir Manuilov Institute of Mechanics of Moscow State University
Catherine Meusburger Perimeter Institute for Theoretical Physics
Ryszard Nest Københavns Universitet (University of Copenhagen)
Mikael Pichot
Jorge Plazas
Roger Plymen University of Manchester
Vladimir Retakh
Marc Rieffel University of California
Andrzej Sitarz
J Toby Stafford University of Michigan
Vadim Vologodsky University of Chicago
Antony Wassermann
George Wilson University of Oxford
Mariusz Wodzicki University of California
Stanislaw Lech Woronowicz
Ping Xu Pennsylvania State University
Nahum Zobin

Show All

Noncommutative geometry

Programme theme

Preprints

Geometrization of the strong Novikov conjecture for residually finite groups

Dyson Schwinger equations: From Hopf algebras to number theory

Noncommutative Batalin-Vilkovisky geometry and matrix integrals

The isospectral Dirac operator on the 4-dimensional quantum euclidean sphere

Noncommutative resolutions and rational singularities

A class of noncommutative projective surfaces

Naive noncommutative blowups at zero-dimensional schemes

Matched pairs approach to set theoretic solutions of the Yang-Baxter equation

Bar categories and star operations

Quantisation of twistor theory by cocycle twist

Set theoretic solutions of the Yang-Baxter equation, graphs and computations

$\ast$-compatible connections in noncommutative Riemannian geometry

Workshops

Noncommutative geometry and cyclic cohomology

Noncommutative geometry and physics: fundamental structure of space and time

Trends in noncommutative geometry

Noncommutative geometry

Seminars

Organisers

Speakers

Supported By

Noncommutative geometry

Programme theme

Preprints

Geometrization of the strong Novikov conjecture for residually finite groups

Dyson Schwinger equations: From Hopf algebras to number theory

Noncommutative Batalin-Vilkovisky geometry and matrix integrals

The isospectral Dirac operator on the 4-dimensional quantum euclidean sphere

Noncommutative resolutions and rational singularities

A class of noncommutative projective surfaces

Naive noncommutative blowups at zero-dimensional schemes

Matched pairs approach to set theoretic solutions of the Yang-Baxter equation

Bar categories and star operations

Quantisation of twistor theory by cocycle twist

Set theoretic solutions of the Yang-Baxter equation, graphs and computations

$\ast$-compatible connections in noncommutative Riemannian geometry

Workshops

Noncommutative geometry and cyclic cohomology

Noncommutative geometry and physics: fundamental structure of space and time

Trends in noncommutative geometry

Noncommutative geometry

Seminars

Organisers

Speakers

Supported By

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Noncommutative Batalin-Vilkovisky geometry and matrix integrals