#
**Workshop on Noncommutative Manifolds **

##
**International School for Advanced Studies (SISSA), Trieste, Italy **

October 18-22, 2004

### Supported in part by
the Italian Research Project
"Singularities, Integrability, Symmetries"
and
Friuli-Venezia Giulia Research Project
"Geometry of moduli spaces and applications to mathematical physics"

### The International School for Advanced
Studies (SISSA) in collaboration with the Dipartimento di Matematica e Informatica,
Universita` di Trieste and the Abdus Salam International Centre for Theoretical Physics, Trieste,
organizes a workshop on Noncommutative Manifolds. The workshop
will be devoted to some recent developments in Noncommutative Differential Geometry with emphasis on the definition and examples
of noncommutative manifolds,
the construction of spectral triples and in particular of the Dirac operators,
relations to quantum groups and applications in mathematical physics.

###

**Advisory Committee: ** A. Connes (IHES Paris),
B. Dubrovin (SISSA Trieste), Yu. I. Manin (MPI Bonn), N. Teleman (Ancona),
S. L. Woronowicz (Warsaw).

**Scientific and Organizing Committee: ** Ludwik Dabrowski (SISSA Trieste), Giovanni Landi (University of Trieste), Le Dung Trang (ICTP Trieste).

The International School for Advanced Studies, together with the
adjacent International Centre for Theoretical Physics, is located
within the Miramare Castle Natural Park, in a pinewood on the seaside
at about 6 km west from downtown Trieste.

**Accommodation:**
Participants will be accommodated in one of the guest houses of the
International Centre for Theoretical Physics or in hotels in downtown
Trieste.

**
Travel
information:** For information about travel please link to the SISSA or ICTP web pages.

**
Current weather**

**Programme**

**Venue: Main Lecture Hall, ICTP Main Building, Strada Costiera 11**

##
**Monday, October 18**

**9:10-10:10 S. L. WORONOWICZ: Problems with unbounded operators related to some quantum groups**
### 10:10-10:40 Coffee break

**10:40-11:40 H. MOSCOVICI: Hopf actions, modular symbols and Eisenstein cocycles**

**11:50-12:30 M. GRANDIS: Directed algebraic topology and noncommutative tori**
### 12:30-14:00 Lunch

**14:00-15:00 M. DUBOIS-VIOLETTE: Graded algebras and multilinear forms**

**15:10-15:50 R. LONGO: Noncommutative Spectral Invariants and Black Hole
Entropy**
### 15:50-16:10 Break

**16:10-16:50 F. CIPRIANI: Fredholm module associated to a Dirichlet form
**

**17:00-17:40 D. GUREVICH: Quantum bundles via Cayley-Hamilton identities
**

##
**Tuesday, October 19**

**9:10-10:10 A. CONNES: Renormalization and motivic Galois theory**
### 10:10-10:40 Coffee break

**10:40-11:40 M.MARCOLLI: Noncommutative geometry and arithmetics**

**11:50-12:30 H. GROSSE: Renormalization of noncommutative scalar quantum field
theories
**

### 12:30-14:00 Lunch

**14:00-14:40 N. TELEMAN: Distance functions, linear quasi-connection and Chern character**

**14:50-15:30 M. TARLINI: Quantum spheres from unitary quantum groups and
Poisson geometry**
### 15:30-15.50 Break

**15:50-16:30 T. HADFIELD: Twisted homology of quantum
groups**

**16:40-17:20 W. van SUIJLEKOM: Dirac operator on SU_q(2)**

### 17:20 Discussion

**Wednesday, October 20**

**9:10-10:10 A. CONNES: Noncommutative Geometry and Physics**

### 10:10-10:40 Coffee break

**10:40-11:40 M. MARCOLLI: Noncommutative geometry and arithmetics **

**11:50-12:30 S. DOPLICHER: Quantum spacetime and quantum field theory**

### 12:30-14:00 Lunch

**14:00-14:40 V. GAYRAL: Non-compact isospectral deformations and field theories**

**14:50-15:20 C. PAGANI: A Hopf bundle over a quantum four-sphere from the symplectic group**
### 15:20-15:40 Break

**15:40-16:20 T. KRAJEWSKI: Noncommutative phase factors
**

**16:30-17:10 P. M. HAJAC: The K-theory of Heegaard-type quantum 3-spheres
**

**17:20-18:00 E. BEGGS: The necessity of nonassociativity in quantised differential
geometry**

##
**Thursday, October 21**

**9:10-10:10 A. SITARZ: Spectral geometry and quantum deformations**

### 10:10-10:40 Coffee break

**10:40-11:40 J. MICKELSSON: Moyal product and gauge group extension
**

**11:50-12:30 A. ZAMPINI: The beat of a fuzzy drum**

### 12:30-14:00 Lunch

**14:00-15:00 P. BIELAVSKY: Noncommutative Symmetric Spaces and Universal
Deformation Formulae for Lie Group Actions
**

**15:10-15:50 T. BRZEZINSKI: Uses for corings**
### 15:50-16:10 Break

**16:10-16:50 R. COQUEREAUX: Comments on Ocneanu finite quantum groupoids and
Coxeter Dynkin systems**

**17:00-17:30 J. WAWRZYCKI: Noncommutative Spacetime and Quantum Mechanics**

**17:40-18:10 P. MARTINETTI:On the time interpretation of von Neumann automorphisms **

##
**Friday, October 22**

**9:00-10:00 J. GRACIA-BONDIA: Remarks on the structure of renormalization Hopf
algebras**

### 10:00-10:30 Coffee break

**10:30-11:10 T. R. GOVINDARAJAN: Spacetime noncommutativity and quantum theory**

**11:15-11:55 P. ASCHIERI: Noncommutative bundles and bundles gerbes via deformation quantization**

**12:00-12:30 T. MASZCZYK: Noncommutative arithmetic geometry**
### 12:30-14:00 Lunch

**14:00-15:00 T. SCHUCKER: Noncommutative geometry and the standard model**

**15.05-16:05 L. TUSET: A local index formula for the quantum sphere**