April 17, 2024


March 16-18, 2015
Workshop on the Geometry of Noncommutative Manifolds
at the Fields Institute, Toronto

Organizing Committee
George ELLIOTT, Piotr M. HAJAC, Jonathan ROSENBERG

Register HERE

A funding application for US-based participants is available with the registration page. Deadline to apply, February 28, 2015.

(On-line registration available until March 8, on-site to March 16).

Map to Fields Reimbursement information for funded participants
Accommodation in Toronto Information for speakers

This Workshop will include two minicourses intended for graduate students, each approximately three hours long, together with more specialized lectures for experts, and some time for informal discussions. Two of the main experts in the subject, Masoud Khalkhali from Western Ontario and Henri Moscovici from Ohio State, have tentatively confirmed.


While there is no universal agreement on a definition of a noncommutative manifold, there is general agreement on the most basic examples. Aside from such manifolds which are "almost commutative," such as Azumaya algebras over the algebra of functions on an ordinary (commutative) manifold, there are the noncommutative tori, which have attracted a huge amount of attention. In dimension 2, these specialize to the famous "irrational rotation algebras." Other examples of noncommutative manifolds are noncommutative Riemann surfaces, the quantum group SUq(2) (which can be viewed as a noncommutative S3), and the Podleś spheres.

Geometry on the noncommutative 2-torus or irrational rotation algebra has now advanced to the point where there is work on analogues of many classical theorems in the classical differential geometry of surfaces. The approach that has been tried most is studying the zeta function of the "Laplacian" for a conformal deformation of a flat metric Laplacian by a conformal factor in the (noncommutative) algebra. By this method Connes and Tretkoff have proved a kind of Gauss-Bonnet theorem, and more recently, Connes and Moscovici and Fathizadeh and Khalkhali have studied the analogue of the scalar curvature function. An alternative approach of Rosenberg starts with a more general notion of Riemannian metric and gives a unique associated "Levi-Civita connection" from which various geometric invariants can be extracted. One of the purposes of this workshop will be to try to reconcile these two very different approaches. Another focus of the workshop will be attempts to carry over what has been done for noncommutative 2-tori to other noncommutative manifolds, such as higher-dimensional noncommutative tori (for which there are some partial results) and noncommutative spheres and Riemann surfaces of genus > 1.

This workshop is supported by the Fields Institute and by US National Science Foundation grant DMS-1266158. We thank them for their generous support.


Noncommutative Manifolds Workshop Schedule, March 16-18, 2015
Time Monday March 16 Tuesday March 17 Wednesday March 18
9:00-9:30 Registration Masoud Khalkhali, Minicourse, II: From Spectral Geometry to NCG

Henri Moscovici, Minicourse, III: The Spectral Way in NCG

9:30-10:00 Henri Moscovici, Minicourse, I: The Spectral Way in NCG

10:00-10:30 coffee/tea break coffee/tea break
10:30-11:00 coffee/tea break Henri Moscovici, Minicourse, II: The Spectral Way in NCG

Masoud Khalkhali, Minicourse, III: From Spectral Geometry to NCG

11:00-11:30 Masoud Khalkhali, Minicourse, I: From Spectral Geometry to NCG

11:30-12:00 lunch break lunch break
12:00-13:00 lunch break
13:00-13:30 Farzad Fathizadeh, On the scalar curvature for NC 4-tori
13:30-14:00 Piotr M. Hajac, Odd-dimensional multi-pullback quantum spheres

14:00-14:30 George Elliott's class *

George Elliott's class *

14:30-15:00 coffee/tea break
15:00-15:30 R. Ó Buachalla, NC Kähler Quantum Homogen. Spaces

Joakim Arnlind, Riemannian curvature for NC spheres

coffee/tea break
15:30-16:00 Branimir Ćaćić, Splitting Homomorphisms in Strict Deformation Quantisation
16:00-16:30 coffee/tea break
coffee/tea break
16:30-17:00 Sasha Peterka, Vector Bundles over Noncommutative Complex Projective Spaces Ralph Kaufmann, Condensed matter, C*-geometry and topological invariants
~18:00   Informal conference dinner (local restaurant) - details to be announced
* George Elliott is teaching a graduate functional analysis course. This is not officially part of the workshop, but you can attend if you wish.
Location is HU1018

Participants List:

Full Name University/Affiliation

2015 Participants

Click for larger image


  Andrews, Rob  
  Arnlind, Joakim Linköping University
  Boyle, Latham Perimeter Institute for Theoretical Physics
  Cacic, Branimir Texas A&M University
  Elliot, George University of Toronto
  Eshmatov, Alimjon University of Western Ontario
  Farah, Ilijas York University
  Farnsworth, Shane Perimeter Institute
  Georgescu, Magdalena University of Toronto
  Ghasemi, Saeed York University
  Ghorbanpour, Asghar University of Western Ontario
  Hajac, Piotr M. IMPAN
  Im, Jeffrey University of Toronto
  Kaufmann, Ralph Purdue University
  Khalkhali, Masoud University of Western Ontario
  Liu, Yang Ohio State University
  Lupini, Martino York University
  Moscovici, Henri Ohio State University
  O Buachalla, Reamonn IMPAN
  Peterka, Mira University of Kansas
  Rosenberg, Jonathan University of Maryland
  Song, Yanli York University
  Strung, Karen Institute of Mathematics Polish Academy of Science
  Xu, Chao Ohio State University
  Ugurcan, Baris Evren University of Western Ontario
  Vignati, Alessandro York University
  Wang, Kun University of Toronto
  Wilson, Mitsuru Western Univerity
  Yang, Tao Ohio State University
  Yashinski, Allan University of Hawaii at Manoa

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