
SCIENTIFIC PROGRAMS AND ACTIVITIES 

August 4, 2024  
Bimonthly Canadian Noncommutative Geometry Workshop 200910

Upcoming talks 200910 

TBA 
TBA 
Past Workshops 

Oct. 3, 2009 
10:30 am Sheldon Joyner (University of Western Ontario) The geometry of the functional equation of Riemann's zeta function In a seminal 1859 paper, Riemann gave two proofs of the analytic continuation and functional equation of his zeta function. The ideas behind his theta function proof were later developed into a powerful theory of Fourier analysis on number fields, in work of Hecke, Tate and others. In this talk, I will focus instead on the contour integral proof, and based on the ideas therein, will present two infinite families of new proofs of the analytic continuation and functional equation. The proofs are facilitated by geometric data coming from the fact that the polylogarithm generating function is a flat section of the universal unipotent bundle with connection over P^1\{0, 1, \infty}. 1:30 pm In this talk, we will introduce eta forms for a general family of elliptic selfadjoint pseudodifferential operators. These eta forms can intuitively be understood as a regularized version of the Chern character. Although their definition is not local, we will see that their exterior differential is and in fact represents the Chern character of the odd index of the family. The proof will be topological in nature and will involve a short exact sequence of groups of pseudodifferential operators that are classifying spaces for Ktheory. If time permits, we will also explain how these eta forms can be used to compute the curving of a certain bundle gerbe naturally associated to the family. This is a joint work with Richard Melrose.

Aug. 15, 2009 
Raphael Ponge (University of Tokyo) 
Aug. 15, 2009 2:00 pm 
Piotr Hajac (University of Warsaw) Toeplitz Quantum Projective Spaces We define the C*algebra of a quantum complex projective space TP(n) as a multirestricted fiber product build from (n+1)copies of the nth tensor power of the Toeplitz algebra (Toeplitz cubes). Replacing the Toeplitz algebra by the algebra of continuous functions on a disc, one obtains the algebra of continuous functions on CP(n). Using Birkhoff's theorem on distributive lattices, we show that the lattice generated by the ideals defining this fibre product is free. This means that the fiber product structure is "maximally nontrivial" or, in geometric terms, that all possible intersections obtained from pieces of Toeplitz cubes covering this quantum projective space are nonempty. This is a property inherited from the affine covering of a projective space. All this is used as an example to illustrate the classification of finite closed coverings of compact quantum spaces by finitely supported flabby sheaves of algebras over the universal partition space (the infinite projective space over Z/2 equipped with the Alexandrov topology). Based on joint work with Atabey Kaygun and Bartosz Zielinski. 
Support for graduate
students is available, please enquire, ncgworkshop<at>unb.ca.
This workshop is associated with the Center for Noncommutative Geometry
and Topology at the University of New Brunswick and the Noncommutative
Geometry Group at the University of Western Ontario.
www.math.unb.ca/~dan/copal/Centre_main.htm
We thank the Fields Instutute for financial support.