Noncommutative Geometry

Speaker: Sajad Sadeghi (Western)

"NCG Learning Seminar: Hecke C*-algebras"

Time: 14:30

Room: MC 107

In this lecture we first give some examples of states and GNS constructions. Then we introduce the reduced group $C^*$-algebra of a discrete group. Moreover, the Hecke pair $(G,H)$ consisting of a group $G$ and an almost normal subgroup $H$ will be introduced. Indeed, a subgroup $H$ of a group $G$ is called almost normal if every double coset $HgH$ can be written as a union of finite number of left cosets. Using Hecke pairs we introduce Hecke $C^*$-algebras as a generalization of group $C^*$-algebras. Finally we piont to the Bost-Connes pair and its Hecke $C^*$-algebra.

Pizza Seminar

Speaker: Masoud Khalkhali (Western)

"Fun with Feynman, part I: Wick`s Theorem"

Time: 16:30

Room: MC 108

This is the first of a series of two talks on finite dimensional Feynman Calculus. The second talk will be in the next week and will be given by Travis Ens. For the background on these series please check the Pizza Seminar blog http://pizzaseminaruwo.blogspot.ca/

Wick's theorem allows us to compute any exponential integral by repeatedly differentiating a Gaussian function. It is a bridge that will take us from Gaussian integrals to Feynman integrals and their evaluations in terms of graph sums and of course to a delicious Pizza at the end! These talks are designed for our undergrads, but good grad students and genius faculty can also attend!

Noncommutative Geometry

Speaker: Farzad Fathizadeh (Western)

"The Gauss-Bonnet theorem and scalar curvature for noncommutative two-tori (2)"

Time: 14:30

Room: MC 107

I will survey on a recent joint work with M. Khalkhali and a paper by Connes and Moscovici on scalar curvature for noncommutative two-tori. The scalar curvature is computed by considering small time heat kernel expansions of the perturbed Laplacian which encodes the metric information of a general translation invariant conformal structure and a Weyl conformal factor on the noncommutative two-torus. There is an equivalent formulation for the scalar curvature in terms of special values of spectral zeta functions. I will also talk about our result on the Gauss-Bonnet theorem for noncommutative two-tori which extends the work of Connes and Tretkoff to the general conformal structures.

Analysis Seminar

Speaker: Roman Dwilewicz (Missouri University of S&T)

"Hartogs Type Holomorphic Extensions"

Time: 14:30

Room: 108

In the talk there will be given a short review of holomorphic extension problems starting with the famous Hartogs theorem (1906), via Severi-Kneser-Fichera-Martinelli theorems, up to some recent results on global holomorphic extensions for unbounded domains obtained together with Al Boggess (Arizona State Univ.) and Zbigniew Slodkowski (Univ. Illinois at Chicago). The classical Hartogs theorem solves the extension problem for bounded domains in C^n and clearly shows the difference between one and many-variables cases. The theorem is considered as an informal beginning of Complex Analysis in Several Variables. Surprisingly, the unbounded case was missed by analysts for more than a hundred years, even though it is important not only in Complex Analysis, but also in Partial Differential Equations and Algebraic Geometry. The problem appeared highly non-trivial and the work is in progress. However the talk will be illustrated by many figures and pictures and should be accessible also to graduate students.

Colloquium

Speaker: Vestislav Apostolov (UQAM)

"Calabi extremal metrics on polarized projective varieties"

Time: 14:30

Room: MC 108

After a brief introduction to the Calabi program concerning the search of canonical riemannian metrics on a smooth compact polarized projective variety, I will discuss some recent developments relating analytical with algebro-geometric aspects of the problem. I will then provide some non-trivial examples of projective varieties on which the Calabi problem can be solved.