Abstract: In this talk, I will introduce the structure of finite real spectral triple first, and then I will focus on how to encode those data of a finite real spectral triple inside the so-called "Krajewski diagram".

Abstract: This talk is continuation of last week's talk with the same title.

Abstract: A model example of a $q$-complete (in the sense of Grauert) manifold is the complement of a projective variety of codimension $q$. In particular, 1-complete manifolds are Stein. Our main results states that the top non-zero integer cohomology class of such a manifold can be represented by analytic cycles. This is a joint work with F. Forstneric and J. Smrekar (Geometry & Topology '16).

Abstract: I am interested in approximation theory, in particular, on a closed subset of an open Riemann surface R. During the talk I will focus on Arakelyan's theorem and its topological conditions and explain that, despite the fact that approximation is not always possible for a closed subset E of R, one can construct a large closed subset of E on which approximation is possible in a strong sense. Also, I will talk about pole-free approximation by meromorphic functions with respect to spherical distance. Finally, I will present an extension of the Schwarz reflection principle for open bordered Riemann surfaces.